TOPSAR Terrain Observation with Progressive SAR. 84

Keywords: topographie, intertidale, télédétection, Radar à Synthèse d'Ouverture, multispectrale, altimétrie satellitaire, SWOT, Arcachon, Baie des Veys topography, intertidal, remote sensing, Synthetic Aperture Radar, multispectral, satellite radar altimetry, SWOT, Arcachon, Veys Bay ix

En lien avec les activités humaines et l'élévation du niveau de la mer dans le cadre du changement climatique, les zones intertidales sont soumises à de fortes pressions. La topographie de ces environnements est ainsi en évolution permanente. Le suivi de la topographie est fondamental pour la modélisation hydrodynamique et morphodynamique des systèmes côtiers. Ce suivi fait face à des importantes difficultés, surtout sur le plan logistique, vu la localisation des zones intertidales entre les limites des plus hautes et des plus basses marées. La télédétection spatiale est une des meilleures approches pour assurer des mesures topographiques intertidale à jour dans l'espace et dans le temps. Cette thèse porte ainsi sur l'utilisation de la télédétection spatiale pour le suivi de la topographie des zones intertidales par des capteurs radar (altimétrie et Radar à Synthèse d'Ouverture (RSO)) et multispectrales. L'objectif principal est d'explorer, de développer ou d'améliorer des méthodes dédiées à la cartographie de la topographie intertidale. Cette thèse étudie également la capacité de la future mission SWOT (Surface Water and Ocean Topography), première mission altimétrique à fournir des élévations au sein d'une fauchée au moyen de la technique d'interférométrie SAR (RSO), à cartographier la topographie dans les zones intertidales. Les méthodologies développées et utilisées dans cette thèse ont été appliquées à deux baies intertidales situées sur la façade Atlantique de la côte française : Le Bassin d'Arcachon et la Baie des Veys. Nous avons d'abord montré que les améliorations techniques des nouvelles missions satellitaires permettaient, pour la première fois, à l'altimétrie satellitaire de fournir des profils topographiques intertidaux le long des traces des altimètres. Deuxièmement, nous avons introduit une approche améliorée de la méthode de la ligne d'eau (méthode la plus courante pour la cartographie de la topographie intertidale) qui sert à générer des Modèles Numériques d'Élévation (MNEs) intertidaux à l'aide des images satellitaires (RSO et multispectrales). Grâce à cette nouvelle approche, la détection des lignes d'eau et leurs post-traitements sont maintenant plus rapides, plus efficaces et quasi-automatiques. Nous avons également mis en évidence la capacité de SWOT à générer des MNEs intertidaux précis en utilisant la méthode de la ligne d'eau.

Les méthodologies développées et utilisées au cours de cette thèse sont capables de mesurer régulièrement la topographie dans les zones intertidales et permettre la détection des changements topographiques dans ces environnements et proposer des bilans morpho-sédimentaire. Ainsi, les deux zones intertidales étudiées sont en érosion sur la période de 2016 à 2018 avec des pertes en volume de 1,12 × 10 6 m 3 et 0,70 × 10 6 m 3 pour le bassin d'Arcachon et la baie des Veys respectivement. Ces informations sont utiles et nécessaires pour plusieurs applications scientifiques (par exemple, le bilan sédimentaire, la modélisation hydrodynamique), mais aussi pour les autorités et les acteurs du littoral dans le but de la mise en oeuvre des politiques d'utilisation et de protection de ces environnements.

1

Spatial extent of the coastal zone, including the coastal plain, shoreface and continental shelf. Note that the widths of these zones are globally highly variable. (Source: [START_REF] Masselink | Introduction to Coastal Processes and Geomorphology[END_REF] General patterns of zonation of tidal flats [START_REF] Reineck | Depositional Sedimentary Environments : With Reference to Terrigenous Clastics[END_REF]. HWS: High water on springs; LWS: Low water on springs. (Source: from Gao ( 2019 Différentes définitions ont été proposées afin de définir l'étendue géographique des zones côtières dont la majorité considère que ces zones s'étendent de part et d'autre du trait de côte. Ces zones englobent une variété de milieux marins comprenant les estuaires, les lagunes côtières, les estrans (zone intertidale), les barrières, les deltas, les falaises maritimes, les côtes rocheuses, les marais, les dunes et les plages de sable, etc. [START_REF] Wong | Coastal systems and low-lying areas[END_REF].

La position géostratégique des zones côtières les associe à des densités de population et taux de croissance démographique et d'urbanisation élevés malgré que géographiquement ces zones ne représentent que 5% de la superficie terrestre [START_REF] Agardy | Ecosystems and human well-being: current state and trends[END_REF][START_REF] Neumann | Future Coastal Population Growth and Exposure to Sea-Level Rise and Coastal Flooding -A Global Assessment[END_REF][START_REF] Small | A global analysis of human settlement in coastal zones[END_REF]. La population côtière est toutefois exposée à une série de dangers, notamment l'érosion, l'intrusion d'eau salée, la subsidence, les tsunamis et les inondations [START_REF] Nicholls | Rising sea levels: potential impacts and responses[END_REF]. Ces dangers sont susceptibles de s'aggraver dû au changement climatique et ses effets (l'élévation du niveau de la mer et l'augmentation des tempêtes) [START_REF] Switzer | Coastal Hazards: Storms and Tsunamis[END_REF]. L'élévation du niveau de la mer et l'augmentation des tempêtes, ainsi que le surdéveloppement en terme d'infrastructure et d'urbanisation auquel ces zones sont confrontées, ont augmenté la vulnérabilité des zones côtières à l'érosion et aux inondations [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF]. La pression exercée par la croissance démographique, les diverses utilisations de la zone côtière (développement industriel et résidentiel, exploitation des ressources, infrastructure, tourisme et loisirs [START_REF] Kay | Coastal planning and management[END_REF]) et les risques côtiers soulignent la nécessité d'adopter des pratiques de gestion durable dans ces régions [START_REF] Haslett | Coastal systems[END_REF].

La gestion des zones côtières nécessite le suivi des changements qui se produisent dans ces environnements dynamiques qui subissent en permanence des variations morphologique. En effet, la morphologie des zones côtières a un certain contrôle sur son propre développement puisqu'elle est contrôlé par les processus côtiers affectés à leur tour par les changements morphologiques [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF].

Des informations topographiques et bathymétriques précises et actualisées sont alors cruciales pour garantir une gestion efficace et permettre aux scientifiques d'étudier l'évolution de ces systèmes complexes.

Situées entre les limites des plus hautes et des plus basses marées, les zones intertidales constituent l'un des environnements les plus difficiles sur le plan logistique et les plus dangereux pour le suivi topographique. Les zones intertidales (les estrans ou zones de balancement des marées) sont des zones de faible pente, légèrement inclinées, immergées ou émergées en fonction du cycle de marée. Ces écosystèmes côtiers très répandus se trouvent principalement dans des environnements dominés par les marées et dans les zones côtières abritées où l'action de la houle est faible [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. Il s'agit de zones très productives, caractérisées par une forte biodiversité, qui aident à la stabilisation du littoral, et qui offrent une protection contre les tempêtes et les inondations côtières [START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF]. Les environnements méso et macrotidaux 1 favorisent la formation des vasières intertidales parce que dans ces environnements l'action des marées est généralement dominante sur les autres forces hydrodynamiques [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. Cependant, cette dominance est relative, ce qui signifie que les vasières intertidales peuvent se former également dans les environnements microtidaux si l'action des vagues est inférieure à celle de la marée. Par contre, même si l'amplitude de la marée est importante, les vasières intertidales ne peuvent pas se former si l'action des vagues domine celle de la marée [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. Le développement des zones intertidales dépend de l'apport en sédiments. Toute pénurie ou coupure de cet apport peut entraîner l'érosion et le rétrécissement de ces milieux [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. Les interventions humaines (développement côtier, dragage, barrages en amont, pollution, etc.), accompagnées d'une élévation du niveau de la mer due au changement climatique, ont mis ces régions sous forte pression. Une étude récente menée par [START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF] a montré que les zones intertidales subissent une régression rapide à l'échelle mondiale (diminution de 16% entre 1984 et 2016), mettant en évidence leur vulnérabilité à l'extension des activités humaines. Une cartographie précise et continue de la topographie des zones intertidales est essentielle pour la prévision des inondations côtières, la défense côtière, l'identification de l'érosion ou de l'accrétion du littoral, la navigation, la pêche, l'exploitation économique et le tourisme [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF][START_REF] Mason | Remote sensing of intertidal morphological change in Morecambe Bay, U.K., between 1991 and 2007[END_REF]. La bathymétrie/topographie de ces zones est notamment un paramètre essentiel pour la modélisation hydrodynamique en eaux peu profondes puisque de nombreux termes de forçage dans l'équation hydrodynamique du mouvement dépendent de la profondeur de l'eau [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF].

Actuellement, il existe une grande variété de techniques de cartographie topographique des zones intertidales. Les techniques conventionnelles terrestres et aéroportées (e.g., stéréo-photogrammétrie, LiDAR et InSAR) fournissent des mesures très précises. Les techniques terrestres sont habituellement dédiées aux petites zones et sont limitées par la lumière du jour, les conditions météorologiques et la marée. Quant aux techniques aéroportées, elles peuvent couvrir des zones plus vastes en peu de temps, tout en couvrant des régions inaccessibles et dangereuses. Toutefois, ces dernières sont également dépendantes des conditions météorologiques, et sont coûteuses et non adaptées à cartographier la topographie complète (marnage complet) des zones relativement vastes. Les techniques satellitaires (la télédétection spatiale) offrent donc une alternative viable et rentable à la cartographie topographique en raison de leur nature synoptique, en particulier dans les régions éloignées et dangereuses.

La première définition officielle de la télédétection spatiale a été donnée lors de la réunion plénière des Nations Unies du 3 décembre 1986 comme la suivante : Le terme télédétection désigne la détection de la surface de la Terre depuis l'espace en utilisant les propriétés des ondes électromagnétiques émises, réfléchies ou diffractées par les objets détectés, dans le but d'améliorer la gestion des ressources naturelles, l'utilisation des sols et la protection de l'environnement. Il existe deux approches de télédétection : active et passive. L'approche active consiste à émettre des ondes électromagnétiques et à enregistrer le signal réfléchi ou diffusé [START_REF] Lavender | Practical handbook of remote sensing[END_REF] ; Tandis que l'approche passive ne mesure que le rayonnement réfléchi ou émis par un objet [START_REF] Lavender | Practical handbook of remote sensing[END_REF]. Grâce à nos connaissances sur l'interaction entre les ondes électromagnétiques et les matériaux de la surface terrestre, le traitement et l'analyse des signaux reçus nous permettent de déduire diverses propriétés de la Terre (physiques, chimiques et biologiques), tel que la topographie. Actuellement, une vaste gamme de capteurs de télédétection spatiales sont en orbite autour de la Terre, parmi lesquelles deux types de capteurs sont les plus utilisés pour mesurer la topographie des zones intertidales: Les capteurs radar (actifs) et les capteurs multispectraux (passifs).

Les détecteurs multispectraux sont des détecteurs optiques passifs qui mesurent les rayonnements électromagnétiques dans différentes bandes spectrales. Ils détectent les rayonnements électromagnétiques solaires visibles et infrarouges (proche infrarouge et infrarouge moyen) réfléchis par la surface de la Terre et les rayonnements électromagnétiques infrarouges thermiques émis par la Terre. Landsat 1 a été le premier satellite multispectral civil lancé par la NASA en 1972. La série de satellites LandSat s'est poursuivie jusqu'à aujourd'hui. Landsat 8, lancé en 2013, a été le dernier de cette série. L'agence spatiale française (Centre National d'Études Spatiales (CNES)) a également apporté une contribution très importante aux capteurs multispectraux avec la série SPOT. Cette série a débuté avec le lancement de SPOT-1 en 1986 et s'est poursuivie jusqu'à la constellation actuelle composée de SPOT-6 et SPOT-7 lancés respectivement en 2012 et 2014. D'autres satellites ont fourni et continuent de fournir des données très utiles pour l'observation de la Terre, tels que IKONOS (1999), QuickBird (2001), WorldView-1 (2007), GeoEye-1 (2008), WorldView-2 (2009), Pléiades (2011), la constellation Sentinel-2 (2015), entre autres.

Contrairement aux capteurs optiques passifs, les capteurs radar ont une capacité à fonctionner de jour comme de nuit et indépendamment des conditions climatiques. Les systèmes radars actifs émettent des micro-ondes électromagnétiques et reçoivent l'énergie rétrodiffusée par la surface. Dans les années 1950, Carl Wiley a établi le principe de système de Radar à Synthèse d'Ouverture (RSO) [START_REF] Wiley | Synthetic aperture radars-A paradigm for technology evolution[END_REF] qui est un système d'imagerie pouvant acquérir des images radar de la surface de la Terre. Seasat a été le premier satellite civil à transporter un instrument RSO développé par le Jet Propulsion Laboratory (JPL) (NASA). Depuis les années 1990, plusieurs satellites RSO ont été lancés tels que les satellites ERS-1/-2 et ENVISAT de l'Agence Spatiale Européenne (ESA), les satellites RADARSAT-1/-2, les satellites COSMO-SkyMed, TERRASAR-X et TanDEM-X, GAOFEN-3, entre autres. Récemment, l'ESA a lancé une nouvelle génération de satellites RSO (Sentinel-1A en 2014et Sentinel-1B en 2016). Le caractère open source des données Sentinels disponibles pour tous les utilisateurs est très avantageux pour le développement des méthodes spatiales dédiées à fournir des produits actualisés régulièrement (e.g. cartes topographies intertidales).

L'altimétrie satellitaire est un autre type de capteurs radar actifs largement utilisés. A l'origine, l'altimétrie satellitaire a été conçue pour mesurer la forme de la Terre [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF]. L'utilisation de l'altimétrie pour mesurer la topographie de surface des océans a été abordée pour la première fois au congrès de Williamstown en 1969 [START_REF] Kaula | The terrestrial environment: solid earth and ocean physics[END_REF]. La station spatiale Skylab, lancée en 1973 a transporté le premier altimètre. Sa précision de mesure était de l'ordre de 60 cm [START_REF] Fu | Satellite Altimetry: Observing Ocean Variability From Space[END_REF], mais bientôt améliorée par GEOS-3 (NASA, 1975[START_REF] Lyzenga | Passive remote sensing techniques for mapping water depth and bottom features[END_REF] et Seasat (NASA, 1978) avec des précisions de 25 cm et 5 cm [START_REF] Stanley | The Geos 3 Project[END_REF][START_REF] Tapley | The SEASAT altimeter data and its accuracy assessment[END_REF]. Durant les années 80, Geosat (US Navy, 1985[START_REF] Li | Studies of multibaseline spaceborne interferometric synthetic aperture radars[END_REF] était le seul altimètre en orbite effectuant des mesures en permanence [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF]) avec une précision de 4 cm [START_REF] Chelton | Satellite Altimetry[END_REF]. La précision a atteint 3 cm avec ERS-1 (ESA, 1991(ESA, -2000) ) et 2 cm avec Topex/Poseidon (NASA-CNES, 1992-2006) [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF][START_REF] Frappart | Satellite Altimetry: Principles and Applications in Earth Sciences[END_REF]. Dans la continuité de la mission ERS-1, la mission ERS-2 (ESA, 1995(ESA, -2011) ) a été lancée en 1995 suivie par la mission GFO (US Navy-NOAA, 1998-2008) ayant la même orbite que Geosat [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF]. Jason-1 (CNES-NASA, 2001-2013), Jason-2 (CNES-NASA-EUMETSAT-NOAA, 2008-présent), et Jason-3 (CNES-NASA-EUMETSAT-NOAA, 2016-présent) ont été lancés dans la continuation de la mission Topex/Poseidon tandis que l'ESA a lancé le successeur des missions ERS-1/2, ENVISAT (ESA, 2002(ESA, -2012) ) [START_REF] Frappart | Satellite Altimetry: Principles and Applications in Earth Sciences[END_REF]. Les altimètres HY-2 (CNES-CAST, 2011-présent) et SARAL (ISRO-CNES, 2013-présent) partagent aussi l'orbite d'ENVISAT/ERS. Tous les altimètres mentionnés fonctionnaient en mode basse résolution (LRM). Parmi ces altimètres, SARAL est le premier à fonctionner en bande Ka [START_REF] Frappart | Satellite Altimetry: Principles and Applications in Earth Sciences[END_REF]. Une nouvelle génération d'altimètres fonctionnant en mode RSO (mode haute résolution le long de la trace) a débuté avec CryoSat-2 (ESA, 2010-présent) [START_REF] Wingham | CryoSat: A mission to determine the fluctuations in Earth's land and marine ice fields[END_REF]) et a également été adoptée pour la constellation Sentinel-3 (ESA, 2016-présent). Comme indiqué précédemment, l'altimétrie satellitaire est une technique destinée à mesurer la topographie de la surface des océans le long de la trace du satellite. Près des côtes, l'acquisition et le traitement des données souffrent de plusieurs défauts. Cependant, les nouvelles technologies d'altimétries satellitaires fonctionnant en bande Ka et en mode RSO ont augmenté le potentiel de cet outil de télédétection dans les zones côtières et leurs utilisations sont maintenant possibles dans des environnements tels que les zones intertidales.

Prochainement, de nouvelles possibilités de télédétection seront offertes par la future mission d'altimétrie à large fauchée SWOT (Surface Water and Ocean Topography) [START_REF] Morrow | Global Observations of Fine-Scale Ocean Surface Topography With the Surface Water and Ocean Topography (SWOT) Mission[END_REF]. SWOT est une mission conjointe entre la NASA et le CNES, avec des contributions de l'agence spatiale canadienne (CSA) et de l'agence spatiale du Royaume-Uni (UKSA). C'est la première mission altimétrique capable de mesurer l'élévation des eaux de surface. La mission SWOT, dont le lancement est prévu en 2021, durera au moins 3 ans et fournira des mesures de niveau d'eau en 2D. L'instrument principal de la mission sera un interféromètre radar en bande Ka (KaRIn) [START_REF] Biancamaria | The SWOT Mission and Its Capabilities for Land Hydrology[END_REF]) qui est un système RSO bi-statique ayant deux antennes aux extrémités opposées séparées par un mât de 10 m permettant de fournir des observations altimétriques dans une fauchée de 120 km de large [START_REF] Fjortoft | KaRIn on SWOT: Characteristics of Near-Nadir Ka-Band Interferometric SAR Imagery[END_REF]. La charge utile de SWOT comprend également un altimètre conventionnel (bande Ku ) qui sera utilisé pour la validation et la calibration des mesures interférométriques et qui permettra en plus de combler l'écart entre les fauchées [START_REF] Srinivasan | Engaging The Applications Community of The Future Surface Water and Ocean Topography (SWOT) Mission[END_REF]. Contrairement aux missions altimétriques conventionnelles destinées uniquement aux surfaces océaniques, la mission SWOT fournira des mesures de haute précision de l'élévation de l'eau au niveau des océans, des côtes et des eaux de surfaces. Les rivières de plus de 100 m de large et les lacs (zones humides et réservoirs) de plus de 250 km 2 seront résolus avec une précision verticale de 10 cm. Au niveau des eaux terrestres et côtières, SWOT fournira des cartes 2D de la topographie des surfaces d'eau en haute résolution ce qui donne accès à l'élévation, la pente, et les extensions d'eau [START_REF] Biancamaria | The SWOT Mission and Its Capabilities for Land Hydrology[END_REF]. Une amélioration significative de performance va être alors apporter à la surveillance des zones côtières à l'aide de cette mission innovante.

Des études plus orientées vers l'hydrodynamique ont été menées pour évaluer la performance de SWOT dans les zones côtières et estuariennes [START_REF] Chevalier | High-Resolution SWOT Simulations of the Macrotidal Seine Estuary in Different Hydrodynamic Conditions[END_REF][START_REF] Turki | On the Investigation of the Sea-Level Variability in Coastal Zones Using SWOT Satellite Mission: Example of the Eastern English Channel (Western France)[END_REF]. [START_REF] Turki | On the Investigation of the Sea-Level Variability in Coastal Zones Using SWOT Satellite Mission: Example of the Eastern English Channel (Western France)[END_REF] ont étudié la capacité de SWOT à reproduire la variabilité temporelle du niveau de la mer dans la Manche ; tandis que [START_REF] Chevalier | High-Resolution SWOT Simulations of the Macrotidal Seine Estuary in Different Hydrodynamic Conditions[END_REF] ont évalué la capacité attendue de SWOT en terme de précision de mesure dans différents contextes hydrodynamiques en prenant l'estuaire de la Seine comme site d'étude. Cette thèse s'inscrit aussi dans le cadre de la mission SWOT et du projet SWOT COTEST (Caractérisation, modélisation et potentialité du satellite SWOT à mesurer les phénomènes hydro-météo-marins dans les systèmes côtiers et estuariens) dans le cadre du programme TOSCA (Terre Solide, Océan, Surfaces Continentales et Atmosphère) du CNES, dont un des axes du projet s'intéresse au couplage entre SWOT et les missions satellites en activité appliquées aux zones côtières. D'un point de vue méthodologique, il existe diverses méthodes de télédétection spatiale dédiées à cartographier la topographie intertidale, notamment la méthode de l'interférométrie SAR (InSAR) [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF], la stéréophotogrammétrie [START_REF] Tateishi | Relative DEM production from SPOT data without GCP[END_REF] et la méthode de la ligne d'eau [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]. Les images RSO et optiques sont utilisées par les méthodes InSAR et stéréophotogrammétrie respectivement, tandis que la méthode de la ligne d'eau peut exploiter les deux types d'images. Les méthodes InSAR et stéréophotogrammétrie utilisent deux images RSO ou optiques qui se chevauchent et qui sont acquises de différentes perspectives pour reconstruire des objets tridimensionnels (e.g., des Modèles Numériques d'Élévation (MNEs) topographiques). Quant à la méthode de la ligne d'eau, elle consiste à : (i) l'extraction des lignes d'eau (interface entre les zones intertidales et l'eau) à partir d'une série d'images échantillonnées à différents stades de marée, (ii) l'attribution de hauteurs d'eau aux lignes d'eau en utilisant des informations de niveau d'eau (provenant d'un marégraphe ou d'un modèle de circulation océanique), et (iii) l'assemblage et l'interpolation des lignes d'eau pour former un MNE maillé. Bien que les deux premières méthodes soient capables de fournir des résultats relativement précis, la méthode de la ligne d'eau reste la méthode la plus couramment utilisée pour cartographier la topographie intertidale. Cela est lié à plusieurs raisons notamment la simplicité d'utilisation, la disponibilité des données, la faisabilité de la méthode de l'InSAR pour les missions d'interférométrie à acquisition simultané seulement, et le coût élevé des images de cette dernière et des images stéréophotogrammétrique, etc.. Malgré les progrès de la méthode de ligne d'eau au cours du temps, elle n'est pas encore complètement automatique et requiert un traitement manuel très important.

Suite à la demande croissante aux données topographiques intertidales pour des raisons scientifique, économique et sociétale, ce travail a pour but d'étudier l'utilisation des nouvelles missions de télédétection spatiales pour mesurer la topographie des zones intertidales. Pour atteindre ce but dans le cadre de cette thèse et du projet SWOT, deux objectifs principaux sont définis :

1. Exploration, développement et amélioration des méthodes de télédétection spatiale pour la surveillance de la topographie des zones intertidales.

2. Étudier la capacité et évaluer la performance de la future mission SWOT pour mesurer la topographie des zones intertidales.

Les objectifs proposés conduisent aux questions de recherche spécifiques suivantes : Les méthodologies élaborées ou utilisées dans le cadre de ces travaux pour répondre à ces questions ont été appliquées aux zones intertidales de deux baies : La baie d'Arcachon et la baie des Veys. Ces deux baies sont situées sur la façade atlantique française. Le choix de ces baies intertidales est motivé par la disponibilité des données de validation précises (pour des raisons de comparaison) et par les caractéristiques contrastées (hydrodynamiques et morphologiques) que les deux baies présentent afin de prouver l'applicabilité des méthodologies présentées dans différents environnements intertidaux. La baie d'Arcachon est une lagune mésotidale abritée avec de vastes zones vaseuses où la marée entre dans le système par deux chenaux tidaux, tandis que la baie des Veys est une baie ouverte macrotidale caractérisée par un mélange de matériaux vaseux et sableux, avec une présence abondante de sable.

Cette thèse débute par un chapitre (Chapitre 1) faisant le point sur l'état de l'art des méthodes de télédétection spatiale utilisées pour mesurer la bathymétrie et la topographie des zones côtières. Ensuite, les capacités de l'altimétrie radar satellitaire ont été explorées dans le Chapitre 2 en évaluant ses performances pour le suivi de niveau d'eau et de la topographie intertidale dans une lagune côtière (le bassin d'Arcachon). Dans le Chapitre 3, des améliorations ont été apportées à la méthode de la ligne d'eau en appliquant cette méthode dans la baie d'Arcachon et la baie des Veys en utilisant des données RSO (Sentinel-1) et multispectrales (Sentinel-2). Enfin, le potentiel de la future mission SWOT pour mesurer la topographie intertidale par la méthode de la ligne d'eau a été évalué pour les deux sites étudiés (Chapitre 4), ce qui a permis de faire des projections pour le futur concernant le suivi de la topographie des zones intertidales à partir des observations satellitaires. Le premier chapitre de la thèse présente les méthodes de télédétection spatiale utilisées pour cartographier la bathymétrie et la topographie des zones côtières notamment les plages, les zones intertidales et le nearshore. Les différentes méthodes présentées sont illustrées avec des exemples d'application. Premièrement et en se basant sur une étude mené par [START_REF] Almeida | Deriving High Spatial-Resolution Coastal Topography From Sub-meter Satellite Stereo Imagery[END_REF], la stéréoscopie était présenté pour la cartographie de la topographie des plages et des dunes. En utilisant des données Pléiades à très haute résolution spatiale (2 m), cette méthode est capable de mesurer la topographie des plages avec des erreurs (erreur quadratique moyenne) variant entre 35 cm et 48 cm. Les méthodes dédiées aux zones intertidales ont été présentées dans la section 1.3. Dans cette section, une étude bibliographique détaillée est présentée pour la méthode de ligne d'eau sur laquelle se base une grande partie de cette thèse. La méthode InSAR pour le suivi des zones intertidales a été aussi présentée. Malgré les difficultés techniques que cette méthode présente, elle a un grand potentiel pour le suivi des zones intertidales. Des MNEs intertidales ont été générés à l'aide de cette méthode qui ont présenté des erreurs de 15 cm. L'altimétrie satellitaire est la troisième méthode présentée pour le suivi de la topographie des zones intertidales. Cette méthode est celle utilisée dans le cadre de cette thèse et elle est présentée dans le Chapitre 2. Contrairement aux autres méthodes, elle permet l'extraction des profils intertidales (RMSE peut atteindre 0.23 m pour l'exemple présenté) et non pas des cartes topographiques. Enfin, une dernière section était dédiée pour l'inversion bathymétrique des zones de nearshore à partir des données sur la couleur de l'eau et inversion bathymétrique basée sur les caractéristiques des vagues. Les méthodes mentionnées dans ce chapitre fournissent des données complémentaires. Leur combinaison peut générer des produits de bathymétrie et de topographie multi sources. Cette première étude consiste à examiner, pour la première fois, la capacité de l'altimétrie satellitaire à extraire des profils topographiques intertidaux le long des traces des altimètres. L'étude comprent également une évaluation des performances de l'altimétrie pour mesurer le niveau d'eau dans les lagunes côtières et une tentative d'auto-discrimination entre les points de mesures émergés et submergés en utilisant des paramètres altimétriques intrinsèques (coefficient de rétrodiffusion et Peakiness). L'altimétrie satellitaire fournit une mesure du niveau de la mer au nadir (à la verticale) du satellite à une précision centimétrique. Cependant, l'altimétrie en zone côtière se heurte à des limitations, et les observations altimétriques se dégradent fortement à l'approche des côtes. Cela est dû principalement à la contamination de l'écho radar par les zones terrestres qui se trouvent dans l'empreinte au sol du capteur. Pour une meilleure observation de la dynamique côtière, des efforts majeurs ont été déployés et se poursuivent au niveau de développement des nouvelles techniques de traitement des données et ainsi le développement de nouveaux instruments de mesures. Plusieurs satellites embarquant à leur bord des altimètres radar ont survolé de manière répétitive le bassin d'Arcachon. Dans cette étude, nous avons examiné la performance de quatre altimètres à mesurer les variations de niveau d'eau, et pour la première fois, à estimer la topographie de la zone d'estran du bassin d'Arcachon. Les satellites-altimètres concernés sont : ERS-2 (1995ERS-2 ( à 2011)), ENVISAT (2002à 2012), SARAL (2013à 2018) et CryoSat-2 (2010à 2018). L'analyse des données fournies par ces quatre altimètres a pour but de mettre en évidence l'évolution de performance entre les anciennes technologies (ERS-2 et ENVISAT) et les technologies récentes .

Les comparaisons avec le marégraphe d'Arcachon-Eyrac ont démontré une nette amélioration de précision entre les anciennes (ERS-2 et ENVISAT) et les nouvelles techniques. Un passage d'un biais de 0.79-1.47 m pour ERS-2 et ENVISAT à un biais de 0.17-0.24 m pour SARAL et CryoSat-2 est observé. L'amélioration de la précision présentée par SARAL est essentiellement due à l'utilisation de la bande Ka (37.75 GHz) dont la tache au sol est faible par rapport à la bande Ku (13.5 GHz) employée par ERS-2 et ENVISAT. La bonne précision de Cryosat-2 (qui opère en bande Ku) est lié au fait qu'il opère en mode RSO, ce qui augmente sa résolution spatiale le long de la trace. Cette étude a également démontré la capacité de l'altimétrie satellitaire (SARAL et CryoSat-2) à mesurer la topographie de la zone intertidale grâce à la comparaison des mesures altimétriques à une cartographie LiDAR (biais < 0.25 m).

Cependant, l'auto-discrimination ne peut pas être effectuée, point par point, en utilisant uniquement le coefficient de rétrodiffusion et le paramètres de Peakiness. La limitation la plus importante réside dans la grande taille de l'empreinte au sol des altimètres. Néanmoins, une technique de discrimination automatique entre les mesures effectuées à marée haute et marée basse a été mise en place. Ceci est dû au bon contraste obtenu pour les paramètres mentionnés à l'échelle de la baie entre les marées basses et les marées hautes (de forte variation des paramètres en fonction de la contribution des surfaces émergées à l'empreinte au sol). Des suivis de la zone intertidale du bassin d'Arcachon et d'autres environnements similaires seraient donc envisageables grâce à cette méthode de télédétection. Du fait des passages répétés, la quantification du déplacement de ces zones pourrait être réalisée.

En termes de perspectives, la prochaine étape à franchir est de prouver la qualité des altimètres dans d'autres milieux intertidaux, comme la baie du Mont-Saint-Michel, la baie de Seine (Vasière Nord) en France et la baie de Fundy au Canada (le marnage le plus élevé du monde). Ces environnements intertidaux sont survolés par différents altimètres et présentent des caractéristiques contrastées en termes de taille de site, de type de matériaux et du régime de marée. Pour cela, l'évaluation des performances de l'altimétrie sur ces sites sera très utile et permettra d'obtenir une vision plus complète et extrapolable sur les capacités de l'altimétrie dans l'ensemble des zones intertidales. En ce qui concerne l'auto-discrimination entre les points de mesure émergés et immergés, il faudra se concentrer sur l'analyse des formes d'onde altimétriques (non seulement sur le coefficient de rétrodiffusion et la Peakiness) afin de pouvoir classer plus efficacement les points de mesure. L'altimétrie radar a fourni des mesures relativement précises dans la zone intertidale du bassin d'Arcachon, mais des mesures plus précises pourront être fournies par la mission d'altimétrie laser ICESat-2. Cette mission peut fournir des données de très haute résolution spatiale (0,7 m contre 175 m au mieux pour l'altimétrie). L'intérêt de cette mission présente sera très important surtout pour la calibration et la validation d'autres méthodes utilisées sur des sites d'accès difficile où les mesures in situ sont difficiles à acquérir. Après avoir exploré les capacités de l'altimétrie satellitaire dans les zones intertidales, nous avons abordé les systèmes d'imagerie satellitaire. Ce type de données permet la génération des MNEs intertidaux maillés plutôt que l'extraction des profils topographiques. Cette deuxième étude consiste à améliorer la méthode de la ligne d'eau utilisée pour mesurer la topographie des zones intertidales. La méthode de la ligne d'eau est une technique largement utilisée pour la création des MNEs des zones d'estran. La ligne d'eau fait référence à l'interface terre-mer ou à la ligne de côte dans la zone intertidale. La méthode consiste à détecter le bord de la ligne d'eau des images satellitaires à l'aide des techniques de traitement d'images. Ensuite, la position de cette ligne d'eau est géolocalisée et nivelée à l'aide du niveau d'eau donné par un modèle hydrodynamique de marée et de tempête pour la zone observée au moment de l'acquisition de l'image (ou bien en utilisant des observations marégraphiques). À partir d'une série d'images échantillonnées à différents stades de marée, un ensemble de lignes d'eau est assemblé et ensuite interpolé pour générer une carte topographique complète de la zone. Cette technique suppose qu'il n'y ait pas eu de changement majeur dans la topographie de la zone intertidale pendant la période d'acquisition de l'ensemble des images. Les images RSO sont surtout utilisées en raison de leurs capacités à fonctionner de jour comme de nuit et indépendamment des conditions climatiques. Les images multispectrales ne peuvent être utilisées qu'en absence de couverture nuageuse : il est ainsi recommandé d'utiliser les images acquises pendant la saison estivale durant laquelle il n'y a pas un changement majeur dans la topographie.

Traditionnellement, la méthode de la ligne d'eau souffrait non seulement d'un nombre insuffisant d'images satellitaires, mais aussi du seuillage subjectif effectué dans le processus de détection des contours (lignes d'eau), et du long post-traitement (parfois manuel) des lignes d'eau extraites. Une nouvelle technique de détection des contours a été développée dans le cadre de cette étude pour surmonter ces difficultés. Cette méthode est accompagnée d'une procédure automatique visant à éliminer les images RSO bruitées et à les exclure de tout traitement ultérieur. Cette nouvelle méthode d'extraction des lignes d'eau se base sur une procédure de segmentation (basée sur l'algorithme de clustering non supervisé k-means) et un modèle de contour actif. Cette méthode permet l'extraction des lignes d'eau pour les deux types d'images RSO et multispectrales et elle a été conçue pour créer des contours fermés (des objets). Le seuillage subjectif lors de la méthode de détection de contour a été évité grâce à la segmentation des images à l'aide de l'algorithme de clustering k-means. Le post-traitement des lignes d'eau a été automatisé grâce à l'extraction des lignes d'eau en tant que contours fermés ce qui a permis : (i) l'élimination automatique des sections de lignes d'eau qui se croisent (effectuée manuellement dans les études précédentes) et (ii) la sélection automatique de la ligne d'eau la plus appropriée parmi un ensemble de lignes redondantes (lignes d'eau de hauteurs proches). Cette dernière a été effectuée en se basant sur le nombre d'objets des lignes d'eau (conservation de la ligne d'eau avec le nombre d'objets minimal) et c'est une étape essentielle lorsque les données sont abondantes (cas des missions Sentinel). La deuxième étape a permis une élimination de second degré des images de qualité intermédiaire, qui n'avaient pas été éliminées lors de la première procédure d'élimination automatique. Par conséquent, en utilisant cette méthode, il n'est plus nécessaire de sélectionner manuellement les images à utiliser et de modifier manuellement les lignes d'eau après extraction.

En se basant sur la méthode de ligne d'eau décrite ci-dessus, quatre cartes topographiques ont été produites pour les années 2015, 2016, 2017 et 2018 pour le Bassin d'Arcachon et trois cartes topographiques pour les années 2016, 2017 et 2018 pour la Baie des Veys. L'utilisation des observations Sentinels a permis un échantillonnage complet de l'amplitude de la marée en moins de 4 mois. La validation de la méthode a été effectuée en comparant les cartes topographiques produites aux cartes topographiques précises dérivées du LiDAR. Dans cette étude, les lignes d'eau ont été nivelées à partir des données marégraphiques et à partir des sorties d'un modèle hydrodynamique de SHOM. La procédure d'interpolation a été faite en utilisant deux méthodes différentes, IDW (Pondération inverse à la distance) et krigeage.

Les résultats de cette étude ont mis en évidence que la méthode de la ligne d'eau utilisée généralement sur des grandes zones intertidales est capable de fournir des cartes précises sur des zones relativement petites avec une erreur d'environ 19 à 25 cm. L'étude a également montré que la méthode d'interpolation par krigeage convient mieux à la génération des cartes topographiques, par rapport à la méthode IDW. Des études antérieures ont montré qu'il est préférable de niveler les lignes d'eau à l'aide des sorties de modèles hydrodynamiques maillées afin de prendre en compte la pente de l'eau. Cependant, nos résultats ont montré la même performance entre l'utilisation des sorties maillées et les marégraphes (ou bien les sorties modèle prises en un point précis). Cela est principalement dû à la faible pente des eaux de surface dans les petites zones intertidales.

De plus, l'étude a confirmé la capacité de la méthode de la ligne d'eau à mesurer les changements topographiques dans le bassin d'Arcachon et la baie des Veys à l'aide des images Sentinel-1 et Sentinel-2 où des volumes significatifs d'érosion et de dépôt ont été détectés. La zone intertidale d'Arcachon a montré un comportement globalement stable avec des petites taches d'érosion et de dépôt répartis dans la zone intertidale. Concernant la baie des Veys, des zones d'érosion et de dépôt adjacentes localisés le long des chenaux ont été observées. Cette localisation peut indiquer une migration des chenaux entre les années observées. Entre 2016 et 2018, des pertes en volume de 1,12 × 10 6 m 3 et 0,70 × 10 6 m 3 ont été détectés pour le bassin d'Arcachon et la baie des Veys respectivement. Il faut noter qu'en terme de volumes érodés et accrétés, la baie des Veys à montrer des variations plus fortes malgré le fait que les changements nets observés sont plus faibles par rapport à Arcachon.

L'utilisation de la méthode de ligne d'eau est maintenant plus intéressante que jamais avec l'abondance inédite des données disponibles (e.g., les données Sentinels). Avec le grand nombre d'images fourni par Sentinel pour la méthode de ligne d'eau, ce nombre d'images dépasse parfois nos besoins pour l'application de cette méthode, et il sera essentiel en termes de perspectives d'aborder les questions suivantes à l'avenir : quel est le nombre optimal d'images à utiliser ? Quel est la meilleure fréquence d'échantillonnage ? Comment le nombre optimal et le taux d'échantillonnage évoluent-ils avec la taille du site et la pente de la topographie ? Et sur quels critères la sélection des images doit être basée ? Chapitre 4 : L'utilisation de la future mission SWOT pour le suivi de la topographie intertidale à partir de la méthode de ligne d'eau (Salameh et al. submitted).

Enfin, une dernière étude a abordé le second grand objectif de la thèse consistant à étudier la performance de la mission SWOT pour le suivi de la topographie intertidale. La méthode de la ligne d'eau a été choisie pour générer des MNEs intertidaux en utilisant des données virtuelles de SWOT générées par la boîte à outils SWOT Hydrology Toolbox développée par le CNES. Cette méthode a été choisi car SWOT mesurera l'élévation des eaux en 2 dimensions, fournissant l'élévation des eaux de surface, ainsi que les extensions d'eau (masques d'eau), paramètres sur lesquels repose la méthode de la ligne d'eau. Puisque SWOT fournira des informations sur l'élévation des eaux avec une grande précision, la hauteur sera associée aux lignes d'eau (extraites directement des masques à eau) sans qu'il soit nécessaire d'utiliser des mesures in situ (marégraphes) ou bien des sorties de modèles de circulation océanique. Cela rendra la méthode de ligne d'eau complètement indépendante des mesures in situ. Il est à noter aussi qu'en utilisant les données SWOT, la pente de l'eau sera prise en compte puisque SWOT mesure les hauteurs d'eau en 2D.

En utilisant les MNEs Sentinel générés lors de cette thèse, des MNEs SWOT ont été générés de la façon suivante : (ii) détermination de toutes les orbites ascendantes et descendantes qui ont des fauchées couvrant la zone d'intérêt, (ii) génération des masques d'eau à partir du MNE Sentinel et des élévations d'eau extraites (du marégraphe ou du modèle océanique) à l'instant exact des passages de SWOT au niveau de la zone intertidale, (iii) simulation des masques d'eau que SWOT peut observer en utilisant les masques d'eau extraits dans l'étape précédente comme entrée pour des simulations effectuées par SWOT Hydrology Toolbox (vi) extraction des lignes d'eau des masques à eau simulés (les lignes d'eau sont les contours des masques à eau), (v) nivellement des lignes d'eau à partir des niveaux d'eau simuler par la toolbox (niveau d'eau d'entrée sont les niveaux extraits du marégraphe ou du modèle océanique) et (vi) assemblement puis interpolation des lignes d'eau par krigeage pour générer des MNEs SWOT.

Plusieurs MNEs SWOT ont été générés en suivant cette démarche en utilisant des dates de lancement de mission différentes (ce qui joue sur l'échantillonnage de l'amplitude de marée) et des périodes d'acquisitions différentes (ce qui joue sur la quantité des images utilisées). Les MNEs SWOT ont été comparés aux MNEs Sentinel, considérés comme MNEs réelles dans cette étude. SWOT a démontré une capacité à générer des MNEs intertidaux avec une très bonne précision (∼5 cm). Cependant, cette précision dépend de l'échantillonnage qui dépend lui-même de l'orbite de SWOT. Pour la méthode de ligne d'eau, l'échantillonnage fourni par SWOT varie en fonction de la période d'acquisition choisie. Cela est causé par le phénomène de repliement (aliasing en anglais) lié à la période de révolution du satellite. La période d'acquisition pour générer des MNEs fiables en utilisant uniquement les données SWOT peut atteindre 3 mois, ce qui indique que plusieurs MNEs pourraient être générés pendant une seule année. Par conséquent, et grâce à la bonne précision fournie par les données SWOT, cette mission démontre aussi un grand potentiel pour suivre les changements topographiques saisonniers et interannuels dans les zones intertidales.

Le succès de suivi des changements est plus probable une fois qu'une période d'acquisition favorable qui fournit un échantillonnage adéquat de l'amplitude de la marée a été choisie (phénomène de repliement -Voir Annexe E).

Il est certain que l'apport de SWOT sera bénéfique pour la méthode de la ligne d'eau, comme le confirme cette étude. Cependant, il faut aussi se concentrer sur ses capacités interférométriques, car SWOT est un interféromètre à l'origine. Sa capacité à fournir des mesures interférométriques précises au niveau des estrans présente plus d'avantages que la méthode de la ligne d'eau. Un seul passage au-dessus d'un site d'étude à marée basse suffira pour générer une carte topographique. De plus, moins d'images seront nécessaires et plus de cartes topographiques pourront être créées sans les erreurs qui pourraient être introduites par les changements topographiques.

Conclusions

Ces différentes études effectuées dans le cadre de cette thèse nous ont permis de répondre aux questions de recherche présentées ci-dessus :

1. Grâce à l'utilisation de la bande Ka et du mode RSO, l'altimétrie est capable d'extraire des profils de topographie intertidale avec une précision qui peut atteindre 0,23 m. 7. Avec la bonne période d'acquisition qui fournit un échantillonnage complet de l'amplitude de la marée, SWOT a un grand potentiel pour détecter des changements topographiques dans les zones intertidales.

Cette thèse a ainsi montré l'utilité des missions récentes et futures pour le suivi de la topographie des zones intertidales. Avec le nombre croissant de produits et données gratuits et de nouveaux outils pouvant traiter d'énormes quantités de données (e.g., Google Earth Engine), il est maintenant plus que jamais possible de générer des produits de topographie intertidale à des grandes échelles (e.g., continentale). Cela peut se faire avec les méthodes présentées ici, mais aussi avec d'autres méthodes satellitaires comme l'InSAR et la stéréoscopie. Ces dernières méthodes et celles présentées dans cette étude sont toutes des méthodes directes. L'utilisation de méthodes inverses qui permettent d'inverser la topographie à partir des images acquises (RSO ou optique) à marée haute pourrait être aussi d'un grand intérêt. Beaucoup d'études ont examiné les capacités des méthodes inverses en eaux peu profondes, mais il n'y a toujours pas de test de leurs capacités dans les zones intertidales.

De plus, la capacité des méthodes de télédétection spatiales de fournir régulièrement des cartes topographiques ouvre la porte à de nombreuses applications scientifiques. La génération des MNEs intertidaux précis par couplage de différents types de données de télédétection (imagerie, altimétrie, etc.) permet de suivre l'évolution morpho-sédimentaire des zones intertidales. Par exemple, la méthode de la ligne d'eau permet de suivre les changements topographiques survenus au cours des dernières décennies en utilisant les archives d'images satellites et les relier aux processus hydrodynamiques et aux facteurs anthropiques ou climatiques. De plus, l'évaluation de l'impact des tempêtes pourrait être abordée en générant des MNEs intertidaux avant et après les événements de tempête. La connaissance de la topographie et des niveaux d'eau (à partir des acquisitions altimétriques) devrait permettre également de calculer d'autres paramètres tels que les échanges d'eau entre l'océan et les baies intertidales. Les MNEs générés serviront également pour la modélisation hydrodynamique et morphodynamique à des fins de recherche, mais aussi pour améliorer la gestion intégrée des zones côtières ainsi qu'orienter les décisions prises par les acteurs du littoral dans une optique d'optimisation de la mise en oeuvre des politiques d'utilisation et de protection de ces environnements.

INTRODUCTION

C OASTAL areas are very complex systems located at the interface between the land and the sea. Defining the coastal area may vary from scientific to planning and management standpoints [START_REF] Haslett | Coastal systems[END_REF]. [START_REF] Ketchum | The water's edge : critical problems of the Coastal Zone[END_REF] defined the coastal area as "the band of dry land and adjacent ocean space (water and submerged land) in which terrestrial processes and land uses directly affect oceanic processes and uses, and vice versa". A similar definition was proposed by [START_REF] Carter | Coastal environments : an introduction to the physical, ecological and cultural systems of coastlines[END_REF] defining the coastal zone as the area between the landward limit of marine influence and the seaward limit of terrestrial influence. In a more geology-oriented definition , [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF] defined the coastal zone as the area affected by coastal processes, such as waves and tides, during the Quaternary geologic period (the last 2.6 M years) (Figure 1). Other policy-oriented definitions of coastal areas exist as well and are usually dependent on distance or on usage-based criteria. The majority of definitions consider that the coastal area span over marine and terrestrial components. The natural features located in coastal areas include rocky coasts, beaches, barriers and sand dunes, estuaries and lagoons, deltas, river mouths, wetlands, and coral reefs [START_REF] Wong | Coastal systems and low-lying areas[END_REF]. The focus in coastal research changed with time, from focus on observation and classification of coastal landforms (Before the 1950s), to explanation of observations by studying coastal processes, which led to morphodynamic studies that were introduced after understanding that geomorphology is not only the result of coastal processes but also an active player [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF]. In other words, changes in morphology due to physical processes provide feedback to these processes that continue INTRODUCTION to affect coastal morphology. This means that morphology "has a degree of control over its own development" [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF]. Coastal systems exist in an equilibrium with their surrounding processes. A change in the system induce feedback that aims to recover the original equilibrium or to establish a new state of equilibrium. The dynamics in coastal systems are thus governed by the interactions between three elements: coastal processes (i.e. waves, tides, currents, wind, river outflow, weathering in rocky coasts, and other biological, biophysical, and biochemical processes), sediment transport (erosion and deposition), and morphology (morphodynamic feedback due to the strong links between form and process [START_REF] Cowell | Morphodynamics of coastal evolution[END_REF])) (Masselink and Gehrels 2015) (Figure 2). Coastal processes are linked to morphology through sediment transport and due to their non-static character, coastal areas are permanently changing in width and depth (or height). Coastal areas represent only 5% of Earth's land area, yet they accommodate a large fraction of the world's population [START_REF] Agardy | Ecosystems and human well-being: current state and trends[END_REF] and they are associated with high rate of population growth and urbanization [START_REF] Neumann | Future Coastal Population Growth and Exposure to Sea-Level Rise and Coastal Flooding -A Global Assessment[END_REF][START_REF] Small | A global analysis of human settlement in coastal zones[END_REF]. This is due to the various societal and economic services that these areas can provide. Coastal population are however, exposed to a range of hazards including erosion, saltwater intrusion, subsidence, tsunamis, and floods [START_REF] Nicholls | Rising sea levels: potential impacts and responses[END_REF], which may become more serious due to climate change and its related effects (i.e, sea-level-rise and the increase in storminess) (Switzer 2015) (Figure 3). Sea-level-rise and the increase in storminess, together with the overdevelopment that these areas are facing in terms of infrastructure and urbanization increased the vulnerability of coastal areas to erosion and flooding [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF] and increased the hazard not only on coastal population but also on ecological ecosystems. It should be noted that while sea level change controls the position of the coastline, it is not the only related factor to climate change [START_REF] Nicholls | Coastal systems and low-lying areas[END_REF][START_REF] Wong | Coastal systems and low-lying areas[END_REF]) and other factors are worth mentioning such as ocean acidification, changes in storm patterns, and an increase in precipitation [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF]. The pressure from population growth, various uses of coast (industrial and residential development, resource exploitation, infrastructure, tourism and recreation, and conservation [START_REF] Kay | Coastal planning and management[END_REF]), coastal hazards, and administrative issues stress the need for sustainable coastal management practices [START_REF] Haslett | Coastal systems[END_REF]. The aim of the latter is to protect humans living in coastal areas and their interests from natural and human-induced processes [START_REF] Haslett | Coastal systems[END_REF]. Managing coastal areas involves monitoring changes that occur in coastal areas and require an understanding of the morphological behavior and evolution. Therefore, there is a great need for accurate and up-to-date information about the topography and bathymetry of these systems in order to guarantee an effective management and to enable scientists to study coastal evolution.

Different conventional techniques exist for measuring the topography and bathymetry in coastal areas, such as beach profiling (ground-based), bathymetry sounding (shipborne-based), and airborne-based surveying [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. Topography mapping for coastal dry land areas was traditionally performed with ground-based equipment (e.g., theodolites or total stations) [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. While providing very accurate measurements, ground surveys are unable to map large, inaccessible, and hazardous areas. The topography of such areas is mapped thanks to aerial photography (stereo imagery and radar) that provided and is still providing very valuable measurements for coastal monitoring [START_REF] Gorman | Monitoring the Coastal Environment; Part IV: Mapping, Shoreline Changes, and Bathymetric Analysis[END_REF][START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. Regarding bathymetry mapping, lead lines were the oldest known instrument used for bathymetry sounding (measuring water depth) (Dierssen and Theberge 2014) until they were replaced by single beam echo sounders in the early 20th century [START_REF] Chakraborty | Bathymetric Techniques and Indian Ocean Applications[END_REF]. The German Meteor expedition was the first oceanographic research vessel to use a single beam echosounder [START_REF] Spiess | The Meteor Expedition: Scientific Results of the German Atlantic Expedition[END_REF]. Echosounders kept on acquiring single spot bathymetry measurements until the advent of MultiBeam EchoSounder (MBES) with the ability to strip map the seafloor (Figure 4). The French Jean Charcot vessel was the first research vessel to carry a MBES [START_REF] Allenou | The International hydrographic review[END_REF]. MBESs, which were originally designed for deep water measurements, are now commonly used for high resolution bathymetry retrieval in nearshore areas [START_REF] Janowski | Nearshore Benthic Habitat Mapping Based on Multi-Frequency, Multibeam Echosounder Data Using a Combined Object-Based Approach: A Case Study from the Rowy Site in the Southern Baltic Sea[END_REF][START_REF] Porskamp | Multiscale and Hierarchical Classification for Benthic Habitat Mapping[END_REF], including surveys in challenging tidal environments (e.g., the German Wadden Sea [START_REF] Mielck | High-Resolution Hydroacoustic Seafloor Classification of Sandy Environments in the German Wadden Sea[END_REF]) and Venetian Lagoon [START_REF] Madricardo | High resolution multibeam and hydrodynamic datasets of tidal channels and inlets of the Venice Lagoon[END_REF]). Recent developments have enabled their use in up to 1 m depths with resolutions reaching 0.05 m [START_REF] Madricardo | High resolution multibeam and hydrodynamic datasets of tidal channels and inlets of the Venice Lagoon[END_REF]. In 1980s, airborne light detection and ranging (LiDAR) technique was developed [START_REF] Carter | An introduction to LiDAR technology, data, and applications[END_REF]. In contrast to bathymetry sounding techniques, the use of airborne LiDAR is restricted to shallow coastal waters only, due to penetration limits. The advantage of this technique is its ability to cover land areas as well, providing topography information across the backshore, intertidal, and shallow nearshore zones [START_REF] Carter | An introduction to LiDAR technology, data, and applications[END_REF]. Since 1980s, the LiDAR technique evolved and became one of the most established and accurate techniques for coastal topography monitoring [START_REF] Carter | An introduction to LiDAR technology, data, and applications[END_REF]. The mentioned conventional techniques provide very accurate results (i.e., within a few centimeters), but they are constrained by logistical difficulties and high costs and they are unable to monitor large areas regularly. Among coastal features, intertidal flats alternately exposed and covered by water due to the tidal regime, present one of the most logistically challenging and hazardous environments for topography monitoring [START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF]. Intertidal flats are gently sloped areas located between the high and low water spring tide marks, inundated and exposed periodically due to the ebb and flood tides [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. They are amongst the most widely spread coastal systems [START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF], and occur primarily in tide-dominated environments (which determines whether or not sediments will be deposited) and sheltered coastal embayments where there is an important supply of fine-sediment (i.e., clays, silts, and fine to very fine sands) [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF][START_REF] Klein | Intertidal Flats and Intertidal Sand Bodies[END_REF]. Mesoand macro-tidal environments favor the formation of intertidal flats because the tidal action is usually dominant over other hydrodynamic forces in such environments [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. However, this dominance must be interpreted as a relative dominance, which means that tidal flats can be formed also in microtidal environments if the wave action is lower than tidal action and cannot be formed if the wave action dominates tidal action, even if the tidal range is large [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. A general zonation pattern exists in intertidal flats (Figure 5) that from upper flats (landward) to lower flats (seaward) consists in salt marshes, mud flats, mixed sand-mudflats, and sandflats (fining-upward sequence) [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]). However, this zonation is prone to modification due to different factors resulting in tidal creeks and redistribution of sediments. The growth of tidal flats is dependent upon sediment supply, and any shortage or cutoff in sediments input may result in erosion and shrinkage of these environments [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. Similarly, to other coastal features, intertidal flats provide several services. They provide habitat for a large community of migratory shorebirds [START_REF] Agardy | Ecosystems and human well-being: current state and trends[END_REF], supports millions of people worldwide, stabilize the coastline, defend from storm surges, and provide protection against coastal flooding [START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF]. They are as other coastal features, under stress from anthropogenic and climate change related pressures. Their evolution became nowadays an important research area [START_REF] Vos | The long-term evolution of intertidal mudflats in the northern Netherlands during the Holocene; natural and anthropogenic processes[END_REF]. A recent study conducted by [START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF] showed that intertidal flats have declined by 16% between 1984 and 2016 (Figure 6). There is an important demand for coastal monitoring solutions including intertidal flats. For topography monitoring, spaceborne remote sensing techniques provide a viable cost-effective complementary, and sometimes, alternative tool for topography and bathymetry mapping of coastal areas, especially in remote and hazardous regions. As defined by [START_REF] Sabins | Remote sensing: principles and applications[END_REF], "Remote Sensing is the science of acquiring, processing and interpreting images that record the interaction between electromagnetic (EM) energy and matter". In a broader and simpler definition, [START_REF] Elachi | Introduction to the Physics and Techniques of Remote Sensing[END_REF] defined Remote sensing as "the acquisition of information about an object without being in physical contact with it". Remote sensing data can be collected by sensors mounted on different types of platforms such as aircrafts (e.g., airborne LiDAR), Unmanned Aerial Vehicless (UAVs), ships (sounders), satellites, and even on terrestrial platforms. As the focus here is on spaceborne remote sensing, the first official definition of remote sensing from outer space was given in United Nations Plenary meeting in 3 December 1986 as the following: "The term remote sensing means the sensing of the Earth's surface from space by making use of the properties of electromagnetic wave emitted, reflected or diffracted by the sensed objects, for the purpose of improving natural resource management, land use and the protection of the environment". Remote sensing consists in detecting EM radiation reflected or emitted from Earth's surface. There are two remote sensing approaches: active and passive (Figure 7). Active remote sensing consists in transmitting EM waves and receiving (measuring) the reflected or scattered signal [START_REF] Lavender | Practical handbook of remote sensing[END_REF]. Examples of active sensors: radar, scatterometer, interferometer, altimeter, Global Positioning System (GPS) tracker, sonar, and LiDAR [START_REF] Raizer | Optical remote sensing of ocean hydrodynamics[END_REF]. Passive remote sensing measures only the radiation reflected on or emitted from an object [START_REF] Lavender | Practical handbook of remote sensing[END_REF]. Examples of passive sensors: microwave and infrared radiometers, visible and infrared spectrometers, photographic, digital, electro-optical, and TV cameras (without flash), and ultraviolet spectrophotometer [START_REF] Raizer | Optical remote sensing of ocean hydrodynamics[END_REF]. Based on our knowledge about the interaction between EM waves and different Earth's features, processing and analyzing the received signals enable us to infer various Earth's properties (physical, chemical, and biological) such as topography.

INTRODUCTION

INTRODUCTION

In contrast to passive optical sensors, radar sensors have a day-and-night and all-weather imaging capabilities. Active radar systems emit EM microwaves and receive the backscattered energy from the surface. In the 1950s, Carl Wiley developed the Synthetic Aperture Radar (SAR) system [START_REF] Wiley | Synthetic aperture radars-A paradigm for technology evolution[END_REF] which is an imaging system that can acquire radar images of the Earth's surface. Seasat was the first civilian satellite to carry a SAR instrument which was developed by the Jet Propulsion Laboratory (JPL) (NASA). Several SAR satellites were launched since the 1990s, such as the European Space Agency's (ESA) ERS-1&-2 and ENVISAT satellites, the RADARSAT-1/-2 satellites, the COSMO-SkyMed satellites, TerraSAR-X and TanDEM-X, GAOFEN-3, among others. Recently, ESA launched a new generation of SAR satellites (Sentinel-1A in 2014 andSentinel-1B in 2016), the first to be free and open for researchers. Their open source character will be advantageous for science usage and for developing methods that can produce updated products (such as updated coastal topographies). It also facilitates the combination of radar and optical data such as Sentinel-2 images.

Another largely used active radar sensors are satellite radar altimeters. Originally, satellite radar altimetry was conceived for measuring the shape of the Earth [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF]. The feasibility of using altimetry for measuring the surface topography of oceans was first discussed at the Williamstown congress in 1969 [START_REF] Kaula | The terrestrial environment: solid earth and ocean physics[END_REF]. Skylab space station launched in 1973 carried the first altimeter. Its measurements precision was in the order of 60 cm (in one-second averaging) [START_REF] Fu | Satellite Altimetry: Observing Ocean Variability From Space[END_REF]), but soon to be improved by GEOS-3 (NASA, 1975[START_REF] Lyzenga | Passive remote sensing techniques for mapping water depth and bottom features[END_REF] and Seasat (NASA, 1978) with 25 cm and 5 cm precisions in one-second averaging [START_REF] Stanley | The Geos 3 Project[END_REF][START_REF] Tapley | The SEASAT altimeter data and its accuracy assessment[END_REF]. During the eighties, Geosat (US Navy, 1985[START_REF] Li | Studies of multibaseline spaceborne interferometric synthetic aperture radars[END_REF] was the only altimeter in orbit providing full monitoring [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF]) and acquiring measurements with 4 cm precision [START_REF] Chelton | Satellite Altimetry[END_REF]). The precision attained 3 cm with ERS-1 (ESA, 1991(ESA, -2000) ) and achieved 2 cm with Topex/Poseidon (T/P) (NASA-CNES, 1992-2006) which is considered as the breakthrough to high precision altimetry [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF][START_REF] Frappart | Satellite Altimetry: Principles and Applications in Earth Sciences[END_REF]). In the continuity of the ERS-1 mission, the ERS-2 (ESA, 1995(ESA, -2011) ) mission was launched in 1995 and was followed by the GFO (US Navy-NOAA, 1998-2008) mission having the same orbit as Geosat [START_REF] Benveniste | Radar Altimetry: Past, Present and Future[END_REF].

Jason-1 (CNES-NASA, 2001-2013), Jason-2 (CNES-NASA-EUMETSAT-NOAA, 2008-present), and Jason-3 (CNES-NASA-EUMETSAT-NOAA, 2016-present) were launched as follow-ons to the T/P mission while ESA launched the successor of ERS-1/2 missions, ENVISAT (ESA, 2002(ESA, -2012) ) [START_REF] Frappart | Satellite Altimetry: Principles and Applications in Earth Sciences[END_REF].

HY-2 (CNES-CAST, 2011-present) and SARAL (ISRO-CNES, 2013-present) altimeters shared the ENVISAT/ERS orbit. All mentioned altimeters operated in Low Resolution Mode (LRM) [START_REF] Frappart | Satellite Altimetry: Principles and Applications in Earth Sciences[END_REF]). However, SARAL was the first altimeter operating in Ka-band. A new generation of altimeters known as Delay Doppler (or SAR) altimeters started with CryoSat-2 (ESA, 2010-present) [START_REF] Wingham | CryoSat: A mission to determine the fluctuations in Earth's land and marine ice fields[END_REF]) and was also adopted for Sentinel -3 constellation (ESA, 2016-present).

In the near future, new remote sensing opportunities will be offered by the future SWOT (Surface Water and Ocean Topography) SAR-interferometry wide-swath altimetry mission (Figure 8) [START_REF] Morrow | Global Observations of Fine-Scale Ocean Surface Topography With the Surface Water and Ocean Topography (SWOT) Mission[END_REF]. SWOT is a joint mission between NASA and CNES with contributions from the Canadian Space Agency (CSA) and the United Kingdom Space Agency (UKSA). It is the first altimetry mission with abilities to measure the elevation of inland surface waters bringing together two communities: oceanographers and hydrologists. SWOT mission projected for launch in 2021 will last for at least 3 years providing global 2D water height data. The mission's main instrument will be a Ka-band Radar Interferometer (KaRIn) [START_REF] Biancamaria | The SWOT Mission and Its Capabilities for Land Hydrology[END_REF] which is a bistatic SAR system with two antennas at opposite ends separated by a 10-m boom that will provide observations in a 120 km wide swath [START_REF] Fjortoft | KaRIn on SWOT: Characteristics of Near-Nadir Ka-Band Interferometric SAR Imagery[END_REF]). SWOT's payload includes as well a conventional altimeter (operating in Ku-band) that will be used for validation and calibration of the interferometric measurements and will also allow to fill the gap between the swaths [START_REF] Srinivasan | Engaging The Applications Community of The Future Surface Water and Ocean Topography (SWOT) Mission[END_REF]. In contrast to conventional altimetry missions intended to ocean surfaces only, SWOT mission will provide high precision measurements of water surface elevation over oceans, coastal, and inland water surfaces. Rivers larger than 100 m width and lakes (wetlands and reservoirs) of areas greater than 250 km 2 will be resolved with a vertical precision of 10 cm. Over terrestrial and coastal waters, SWOT will provide water elevation, slope, and water mask measurements [START_REF] Biancamaria | The SWOT Mission and Its Capabilities for Land Hydrology[END_REF]). This thesis is part of the SWOT mission and the SWOT COTEST project (Characterization, Modeling and SWOT Potentiality to Measure Hydro-meteo-marine Phenomena in the Coastal and Estuarine Systems) in the framework of the TOSCA (Terre Solide, Océan, Surfaces Continentales et Atmosphère) program of CNES, with one of the axes of which concerns the coupling of SWOT and current satellite missions for observing coastal areas.

Figure 8: A diagram illustrating the swaths of data that SWOT will collect. The interferometer will produce two parallel tracks, with a Nadir track from a traditional altimeter in the gap between the swaths. The overall width of the swaths will be approximately 120 km.

INTRODUCTION

A variety of spaceborne-based remote sensing methods for intertidal topography monitoring exist, including Interferometric Synthetic Aperture Radar (InSAR) [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF], stereophotogrammetry [START_REF] Tateishi | Relative DEM production from SPOT data without GCP[END_REF], and the waterline method [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]) (thorough explanation given in Chapter 1). SAR and optical images are used by the InSAR and the stereophotogrammetry methods respectively, while the waterline method can exploit both type of images. Both InSAR and stereophotogrammetry methods use overlapping SAR or optical images from different perspectives to reconstruct 3D objects (in this case intertidal Digital Elevation Models (DEMs)). As for the waterline method, it consists in: (i) extracting waterlines (interface between the intertidal flats and water) from a series of images that can provide a complete coverage of the tidal range, (ii) assigning heights to waterlines using sea level information (from tide gauges or ocean circulation models), and (iii) assembling and interpolating the waterlines to form a gridded-DEM. While the first two methods can provide relatively accurate results, the waterline method is still the most commonly used method for mapping intertidal topography since its development by [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF] due to several reasons (simple to use, more accessible data, necessity of single pass interferometry in case of InSAR method, high costs of single pass interferometry or stereophotogrammetry images, etc.). The waterline method experienced an important improvement, yet it is still not completely automatic and relies on significant manual processing.

Recent development in radar (altimetry and SAR) and optical technologies, bring new types of data and enhanced capacities in the study of coastal environment.

Motivated by the increasing need for regular monitoring of intertidal topography for both research and management purposes, the aim of this work is to investigate the use of recent spaceborne remote sensing missions in monitoring the topography of intertidal flats. To achieve this aim in the framework of SWOT project two main objectives are pursued:

1. Exploring, development, and improvement of spaceborne-based remote sensing methods for monitoring the topography of intertidal flats.

2. Investigating the ability and assessing the performance of the future SWOT mission to monitor the topography of intertidal areas.

The proposed objectives lead to the following research questions :

1. Is satellite radar altimetry capable of extracting intertidal topography profiles at low tides?

2. Could satellite altimetry acquisitions be separated between emerged and submerged measurement points based on intrinsic altimetry parameters (The backscattering coefficient (Sigma0 or σ 0 ) and Peakiness).

3. Does the free Sentinel imagery (1 and 2) missions (open source) provide adequate data for monitoring intertidal topography using the waterline method?

4. What improvements could be added to the waterline method in order to reduce the amount of manual processing?

5. Does the application of the waterline method using Sentinel data capable of providing intertidal DEMs regularly, in order to detect significant topographic changes?

6. Is SWOT capable of monitoring the topography of intertidal areas using the waterline method?

7. Can SWOT follow topographic changes using the waterline method?

To answer these questions, two different intertidal study sites were considered: the Arcachon Bay and the Bay of Veys located both on the French coast. The choice of these intertidal bays was motivated by the availability of accurate validation datasets for comparison purposes and by the contrasted characteristics they present in order to prove the applicability of the presented methodologies in different intertidal environments. The Arcachon Bay is a sheltered lagoon with extensive muddy flats where tides enter the system through two tidal inlets while the Bay of Veys is an exposed embayment with a mix of muddy and sandy material, with abundant presence of sand.

This thesis based on a set of 4 papers addresses these research questions in 4 chapters as the following:

Chapter 1 provides a state-of-the-art review on recent spaceborne remote sensing methods used for monitoring the bathymetry and topography of beaches, intertidal, and nearshore areas. For each method, a description of the methodology was presented and illustrated with examples. The methods reviewed are the following:

• Beach and dune: stereoscopy.

• Intertidal flats: the waterline method, InSAR, and satellite radar altimetry.

• Nearshore area: Bathymetry inversion from aquatic color data and bathymetry inversion based on wave characteristics.

Finally, some insights about the potential of the new and future satellite missions regarding the performance of the mentioned techniques was given. It should be noted that the satellite radar altimetry method reviewed in the intertidal flats section, is a method developed in the framework of this thesis and it will be presented in Chapter 2.

Chapter 2 addresses the first objective as we explore the use of satellite radar altimetry in intertidal areas. This study analyzed the ability of radar altimetry observations (intended originally to measure ocean surface topography) to extract, for the very first time, intertidal topography profiles. By comparing the results of different altimetry missions, the evolution of performance between past and current missions was assessed.

The waterline method mentioned above is the most common method used for intertidal topography monitoring. It was developed by [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]. The method involves detecting the land-sea (flat-sea) boundary using image processing techniques and superimposing the sea level (known from the tide gauge or from an ocean circulation model) to this boundary. From a series of images covering the whole tidal range, a set of leveled waterlines is obtained and then interpolated to form a gridded-DEM. This method forms the core part of Chapter 3 were we use Sentinel-1 and Sentinel-2 observations to generate intertidal DEMs for Arcachon Bay and the Bay of Veys using the waterline method. This chapter also addresses the first objective where we developed a unique edge INTRODUCTION detection technique to extract waterlines from Sentinel-1 and Sentinel-2 images. In addition, an improved approach of the waterline method was developed to derive intertidal DEMs. The changes include a faster, more efficient and quasi-automatic detection and post-processing of waterlines. This study investigated also the ability to monitor morphological changes in the Arcachon Bay and the Bay of Veys using the waterline method and Sentinels observations. Finally, and in regards of the great potential of the SWOT mission. Chapter 4 addresses the second objective consisting in studying the performance of SWOT to monitor intertidal topography. The waterline method was chosen to generate intertidal DEMs using SWOT-type observables. The choice of this method was motivated by the fact that SWOT will measure the surface water elevation in 2 dimensions, providing surface water elevation together with water extents (water masks), the parameters on which the waterline method relies. Since SWOT will provide sea height information at high accuracy, height will be associated to waterlines (extracted directly from water masks) without the need of ground-based measurements or modelling of water elevation which will make this method completely independent from in-situ measurements.

Conclusions and outlook are provided at the end of the thesis.

MONITORING BEACH TOPOGRAPHY AND NEARSHORE BATHYMETRY USING SPACEBORNE REMOTE SENSING: A REVIEW

With high anthropogenic pressure and the effects of climate change (e.g., sea level rise) on coastal regions, there is a greater need for accurate and up-to-date information about the topography of these systems. Reliable topography and bathymetry information are fundamental parameters for modeling the morpho-hydrodynamics of coastal areas, for flood forecasting, and for coastal management. Traditional methods such as ground, ship-borne, and airborne surveys suffer from limited spatial coverage and temporal sampling due to logistical constraints and high costs which limit their ability to provide the needed information. The recent advancements of spaceborne remote sensing techniques, along with their ability to acquire data over large spatial areas and to provide high frequency temporal monitoring, has made them very attractive for topography and bathymetry mapping. In this review, we present an overview of the current state of spaceborne-based remote sensing techniques used to estimate the topography and bathymetry of beaches, intertidal, and nearshore areas. We also provide some insights about the potential of these techniques when using data provided by new and future satellite missions.

1 28 1. LITERATURE REVIEW 1.1. INTRODUCTION
C OASTAL zones have always been attractive regions for human settlement because of their rich resources and localization at the interface between land and sea [START_REF] Neumann | Future Coastal Population Growth and Exposure to Sea-Level Rise and Coastal Flooding -A Global Assessment[END_REF]. These zones are densely populated, accounting for about 39% of the global population residing within 100 km from the coast (CIESIN -Center for International Earth Science Information Network 2005). They provide important economical and societal services, including commerce, transportation, fisheries, and tourism [START_REF] Burkett | Coastal Impacts, Adaptation, and Vulnerabilities: A Technical Input to the 2012 National Climate Assessment[END_REF]. Coastal zones are very dynamic natural systems that experience short-term (extreme meteo-oceanographic events) and long-term (seasonal changes in the wave climate, currents and erosion) morphological changes [START_REF] Heege | Satellite Services for Coastal Applications[END_REF]. Due to sea level rise and its related effects, coastal systems are considered among the most threatened environments [START_REF] Nicholls | Coastal systems and low-lying areas[END_REF]. A continuous monitoring of these systems is thus of great importance in order to plan sustainable coastal development and to implement ecosystem protection strategies [START_REF] Benveniste | Requirements for a Coastal Hazards Observing System[END_REF][START_REF] Klemas | The Role of Remote Sensing in Predicting and Determining Coastal Storm Impacts[END_REF]. A great demand exists nowadays for up-to-date bathymetric and topographic maps of shallow water areas and adjacent beaches. Marine-land topography and bathymetry with high spatiotemporal resolution and a reasonable vertical accuracy are essential for a better understanding of the evolution of coastal systems [START_REF] Benveniste | Requirements for a Coastal Hazards Observing System[END_REF]. They are, as well, essential for various types of applications and studies, including: Coastal flood forecasting, erosion forecasting, coastal defense, the monitoring of morphological changes, the identification of shoreline erosion or accretion, navigation, and fishing [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. Coastal DEMs (including topography and bathymetry) are also critical datasets for numerical hydrodynamic models. Inaccurate DEMs limit the performance of such models and may lead to inappropriate results [START_REF] Diaz | On the use of satellite-based Digital Elevation Models to determine coastal topography[END_REF][START_REF] Holman | Remote Sensing of the Nearshore[END_REF].

Conventional techniques, such as ground, ship-borne, and airborne-based surveying provide very accurate measurements (i.e., within a few centimeters) [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. Currently, MBESs, which were originally designed for deep water measurements, are commonly used for high resolution bathymetry retrieval in nearshore areas [START_REF] Janowski | Nearshore Benthic Habitat Mapping Based on Multi-Frequency, Multibeam Echosounder Data Using a Combined Object-Based Approach: A Case Study from the Rowy Site in the Southern Baltic Sea[END_REF][START_REF] Porskamp | Multiscale and Hierarchical Classification for Benthic Habitat Mapping[END_REF], including surveys in challenging tidal environments (e.g., the German Wadden Sea [START_REF] Mielck | High-Resolution Hydroacoustic Seafloor Classification of Sandy Environments in the German Wadden Sea[END_REF]) and Venetian Lagoon [START_REF] Madricardo | High resolution multibeam and hydrodynamic datasets of tidal channels and inlets of the Venice Lagoon[END_REF]). Recent developments have enabled their use in up to 1 m depths with resolutions reaching 0.05 m, which can be compared to LiDAR data [START_REF] Madricardo | High resolution multibeam and hydrodynamic datasets of tidal channels and inlets of the Venice Lagoon[END_REF]). However, these techniques are better suited for relatively small areas and are constrained by logistical difficulties and high costs [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. Spaceborne remote sensing techniques provide a viable cost-effective complementary, and sometimes, alternative tool for topography and bathymetry mapping of coastal areas, especially in remote and hazardous regions. Their synoptic nature and continuous monitoring enable regular and frequent updating of the topographic maps. Several satellite methods exist for mapping the topography and bathymetry of beaches, intertidal, and nearshore areas. These methods make use of various passive (SPOT, LandSat-8/OLI (Operational Land Imager), Sentinel-2/MSI (MultiSpectral Instrument/Imagery), WorldView, Quickbird, IKONOS, Pleiades, etc.) and active (ERS-1 and 2, TerraSAR-X, Sentinel-1, etc.) sensors. By analyzing satellite stereo-pairs [START_REF] Tateishi | Relative DEM production from SPOT data without GCP[END_REF], beach topography can be produced and large coastal stretches can be surveyed using satellite acquired stereo images [START_REF] Almeida | Deriving High Spatial-Resolution Coastal Topography From Sub-meter Satellite Stereo Imagery[END_REF]. Intertidal areas situated between the 1 29 upper and lower limits of spring tides also benefit from the wide range of available satellite data. The waterline method for intertidal topography mapping introduced by [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF] is presently the most adopted technique. In the last decade other methods have also been proven to be reliable for monitoring the topography of these areas, such as the InSAR [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF] and satellite radar altimetry [START_REF] Salameh | Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay[END_REF]. For shallow water bathymetry retrieval, the current methods are traditionally separated between two groups [START_REF] Pleskachevsky | Synergy and fusion of optical and synthetic aperture radar satellite data for underwater topography estimation in coastal areas[END_REF]): (i) Methods based on the modeling of radiative transfer in water for the processing of optical images and (ii) methods based on the influence of topography on hydrodynamic processes (e.g., current variations and wave characteristics). The latter methods can use optical and SAR images. Initial attempts to estimate shallow water bathymetry from remote sensing data started with [START_REF] Lyzenga | Passive remote sensing techniques for mapping water depth and bottom features[END_REF], using aerial multispectral photographs. Lyzenga's technique was expanded to multispectral optical satellite images, with first attempts made using Landsat data [START_REF] Benny | Satellite Imagery as an Aid to Bathymetric Charting in the Red Sea[END_REF][START_REF] Jupp | Remote sensing for planning and managing the great barrier reef of Australia[END_REF][START_REF] Lyzenga | Remote sensing of bottom reflectance and water attenuation parameters in shallow water using aircraft and Landsat data[END_REF][START_REF] Lyzenga | Shallow-water bathymetry using combined lidar and passive multispectral scanner data[END_REF]. Regarding SAR data, Alpers and Hennings [START_REF] Alpers | A theory of the imaging mechanism of underwater bottom topography by real and synthetic aperture radar[END_REF] proposed the first theoretical model to map underwater topography based on sea surface features induced by current variations over the bottom topography.

Here, a review of recent spaceborne techniques (derived from historical methods or those that are newly emerging) for topography and bathymetry mapping of coastal zones is provided. An overview about beach-, intertidal-, and nearshore-dedicated methods will be given in Sections 1.2, 1.3, and 1.4 respectively. For each reviewed method, a description of the methodology will be presented and illustrated with examples, followed in Section 1.5 by a table summarizing the methods described earlier. Finally, in Section 1.6, we will discuss the potential of the new and future satellite missions regarding the performance of the mentioned techniques. It should be noted that in the following sections, we will adopt for depth the usage conventions defined in the scientific literature with negative values (relative to the vertical datum) for intertidal areas and positive values (relative to the datum) for nearshore shallow waters.

BEACH AND DUNE TOPOGRAPHY FROM STEREOSCOPIC SATELLITE OPTICAL IMAGERY

Airborne optical remote sensing and 3D mapping meet the need for low-level imaging and geospatial information gathering on a regional scale [START_REF] Colomina | Unmanned aerial systems for photogrammetry and remote sensing: A review[END_REF]. The increased ease of use of recent UAV equipment with precise on-board positioning, such as ready-to-use UAVs, has led to a significant change in their practical application. The Real-Time Kinematic Global Positioning System (RTK-GPS) positioning of the camera, combined with the large number of overlapping images, makes any additional ground survey insignificant. In addition, the high degree of automation of UAVs and the absolute vertical accuracy, which is in the order of 0.2 m, suggests possible use in the field for natural hazards, disaster response, and high-resolution field analysis [START_REF] Mancini | Using Unmanned Aerial Vehicles (UAV) for High-Resolution Reconstruction of Topography: The Structure from Motion Approach on Coastal Environments[END_REF]. Despite these advantages, some disadvantages remain, such as the cost of photogrammetric software and computer power, which can be relatively high [START_REF] Gonçalves | UAV photogrammetry for topographic monitoring of coastal areas[END_REF], the difficulty of removing dense vegetation to obtain estimates of bare earth elevation [START_REF] Niethammer | UAV-based remote sensing of the Super-Sauze landslide: Evaluation and results[END_REF], the need for electric batteries for longer flights and larger spatial coverage, limitations in use due to weather conditions (Gleyzes 1. LITERATURE REVIEW et al. 2003), locations for take-off and landing, maintaining line-of-sight, and other flying constraints.

Sub-meter stereoscopic satellite imagery has the potential to provide an alternative to these techniques in the field to collect high spatial resolution topographic data over large areas. The first constellation of civilian satellites that acquired stereoscopic images and applied DEM reconstruction to large areas was the French mission SPOT in 1986 [START_REF] Gleyzes | SPOT5: system overview and image ground segment[END_REF]. Since then, several satellites with sensors capable of collecting imagery with a very high spatial resolution and stereo capabilities have been launched to meet the increased demand [START_REF] Panagiotakis | Validation of Pleiades Tri-Stereo DSM in Urban Areas[END_REF]). Among them, the Pleiades constellation (built by the CNES and marketed by AIRBUS Defence and Space), consists of two high spatial resolution optical satellites: Pleiades-1A and -1B. The two satellites fly over the same quasi-polar heliosynchronous orbits at an altitude of 694 km, with a phase of 180°a nd a descending node. The optical sensors of these satellites have the ability to obtain images with a resolution of less than one meter (0.7 m pixels, resampled at 0.5 m) over a maximum area of 350 km × 20 km (swath width of 20 km at nadir). An important aspect of Pleiades is the ability to revisit any place in the world in one day, which is of great interest for monitoring rapidly changing processes (e.g., coastal erosion due to storms).

In [START_REF] Almeida | Deriving High Spatial-Resolution Coastal Topography From Sub-meter Satellite Stereo Imagery[END_REF], beach and dune topography was retrieved using Pleiades-1A stereoscopic imagery. An evaluation of the precision and accuracy of the derived 2-meter Pleiades DEM was performed by [START_REF] Almeida | Deriving High Spatial-Resolution Coastal Topography From Sub-meter Satellite Stereo Imagery[END_REF] through comparison between the satellite derived topography and traditional survey methods, such as airborne LiDAR and RTK-GPS surveys. The pilot site selected for this comparison was a 40 km stretch of coastline in southwest France (Figure 1.1). The derived 2 m Pleiades DEM showed good overall agreement with competing methods (Figure 1.2) (RTK-GPS and LiDAR; correlation coefficient of 0.9), with a vertical Root Mean Square Error (RMSE) (used to characterize the effective error) ranging from 0.35 m to 0.48 m, after absolute co-registration in the LiDAR dataset. The most significant errors (mean square error > 0.5 m) occurred in the steep walls of the dunes, particularly in shaded areas. This work shows that DEMs derived from sub-meter satellite images capture local morphological features (e.g., berm or dune shaped) on a sandy beach over a wide spatial area.

INTERTIDAL TOPOGRAPHY

Monitoring the topography of intertidal flats presents considerable logistical difficulties when compared to other coastal features. Sometimes spaceborne-based techniques are the only techniques available for measuring the intertidal topography. This section will present the spaceborne-based methods for retrieving intertidal topography, including the waterline (well-established) method, the InSAR method (high potential), and the satellite radar altimetry method (which has recently been proven to be valuable for intertidal topography mapping). 1. LITERATURE REVIEW tide/surge model for the observed area at the time of acquisition of the image [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. From a series of images covering the whole tidal range, a set of waterlines is assembled and interpolated to form a gridded DEM (e.g., by Delaunay triangulation [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF]). This technique assumes that there are no major changes occurring in the topography of the intertidal area during the acquisition period [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. It also assumes that wave runup influences on the shoreline elevation are minimal. SAR images are mostly used due to their all-weather imaging capabilities. Optical images can also be used if there is no cloud cover. Usually optical images are used together with SAR images to improve the coverage of the tidal range. It is recommended that the images used are acquired during extended calm periods where no major changes in topography are expected. However, images from other seasons can be added if the coverage of the tidal range is not complete [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF].

The first step of the waterline method is detecting the waterline from the images using edge detection techniques. Several different approaches have been implemented. In [START_REF] Mason | Accurate and efficient determination of the shoreline in ERS-1 SAR images[END_REF], a multi-scale edge detection algorithm based on the Touzi algorithm [START_REF] Touzi | A Statistical and Geometrical Edge Detector for SAR Images[END_REF]), together with an active contouring model, was used. [START_REF] Niedermeier | Detection of Coastlines in SAR Images using Wavelet Methods[END_REF] proposed an edge detection technique for intertidal areas based on Mallat's wavelet-based edge detection method [START_REF] Mallat | Characterization of Signals from Multiscale Edges[END_REF], adapted to SAR images combined with a block tracing algorithm and active contouring. [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF] and [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF] adopted a wavelet-based approach as well, in combination with a segmentation procedure. However, they abandoned the idea of accurate tracking over the scales carried out in [START_REF] Niedermeier | Detection of Coastlines in SAR Images using Wavelet Methods[END_REF] because the gain in quality was low versus the high computational effort [START_REF] Niedermeier | Detection of Coastlines in SAR Images using Wavelet Methods[END_REF]. In some studies, the edge was manually digitized through visual investigation, like in [START_REF] Xu | Estimation of seasonal topographic variation in tidal flats using waterline method: A case study in Gomso and Hampyeong Bay, South Korea[END_REF]. The latter study used imagery data (18 Landsat TM and ETM+ for which the manual digitizing is relatively straightforward and not too time-consuming. However, in the case of a greater number of images and SAR data, the manual approach becomes overwhelming.

After detecting the waterlines in the images time series, topography heights are assigned to them using the hydrodynamic models output made for the period of acquisition of each image or by using sea level data records from nearby tide gauges. A single waterline has a range of heights, and the use of tide gauge records must be performed with care and in study sites where the surface water slope is negligible.

After assembling the waterlines in one map, the points between them are interpolated to form a gridded geo-referenced DEM. Several interpolation methods were also used in different studies, for instance, [START_REF] Mason | Accurate and efficient determination of the shoreline in ERS-1 SAR images[END_REF] and [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF] used triangulation, [START_REF] Xu | Estimation of seasonal topographic variation in tidal flats using waterline method: A case study in Gomso and Hampyeong Bay, South Korea[END_REF] used the Natural Neighbor Interpolation (NNI) algorithm [START_REF] Sibson | A brief description of natural neighbour interpolation[END_REF], while universal block kriging was used in [START_REF] Mason | Interpolation of an Intertidal Digital Elevation Model from Heighted Shorelines: a Case Study in the Western Wash[END_REF], in a paper dedicated to the interpolation part of the method. The advantage of the latter method is that it provides a variance suitable to estimate the error of each interpolated point. Kriging was also used in [START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF] and was compared to Triangulated Irregular Networks (TINs) in [START_REF] Wu | An Improved DEM Construction Method For Mudflats Based on BJ-1 Small Satellite Images: A Case Study on Bohai Bay[END_REF], where both interpolation methods showed reasonable results, with better details obtained by kriging, however. [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF] used Delaunay triangulation to interpolate the waterlines on a gridded DEM. The DEM accuracy obtained by the waterline method depends on the hydrodynamic model accuracy, the number and spatial distribution of tide gauges if no hydrodynamic model was used, the slope of the intertidal zone, the type of the sensor and its horizontal resolution [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF], and the degree of swash excursions at the site. Height accuracies of about 20 cm were attained in the Wash of Eastern England [START_REF] Mason | Interpolation of an Intertidal Digital Elevation Model from Heighted Shorelines: a Case Study in the Western Wash[END_REF]. [START_REF] Mason | A Sensitivity Analysis of the Waterline Method of Constructing a Digital Elevation Model for Intertidal Areas in ERS SAR scene of Eastern England[END_REF] investigated the variation of vertical accuracy in function of beach slopes. The study showed that a standard deviation of 18-22 cm is achieved for a 1:500 slope. Inaccuracy rises to 27 cm on a 1:100 slope and to 32 cm on 1:30 slope beaches. After comparison with in situ measurements, [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF] obtained a standard deviation of 37 cm over the German part of the Wadden flats, while [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF] obtained a standard deviation of 27 cm over the same region due to finer sampling of the tidal range by also including optical Landsat images in the analysis. It should be noted that the edge detection error affects the vertical precision depending on the topography slope. A horizontal uncertainty of 50 m can only cause less than 10 cm vertical error for regular slopes of 1:500 [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF].

Using the waterline method, [START_REF] Xu | Estimation of seasonal topographic variation in tidal flats using waterline method: A case study in Gomso and Hampyeong Bay, South Korea[END_REF] studied the seasonal variation of topography in two major South Korean bays, the Gomso Bay and the Hampyeong Bay, by generating winter (December to February) and summer (June to September) DEMs. By differentiating the two DEMs, [START_REF] Xu | Estimation of seasonal topographic variation in tidal flats using waterline method: A case study in Gomso and Hampyeong Bay, South Korea[END_REF] were able to find regions of erosion and deposition between the winter and summer seasons of 2004 of the Gomso and Hampyeong Bays, which are situated in the southeastern coast of the Korean Peninsula. [START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF] used the waterline method to measure the sediment transport and sediment volume changes of the intertidal area of the Morecambe Bay in England between 1991 and 1997. Thirty images acquired between late 1991 and mid 1998 by ERS-1 and ERS-2 SAR sensors (C-band) were divided between two subsets of images spanning the 1991-1994 and 1995-1998 periods, in order to detect changes in the intertidal area (in [START_REF] Mason | Remote sensing of intertidal morphological change in Morecambe Bay, U.K., between 1991 and 2007[END_REF] the period was extended to 1991-2007). [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF] applied the waterline method to measure the topographic changes over 1996-2009 period over the Wadden flats (Figure 1.3). By including optical Landsat images into the dataset, where in the previous work [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF] only comprised SAR data, the tidal range can be sampled much finer, improving the vertical accuracy of the resulting DEMs [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF]. By analyzing a sequence of generated DEMs, Li (2014) calculated the sediment volume changes and the development of tidal flats after erosion and accretion. Figure 1.3.c-e show the location of the areas where the most topographic changes occurred after being calculated by the standard deviation of each point of the DEMs created between 1996 and 2009 [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF].

However, large-scale and long-term application of the waterline method even allow the analysis of changes at much larger scales in space and time. The long-term changes of the complete Schleswig-Holstein Wadden Sea intertidal flat area of 90 × 40 km 2 total extent were characterized in maps of various statistical parameters. As an example, Figure 1

INTERFEROMETRIC SAR (INSAR)

Intertidal DEMs can be generated using the InSAR technique. The first use of this method with a spaceborne system was performed by [START_REF] Li | Studies of multibaseline spaceborne interferometric synthetic aperture radars[END_REF] using SeaSat data. It uses two (or more) complex-valued SAR images taken from different positions, different times, or both, in order to extract topography information from their phase difference. The images are known as master and slave(s) images and the method consists of the following steps [START_REF] Bamler | Synthetic aperture radar interferometry[END_REF][START_REF] Bürgmann | Synthetic Aperture Radar Interferometry to Measure Earth's Surface Topography and Its Deformation[END_REF][START_REF] Moreira | A tutorial on synthetic aperture radar[END_REF][START_REF] Rosen | Synthetic aperture radar interferometry[END_REF][START_REF] Simons | Interferometric synthetic aperture radar geodesy[END_REF]):

• Co-registration: The alignment of the pixels in a way that the ground scatterers contribute to the same pixel for both images. By convention, the slave image is resampled to the master image grid (range, azimuth).

• interferogram formation and coherence estimation: The complex interferogram is obtained by multiplying each complex pixel of the master image to the complex conjugate of its corresponding pixel in the slave image (Z 1 and Z 2 below). The interferogram itself is a complex image with an amplitude measuring the cross-correlation of the images and a phase representing the phase difference between the two images that contains the topographic information [START_REF] Bürgmann | Synthetic Aperture Radar Interferometry to Measure Earth's Surface Topography and Its Deformation[END_REF]. It should be noted that the accuracy of the phase measurement and thus the resulting topography heights are limited by the coherence which reflects the degree of correlation between the two images. The coherence (also called the complex correlation coefficient) is locally (on a small window around the pixel) computed as follows:

γ = E [Z 1 Z * 2 ] E [|Z 1 | 2 ]E [|Z 2 | 2 ] (1.1)
where E [x] is the expected value of random variable x. The factors that impact the interferogram coherence in intertidal areas are discussed below.

• Flat-earth removal: This consists of the removal of the phase generated by a flat featureless Earth by subtracting the expected phase from a surface of constant elevation.

• Phase unwrapping: This step consists of removing the modulo-2π ambiguity to obtain a phase field directly proportional to the topography.

• Phase-to-height conversion.

• Geocoding: Transforming the converted height from the radar image geometry to the coordinates of a geodetic reference system.

This method is an established technique for generating DEMs for inland areas [START_REF] Gens | Review Article SAR interferometry-issues, techniques, applications[END_REF]. However, the ability to derive reliable and accurate intertidal DEMs using this method depends on various criteria and conditions. The coherence is a crucial parameter for DEM generation using the InSAR method [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF][START_REF] Won | ERS SAR Interferometry for Tidal Flat DEM[END_REF]. It reflects the quality of the interferogram and the similarity between the pixels of the master and slave images. High coherence is an essential criterion for the generation of accurate DEMs. Many decorrelation factors reduce the magnitude of the coherence. These decorrelation factors can be classified as: Volumetric, Signal to Noise Ratio (SNR), temporal, and geometric decorrelations [START_REF] Just | Phase statistics of interferograms with applications to synthetic aperture radar[END_REF][START_REF] Moreira | A tutorial on synthetic aperture radar[END_REF][START_REF] Zebker | Decorrelation in interferometric radar echoes[END_REF]:

γ = γ V ol .γ SN R .γ Temp .γ Geo (1.2)
For intertidal areas, the impact of the volumetric decorrelation on the coherence is too low and can be considered as negligible. This is due to the high moisture content and high conductivity of the intertidal areas that block the microwaves from penetrating into the 1 37 soil [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Gade | Classification of sediments on exposed tidal flats in the German Bight using multi-frequency radar data[END_REF]. The SNR decorrelation is caused by the sensor thermal noise, and in contrast to volumetric decorrelation, it cannot be neglected for coastal areas due to their low backscattering intensity [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF]. The temporal decorrelation is a major limiting factor for the InSAR technique. This type of decorrelation results from physical changes (e.g., changes in surface water and surface roughness, remnant water, change of sand ripples by tides for sandy areas, etc.) in the scene occurring between two time-separated SAR acquisitions. Therefore, an accurate intertidal DEM requires a short temporal baseline. For this reason, it is recommended to use single-pass interferometry (two antennas on the same platform) systems with no temporal baseline over multi-pass interferometry systems, for which the temporal decorrelation between the pixels is too important. Nevertheless, [START_REF] Won | ERS SAR Interferometry for Tidal Flat DEM[END_REF] generated DEMs with the InSAR technique using ERS-1/2 tandem pairs (1-day time separation) in the Youngjeong-do tidal flat area and obtained acceptable results. More precise DEMs were obtained by [START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF] using the single-pass TanDEM-X data (Figure 1.5). The two major geometric parameters that affect the coherence are the perpendicular baseline and the incidence angle. A large spatial baseline is required to obtain accurate results [START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF], however if the baseline is too long, serious geometric decorrelation may occur [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF]. The optimal baseline to generate intertidal DEMs with single-pass SAR system was investigated in [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF]. They found that a baseline of 1500 m with an incidence angle of 29°produced a minimal height error of 15 cm.

SATELLITE RADAR ALTIMETRY

Over intertidal zones, direct estimates of the bottom topography can also be directly derived from radar altimetry measurements during low tide. A first demonstration of this technique was undertaken in the Arcachon Bay (Figure 1.6.b) [START_REF] Salameh | Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay[END_REF], a mesotidal shallow semi-confined lagoon on the west coast of France with a surface of 174 km 2 (Figure 1.6a), using altimetry data acquired by ERS-2 (1995ERS-2 ( -2003)), ENVISAT (2002ENVISAT ( -2010)), Cryosat-2 (since 2010), and SARAL (2013[START_REF] Shepard | A two-dimensional interpolation function for irregularly-spaced data[END_REF] on their nominal orbits. The spatial coverage of these missions is presented in Figure 1.6.c-f for ERS-2, ENVISAT, SARAL, and Cryosat-2 respectively. Surface heights were obtained using altimeter ranges retracked with the Offset Center Of Gravity (OCOG, or ICE-1, or Sea-Ice) retracking algorithm [START_REF] Wingham | New Techniques in Satellite Altimeter Tracking Systems[END_REF], which is commonly used over land (e.g., (Frappart et al. 2006a)), applying the following corrections to the range (ionosphere, dry and wet troposphere corrections to take into account the delays of propagation in the atmosphere, solid Earth and pole tides to take into account the crustal vertical motions). These surface heights were related to either the intertidal topography of the Arcachon lagoon or to the SSH depending on the time of acquisition of the radar altimetry data. Note that the Sea State Bias (SSB) corrections was not applied as it is not estimated within the OCOG processing and can be neglected as the significant wave heights are generally low in the Arcachon Bay.

The data used in this study [START_REF] Salameh | Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay[END_REF]) are the following: (i) Water level records from the Arcachon-Eyrac tide gauge, managed by the French hydrographic service (SHOM) and the Gironde sea and land state office (DDTM) and (ii) an airborne topographic LiDAR image acquired at low tide, on 25 June 2013, interpolated on a regular 1 × 1 m grid to produce an RGE ALTI ® product, which was provided by the Institut national de l'information géographique et forestière (previously Institut Géographique National) (IGN), with an altimetric precision of 0.2 m. The tide gauge data are used to fill the LiDAR topography with water, allowing discrimination between the emerged and submerged areas. Altimetry data were processed either manually, using Multi-mission Altimetry Processing Software (MAPS) [START_REF] Frappart | Preliminary Assessment of SARAL/AltiKa Observations over the Ganges-Brahmaputra and Irrawaddy Rivers[END_REF][START_REF] Normandin | Evolution of the Performances of Radar Altimetry Missions from ERS-2 to Sentinel-3A over the Inner Niger Delta[END_REF], or automatically, using a classification approach based on the statistical distributions of radar altimetry-based surface heights and radar echoes-derived parameters, namely the backscattering coefficient and peakiness (see [START_REF] Salameh | Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay[END_REF] for more details). Examples of along-track topography retrievals are presented in Figure 1.7 for SARAL and Cryosat-2.

To demonstrate the capability of satellite altimetry to retrieve topographic profiles over the intertidal area of the Arcahcon Bay, altimetry measurements were compared to the emerged areas of the LiDAR-derived topography. The results of the comparisons are the following: R (Pearson correlation coefficient) of 0.17, 0.54, 0.71, and 0.79 and RMSE of 2.01, 0.95, 0.23, 0.44 m were respectively found using ERS-2, ENVISAT, SARAL, and Cryosat-2. If no agreement was observed between the LiDAR topography and ERS-2 and ENVISAT estimates, more accurate results were found using SARAL and Cryosat-2 data. These differences can be attributed to the differences in: (i) Footprint size between the data acquired in LRM mode at the Ku-band (footprint radius of 18 km for ERS-2 and ENVISAT), at the Ka-band (footprint radius of 8 km for SARAL), and at the Ku band in the SAR mode (footprint of 300 m along-track per 18 km cross-track) and (ii) bandwidth (20, 80, or 320 MHz for ENVISAT, depending on the chirp bandwidth operation mode and 320

In scientific literature, the inversion of water depth (h, m) from ACR is mainly addressed by the analytical optically shallow water reflectance model initially proposed by [START_REF] Lyzenga | Passive remote sensing techniques for mapping water depth and bottom features[END_REF], which has been improved by [START_REF] Philpot | Bathymetric mapping with passive multispectral imagery[END_REF] and [START_REF] Maritorena | Diffuse reflectance of oceanic shallow waters: Influence of water depth and bottom albedo[END_REF] and reformulated by [START_REF] Lee | Hyperspectral remote sensing for shallow waters: 2 Deriving bottom depths and water properties by optimization[END_REF] and [START_REF] Albert | Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties[END_REF]. This analytical model allows the expression of r r s as a function of a large number of unknowns, which include h, the bottom albedo, and the concentration of different optically active components of water. Solving this model is based on optimization methods which require hyperspectral data [START_REF] Petit | Hyperspectral remote sensing of coral reefs by semi-analytical model inversion -Comparison of different inversion setups[END_REF]). However, when topography is characterized by a small spatial scale variability, only high and very high resolution multispectral satellite missions can address the high spatial heterogeneity of coastal and inland aquatic systems [START_REF] Capo | Assessment of the decadal morphodynamic evolution of a mixed energy inlet using ocean color remote sensing[END_REF]. In this case, the analytical model can be simplified in order to provide an approximation of the radiative transfer solution in water [START_REF] Lyzenga | Multispectral bathymetry using a simple physically based algorithm[END_REF]. h can then be expressed as a function of three unknown parameters, namely the vertical averaged effective or operational attenuation coefficient (K , m -1 ), the value of r r s of the bottom substrate (r r s_bot t om , sr -1 ), and the value of r r s over hypothetical optically deep water (r r s_d eep , sr -1 ):

h = 1 2K [ln(r r s_bot t om -r r s_d eep ) -ln(r r s -r r s_d eep )] (1.3)
Based on this formula, two different approaches using empirical and semi-analytical algorithms were developed. Empirical algorithms require a training dataset composed of in situ water depth in order to calibrate from statistical methods a non-linear relationship between h and the reflectances measured in different bands. These approaches perform well for optically homogeneous environments [START_REF] Bramante | Multispectral derivation of bathymetry in Singapore's shallow, turbid waters[END_REF][START_REF] Dekker | Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments[END_REF][START_REF] Su | Automated Derivation of Bathymetric Information from Multi-Spectral Satellite Imagery Using a Non-Linear Inversion Model[END_REF]), but are site-and time-dependent [START_REF] Lyzenga | Multispectral bathymetry using a simple physically based algorithm[END_REF][START_REF] Stumpf | Determination of water depth with high-resolution satellite imagery over variable bottom types[END_REF]. To overcome these limitations, empirical approaches are now associated with machine learning and multi-temporal techniques [START_REF] Evagorou | Bathymetric maps from multi-temporal analysis of Sentinel-2 data: The case study of Limassol, Cyprus[END_REF][START_REF] Sagawa | Satellite Derived Bathymetry Using Machine Learning and Multi-Temporal Satellite Images[END_REF].

For semi-analytical algorithms, no field data are required. This advantage ensures reproducibility to any site and reproducibility over a long-term time series. The quasi-analytical multispectral model for shallow water bathymetry inversion (QAB), developed by [START_REF] Capo | Assessment of the decadal morphodynamic evolution of a mixed energy inlet using ocean color remote sensing[END_REF], provides an illustration of this kind of method (see Figure 1.8 for an application to Sentinel-2/MSI data). A brief description of the QAB is given here. The reader may refer to [START_REF] Capo | Assessment of the decadal morphodynamic evolution of a mixed energy inlet using ocean color remote sensing[END_REF] for a full description of the method. In the QAB, h is directly derived from r r s . Thus, a preliminary step is to apply atmospheric correction in order to extract the remote sensing reflectance (R r s ) to the top-of-atmosphere signal. r r s is then computed using the following expression [START_REF] Gordon | A semianalytic radiance model of ocean color[END_REF]):

r r s = R r s n 0 + n 1 R r s (1.4)
where n 0 and n 1 are two constants equal to 0.52 and 1.7, respectively [START_REF] Lee | A semi-analytical scheme to estimate Secchi-disk depth from Landsat-8 measurements[END_REF]). Then, step 1 is dedicated to the automatic extraction of r r s_bot t om and r r s_d eep using a supervised classification approach with a random forests classifier.

Step 2 allows the derivation of the total absorption (a) and backscattering coefficients (b b ) at 559 nm from r r s_d eep using the quasi-analytical algorithm (QAA) version 5 [START_REF] Lee | An update of the quasi-analytical algorithm (QAA_v5)[END_REF]) with the current default algorithm coefficients [START_REF] Lee | A semi-analytical scheme to estimate Secchi-disk depth from Landsat-8 measurements[END_REF]).

Step 3 derives K d at 559 nm from a and b b using the model of [START_REF] Lee | Penetration of UV-visible solar radiation in the global oceans: Insights from ocean color remote sensing[END_REF].

Step 4 is dedicated to the inversion of h using 1. LITERATURE REVIEW Equation 1.4. Finally, the tidal height (T ) provided by a gauge station located at Arcachon allows to compute the bathymetry (Z ) using the following expression:

Z = h -T (1.5)
Figure 1.8.a,b shows the bathymetry inverted from Sentinel-2/MSI images acquired on 2017-10-06 (MSI-17) and 2018-09-01 (MSI-18). MSI-17 and MSI-18 were acquired 30 min after low tide and 4 h after high tide (ebb conditions), respectively, with a tide correction of 0.6 m and 1.5 m. In this example, Sentinel-2 data are corrected from atmospheric effects using the SWIR-ACOLITE algorithm version 20190326.0 [START_REF] Vanhellemont | Advantages of high quality SWIR bands for ocean colour processing: Examples from Landsat-8[END_REF], which provides good performance over turbid waters (Bru et al. 2017;[START_REF] Ilori | Analyzing Performances of Different Atmospheric Correction Techniques for Landsat 8: Application for Coastal Remote Sensing[END_REF][START_REF] Novoa | Atmospheric Corrections and Multi-Conditional Algorithm for Multi-Sensor Remote Sensing of Suspended Particulate Matter in Low-to-High Turbidity Levels Coastal Waters[END_REF]. The marine optics conditions associated with these images are in the range observed by [START_REF] Capo | Assessment of the decadal morphodynamic evolution of a mixed energy inlet using ocean color remote sensing[END_REF] with a K d value of 0.5 m -1 and 0.3 m -1 , a r r s_d eep value of 0.022 sr -1 and 0.019 sr -1 , a r r s_bot t om value of 0.094 sr -1 and 0.087 sr -1 , and an environmental noise equivalent reflectance difference (N E ∆r r s ), computed from the method of [START_REF] Wettle | A methodology for retrieval of environmental noise equivalent spectra applied to four Hyperion scenes of the same tropical coral reef[END_REF], of 0.0023 sr -1 and 0.0039 sr -1 . These optical conditions allow computation of the maximum optical depth (h max ), which represents the depth from which the bottom is no longer "optically" visible by the sensor, using Equation 10 in [START_REF] Capo | Assessment of the decadal morphodynamic evolution of a mixed energy inlet using ocean color remote sensing[END_REF]. Although, (N E ∆r r s ) for MSI-18 is higher than for MSI-17, h max is higher (4.8 m versus 3.4 m) because of a lower value of K d . In consequence, the range of bathymetry inverted from the QAB is higher for MSI-18 (from -1.5 m to 3.3 m) than for MSI-17 (from -0.6 m to 2.8 m).

Figure 1.8.c displays the location of in situ acoustic bathymetry (Z i n-si t u ) data used to evaluate the performance of the QAB and the uncertainty associated with the QAB-derived bathymetry (Z sat ) product. Because of the high dynamics of the nearshore morphology, the Z i n-si t u values used for the evaluation were recorded during bathymetric surveys conducted in a time interval of ±2 months around the acquisition date of Sentinel-2/MSI images. It is worth noting that the dataset covers the entire study area, except the south channel. The performances calculated for 2017 and 2018 (N = 2902) are better than [START_REF] Capo | Assessment of the decadal morphodynamic evolution of a mixed energy inlet using ocean color remote sensing[END_REF], with an absolute mean error of 0.06 m and a root mean square error of 0.52 m (Figure 1.8.d). However, the dispersion of observations around the line 1:1 indicates a significant uncertainty. It is important to note here that only few studies provide this information, which nevertheless represents a decisive evaluation criterion with regard to International Hydrographic Organization standards. Figure 1.8.e provides the MAE and the 95% Confidence Interval (CI) C I 95 (under the assumption that error follows a normal distribution) calculated per year and for each 0.5 m depth intervals. In 2017, the mean error and C I 95 vary between -0.03 m and 0.16 m and 1.34 m and 2.42 m, respectively. In 2018, the mean error and C I 95 show higher values, ranging from -0.36 m to 1.18 m and 1.10 m to 4.30 m, respectively. These high uncertainties are mainly due to observations located in the northeastern part of the lagoon, where the K d and r r s_bot t om values are significantly different from the values in other areas of the inlet.

In the QAB, the inversion of Z from r r s is performed using a sequential process, which generates, at the different steps, errors and uncertainties that will propagate in the following steps. Uncertainties are associated with the estimation of r r s (through the atmospheric corrections, including the water interface corrections as the sunglint and adjacency effects), the inversion of a, b b (through the QAA), K d , (through the model of [START_REF] Lee | Penetration of UV-visible solar radiation in the global oceans: Insights from ocean color remote sensing[END_REF]), h (through Equation 1.4), and the computation of Z (through the tidal 1.4. NEARSHORE BATHYMETRY 1 43 correction). Another major source of uncertainty is the intra-pixel heterogeneity of bathymetry, particularly when the slope of the bottom is high. For bathymetry inversion from high resolution multispectral sensors, readers may find an exhaustive review of the different sources of uncertainty in [START_REF] Botha | Effects of Per-Pixel Variability on Uncertainties in Bathymetric Retrievals from High-Resolution Satellite Images[END_REF]. However, the quantification of errors and uncertainties remains a challenge and a major issue in ACR [START_REF] Ioccg | Remote Sensing of Inherent Optical Properties: Fundamentals,Tests of Algorithms, and Applications[END_REF][START_REF] Lee | Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm[END_REF].

NEAR COAST BATHYMETRY BASED ON WAVE CHARACTERISTICS

Among the existing bathymetry spaceborne estimation studies, MSI satellite imagery enables measuring bathymetry using the optical properties of shallow waters. Nevertheless, this technique applies mainly in the immediate vicinity of the coast, for optically shallow waters, as it requires sufficient water transparency to measure the impact of the bottom on the water-leaving radiometric signal.

Other satellite techniques use the measurable wave characteristics to produce bathymetry. Indeed, most of these techniques are based on the dispersion relation resulting from the linear wave theory:

h = λ 2π .t anh -1 (2πc 2 /g λ) (1.6)
where h is the water height, c is the wave celerity, λ is the wavelength, and g is the acceleration of gravity.

The dispersion relation is particularly well suited for determining the intermediate depth bathymetry (i.e., as λ/20 < h < λ/2). In the surf zone, nonlinear effects greatly limit the validity of the linear dispersion relation to derive depths [START_REF] Bergsma | Video-based depth inversion techniques, a method comparison with synthetic cases[END_REF][START_REF] Holland | Application of the linear dispersion relation with respect to depth inversion and remotely sensed imagery[END_REF]). Waves generally travel with greater speeds than the linear dispersion relation, hence depths are over estimated. To overcome this, non-linear inversion approaches include the incident wave height [START_REF] Catálan | Remote sensing of breaking wave phase speeds with application to non-linear depth inversions[END_REF][START_REF] Stockdon | Estimation of wave phase speed and nearshore bathymetry from video imagery[END_REF].

The use of the dispersion relation to estimate the bathymetry is based on the choice of pairs ((c, λ) or ( f , λ)), with f constituting the frequency of waves (all the λ-dependent values vary with the change of local depths). Most satellite techniques based on wave characteristics, both optical [START_REF] Leu | Remotely sensing in detecting the water depths and bed load of shallow waters and their changes[END_REF] and radar [START_REF] Pleskachevsky | Synergy and fusion of optical and synthetic aperture radar satellite data for underwater topography estimation in coastal areas[END_REF], use a wave frequency estimated offshore (by wave buoys or model, see [START_REF] Marieu | Bathymétrie de l'embouchure du bassin d'Arcachon par fusion de données hétéroclites et reconstruction bathymétrique[END_REF] for example) and consider it to be constant when the wave approaches the coast. This dispersion relation does not take into account currents. Currents are known to influence the measurement of swell celerity, which has an impact on bathymetry estimation. In this case study, we assume that currents are weak (supported by field measurements). In a more general case study, currents need to be taken into account by using the equation described in [START_REF] Holland | Application of the linear dispersion relation with respect to depth inversion and remotely sensed imagery[END_REF]

CORRELATION-WAVELET-BATHYMETRY (CWB) METHOD (MULTI-SPECTRAL)

The present example is based on the study described by [START_REF] Poupardin | Water Depth Inversion From a Single SPOT-5 Dataset[END_REF]. The preliminary work of De Michele et al. ( 2012) has shown that it is possible to determine wave celerity directly from optical satellite imagery from the SPOT-5 sensor, thanks to the technical characteristics of the SPOT-5 satellite. A short temporal shift (2.04 s) exists between the acquisition of panchromatic and multispectral images, which makes it possible to calculate the celerity of waves between two instants by inter-band correlation. This represents an opportunity to locally identify several (c, λ) pairs in order to estimate the bathymetry using the dispersion relation.

The wave characteristics are extracted from the panchromatic and multi-spectral images of the SPOT-5 satellite by applying a wavelet analysis. It is noteworthy that the method can be generalized to any high resolution spaceborne sensor affected by small time-lags (e.g., between 0.5 s and 5 s) between bands (not only panchromatic and multi-spectral). 3. For each dominant wave n, the estimation of the M celerities c n,m is associated to the wavelengths λ n,m included the wave-packet centered on λ n with the angle t het a n .

We therefore obtain a (λ, c) cloud associated to each dominant wave.

4. Use of the point cloud, M (λ, c) pairs to determine the water depth h n by fitting the dispersion curve (by least squares minimization).

5. Selection of the final depth ĥ among the h n computed for the N dominant waves based on the spectral energy associated to the corresponding waves.

The method has been validated using a SPOT-5 satellite acquisition taken on 6 February 2010 at 10:30 (1 h and 30 min before low tide) in the area of Saint Pierre, southwest of Reunion Island (Figure 1.9). The area of Saint Pierre is characterized by a narrow continental shelf and the current is negligible at the acquisition date (between 0.1 and 0.14 m/s (Navy Coastal Ocean Model of the National Oceanic and Atmospheric Administration)). This site was chosen because high resolution data were available.

The SPOT-5 satellite is equipped with high resolution sensors (HRG1-2) that allow the acquisition of MSI (XS1-3) and panchromatic images (HMA) at resolutions of 10 and 2.5 m, respectively. The time difference between these images is 2.04 s. This configuration makes it possible to measure the displacements of pixel-sized features of the image [START_REF] De Michele | Direct measurement of ocean waves velocity field from a single SPOT-5 dataset[END_REF]. The green band (XS1) of the multispectral image has been used for the correlation processing with the panchromatic image (HMA) because its bandwidth is centered on 0.55 microns, which was closer to the panchromatic image.

The bathymetry estimated by the CWB method was obtained at a spatial resolution of 20 m × 20 m Nevertheless, the actual resolution of the bathymetry cannot be so fine since the size of the sub-images used for the inter-correlation is 320 m × 320 m offshore and 160 m × 160 m near the coast, and these sub-images overlap each other. The bathymetry estimated by the CWB method was interpolated on a grid of 80 m × 80 m (Figure 1.10.b).

The bathymetry results were compared with the in situ measurements (LiDAR data from LITTO3D products for depths shallower than 30 m and SHOM data obtained by MBES for the largest depths), also interpolated on the grid of 80 m × 80 m (Figure 1.10.a).

To illustrate the quality of the method, Figure 1.11 shows the estimated bathymetry as a function of in situ bathymetry measurements. We can observe that dispersion is low up to h i n-si t u = 25 m but increases for deeper depths. In addition, the centiles (blue crosses on Figure 1.11) show that on average the method is particularly reliable over the in situ depth range [2 m, 25 m], then, a drift appears for depths larger than h i n-si t u = 25 m, reducing its accuracy.

The CWB method uses wavelet analysis coupled with an inter-band correlation calculation to determine N point clouds in the (λ, c) space, corresponding to dominant waves. The dispersion relation is then used to determine the water depths associated with these waves. Finally, the "best" estimated water depth is selected from an analysis of the energy spectra. This allows estimation of bathymetry from optical satellite imagery to a 1. LITERATURE REVIEW moderate degree of accuracy, namely a 20-30% error for a depth range of 3 to 80 m. The results may seem limited when compared to other existing methods to map bathymetry. Nevertheless, the method represents a real opportunity to estimate bathymetry where no other more conventional methods could be applied, while further developments are required to improve the accuracy of the method.

In [START_REF] Bergsma | Radon-Augmented Sentinel-2 Satellite Imagery to Derive Wave-Patterns and Regional Bathymetry[END_REF], a Radon transform-based wave-pattern extraction and depth inversion method is presented. Wave patterns are extracted by applying a Radon transform and subsequent angle filtering to Sentinel-2 imagery, such that the wave signal contains the most-dominant wave directions. Depth is derived by exploiting the time-lag between color bands. The wave-phase per band, and after the phase shift, is obtained by applying a discrete Fourier transform to the Radon transform sinogram over a local sub-domain. In the study, depths were derived with good correlation, with good correlation of 0.82, and an RMSE of 2.58 m over the surveyed domain. These results are beyond the expectations, considering the challenging environment, including a deep-water canyon and its effect on surrounding wave patterns. In addition to the wave pattern enhancement and depth derivation, the Radon transform can be used to augment image resolution.

Twenty meter resolution image bands, from Sentinel-2, were augmented to match the 10 m resolution bands, allowing those four extra bands to be used in the depth estimation method, with time-lags ranging between 1.005 s to 2.055 s (Bergsma et al. 2019a).

SYNTHETIC APERTURE RADAR (SAR)

The computations of directional wave spectra by a Fast Fourier Transform (FFT) from the SAR images have been used to retrieve the wavelength and wave direction, and to estimate the water depth by solving the linear dispersion relation (Equation 1.6). The methodology calculates the 2D image spectrum in a cell of the image. The computation progress from open sea to shoreline in cells, which are either centered at fixed grid points [START_REF] Pereira | Estimation of the nearshore bathymetry from high temporal resolution Sentinel-1A C-band SAR data -A case study[END_REF] or along a wave ray [START_REF] Brusch | Underwater bottom topography in coastal areas from TerraSAR-X data[END_REF], which allows tracking of the change in the wave length and wave direction as waves progress to the shore. [START_REF] Brusch | Underwater bottom topography in coastal areas from TerraSAR-X data[END_REF] have attempted to establish the applicability of SAR data obtained from the commercially available TerraSAR-X data to two sites: Port Phillip in Australia and the Duck Research Pier in North Carolina, United States. The comparison of the results with local bathymetric data for depths between 2 and 40 m show a considerable dispersion, namely for shallower depths up to 10 m. [START_REF] Pleskachevsky | Synergy and fusion of optical and synthetic aperture radar satellite data for underwater topography estimation in coastal areas[END_REF] explored the synergy and fusion of optical and SAR data for bathymetric estimation (radar data from TerraSAR-X and optical data from QuickBird satellite). Water depths between 20-60 m were obtained from the SAR-based method with an accuracy the in order of 15%. [START_REF] Mishra | Estimation of Coastal Bathymetry Using RISAT-1 C-Band Microwave SAR Data[END_REF] evaluated the applicability of SAR data obtained from the RISAT-1 C-band commercial products to a coastal region near Mumbai, India, and the obtained results qualitatively agree with available bathymetric information. [START_REF] Bian | Underwater Topography Detection in Coastal Areas Using Fully Polarimetric SAR Data[END_REF] have developed a detection method based on swell patterns and the scattering mechanism using fully polarimetric SAR for the nearshore of Hainan Island, China. The comparison with navigational charts shows an average relative error of 9.73%, which improves the results obtained via single polarization SAR data. [START_REF] Pereira | Estimation of the nearshore bathymetry from high temporal resolution Sentinel-1A C-band SAR data -A case study[END_REF] have applied Sentinel-1A with C-band SAR images to retrieve the bathymetry of the Aveiro (northwestern Portugal) study site. They have investigated the repeatability of the FFT methodology in retrieving the nearshore bathymetry, considering a set of four high temporal resolution images and analyzing the sensitivity of the results to internal factors related to the estimation of the wave length, either offshore or local. Their results show that a combined solution that merges the results of all the image set slightly improves the results. The relative error of the water depth ranges between 6% and 10% for water depths between 15 and 30 m.

Figure 1.14 presents a comparison between the ensemble calculated bathymetry using the [START_REF] Pereira | Estimation of the nearshore bathymetry from high temporal resolution Sentinel-1A C-band SAR data -A case study[END_REF] method with in situ measurements. The computed values are averages for each cell and the results were obtained with the four SAR images. Figure 1.15 shows the computed versus measured dispersion for water depths between 10 and 35 m, showing large errors for higher water depths. Increasing number of sensors in orbit allow better sampling.

SUMMARY OF METHODS

Swell wave conditions are mandatory to obtain a reliable bathymetric estimation (wave period higher than 15 s).

The relative error of the water depth ranges between 6% and 10% for water depths between -15 and -30 m according with [START_REF] Pereira | Estimation of the nearshore bathymetry from high temporal resolution Sentinel-1A C-band SAR data -A case study[END_REF].

DISCUSSION

Various methods are widely used for the quantification of beach and intertidal topography and nearshore bathymetry, ranging from echosounder to LiDAR surveys, X-band radar images, photographic imagery, UAVs, and video systems. Land-based video camera systems have the ability to capture a large number of incident waves with multiple frames per second. Due to the duration of the videos, bathymetry errors are limited to tens of centimeters [START_REF] Bergsma | Video-based nearshore bathymetry estimation in macro-tidal environments[END_REF]Holman et al. 2013). The same holds true for UAV applications. Both video systems and discrete bathymetric profiles have limited longshore spatial coverage and are not able to address nearshore bathymetry dynamics over large longshore distances (i.e., tens of kilometers). The satellite images which became available in the recent years (such as Sentinel-1 and more recently Sentinel-2), characterized by higher spatial and temporal resolution, can provide an optimal solution to retrieve the bathymetry using the different approaches presented above.

BEACH TOPOGRAPHY (SUPRATIDAL)

Stereoscopy would beneficiate from improvements in spatial resolution using pairs of panchromatic images acquired at sub-meter spatial resolutions, e.g., from sensors onboard the IKONOS (0.82 m), Quickbird (0.61 m), Pleiades (0.5 m), WorldView2 (0.5 m) GeoEye-1 (0.41 m), and WorldView 3-4 (0.31 m) satellite systems, and combining the data from these different systems. Recent results obtained using some of these datasets provide very accurate results (e.g., [START_REF] Chénier | Bathymetric Photogrammetry to Update CHS Charts: Comparing Conventional 3D Manual and Automatic Approaches[END_REF]). Nevertheless, the cost of acquisition of these images is one of the major drawbacks limiting their use.

INTERTIDAL TOPOGRAPHY

When using the waterline method, the frequent sampling of the Sentinel constellation helps to overcome the limitations induced by a shortage of images. The combined use of Sentinel-1 and -2 can provide an adequate number of images that covers the whole tidal cycle in a relatively short period. Figure 1.16 shows the coverage of the tidal cycle provided by Sentinel-1 (A and B) over the Arcachon Bay for a four-month period (June-September), enhanced by Sentinel-2 (A and B) free cloud images. As can be seen in Figure 1.16, the combination of acquisitions from Sentinel-1A, -1B, and -2A, -2B provides a very dense sampling of the tidal cycle, which could not be reached before.

Regarding the monitoring of intertidal areas with satellite radar altimetry, the use of SAR mode has proven to be more accurate than conventional altimeters. It was shown in [START_REF] Salameh | Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay[END_REF] that CryoSat-2, when operating in SAR mode, provided more accurate intertidal topography profiles than the ERS-2 and ENVISAT conventional altimeters (the three sensors operate in the Ku-band). The use of radar altimetry to monitor intertidal topography can thus benefit from the SAR radar altimeters of the Sentinel-3 mission (Sentinel-3A and -3B). The Sentinel-3 Synthetic aperture Radar ALtimeter (SRAL) instrument is similar to that of CryoSat-2 (Synthetic Aperture Interferometric Radar Altimeter (SIRAL)), with an along-track resolution of about 300 m (350 m for CryoSat-2) [START_REF] Donlon | The Global Monitoring for Environment and Security (GMES) Sentinel-3 mission[END_REF]. In contrast to CryoSat-2, Sentinel-3 provides 100% SAR coverage. In addition to Sentinel-3 and in the continuity of the Jason satellite altimeter data services, another satellite radar altimetry mission is proposed, the Sentinel-6 mission, with two identical satellites (Jason-CS A and Jason-CS B) to be 1. LITERATURE REVIEW of backscattering coefficients), beach berm (with a low temporal variability with high temporal average of backscattering coefficients), and intertidal flats (with a high temporal variability). After discrimination, a final selection of intertidal pixels from the set of candidate pixels obtained by the first step is performed. This final selection is based on the following criterion: A correlation exists between the temporal evolution of the intensity of intertidal pixels and tidal stage (height), and this evolution can be modelled with the logistic function (pixels with backscattering coefficient profiles that cannot be modelled by this function are also eliminated by an automatic approach). The height of intertidal pixels is then computed by minimizing the following energy function:

E = M i =1 h i -h t + 1 a ln J i k -J -i -1 (1.7)
where M is the number of images, h i is the tide height, h t is the terrain height at pixel (x, y), J i is the intensity at pixel (x, y), and a and k are the parameters of the logistic function. The major advantage of this method is the complete automatization of the procedure, with an estimated accuracy of 24 cm (Catalão and Nico 2017).

NEARSHORE BATHYMETRY (SUBTIDAL)

The monitoring of submerged features in high energetic coastal regions requires remote sensing data with specific characteristics. Determining the swell properties in the wave field is the main feature from which a good spatial resolution remote sensing product is required, in order to be able to detect changes in the underwater topography. Repeatability is another crucial factor, since the production of merge solutions from a set of Sentinel images can improve the results. A good correlation between the bathymetric estimation from Sentinel-1 images and the observed bathymetry from in situ bathymetric measurements was observed, showing that the proposed approach can be successfully used and is relatively cost effective when compared with the previously mentioned methods.

In order to address the small-scale variability of under-water topography, a lot of studies investigate the potential of very high-resolution MS missions. However, to overcome the instrumental limitations (a low spectral resolution and SNR) inherent in these sensors, recent developments focus on the use of multi-temporal and machine learning approaches to derive bathymetric maps in shallow waters. For example, various machine learning approaches have been employed, such as using Artificial Neural Network (ANN) [START_REF] Ceyhun | Remote sensing of water depths in shallow waters via artificial neural networks[END_REF][START_REF] Gholamalifard | Remotely Sensed Empirical Modeling of Bathymetry in the Southeastern Caspian Sea[END_REF]Liu et al. 2015a), Support-Vector Machine (SVM) [START_REF] Misra | Shallow water bathymetry mapping using Support Vector Machine (SVM) technique and multispectral imagery[END_REF][START_REF] Vojinovic | A machine learning approach for estimation of shallow water depths from optical satellite images and sonar measurements[END_REF]Wang et al. 2019a), and Random Forest (RF) [START_REF] Manessa | Satellitederived bathymetry using Random Forest algorithm and Worldview-2 imagery[END_REF][START_REF] Sagawa | Satellite Derived Bathymetry Using Machine Learning and Multi-Temporal Satellite Images[END_REF]) approaches. Good accuracies can be obtained using these methods, with RMSEs that can reach 35 cm by comparing to observations with high accuracies [START_REF] Misra | Shallow water bathymetry mapping using Support Vector Machine (SVM) technique and multispectral imagery[END_REF]. Furthermore, the benefits of the free and open MS mission data policy for many segments of society is widely demonstrated [START_REF] Zhu | Benefits of the free and open Landsat data policy[END_REF]. In particular, with its decametric resolution and 5-day repetitivity, the Sentinel-2 mission is recognized as one of the most promising data sources to provide Satellite-Derived Bathymetry (SDB) at a worldwide scale. The development of algorithms and processes that use different sources of data could significantly improve the performances of SDB products. The next-generation wide swath interferometric altimetry mission for surface water and ocean topography SWOT has great potential for coastal topographic and bathymetric mapping. Various techniques can be used, such as radar altimetry using SWOT nadir altimeter, the waterline method, and the inversion from wave characteristics using the collected SAR images, and potentially the InSAR method, which may be the most problematic, however. For the waterline method, one major advantage for using SWOT is that there is no need for tide gauge records or ocean modelling because SWOT will provide sea height information at high accuracy [START_REF] Morrow | Global Observations of Fine-Scale Ocean Surface Topography With the Surface Water and Ocean Topography (SWOT) Mission[END_REF]).

CONCLUSIONS

Coastal topography and bathymetry information are key parameters for several applications. Mapping the nearshore bathymetry and the foreshore topography is considered as an "observational priority" [START_REF] Benveniste | Requirements for a Coastal Hazards Observing System[END_REF]. Their highly dynamic behavior requires frequent monitoring. Ground-, ship-, and airborne-based methods provide very accurate measurements, yet they lack the ability to provide repeated observations. Spaceborne-based methods are most suited to accomplish repeated observations while providing a large spatial coverage as well. This review focuses on spaceborne-based methods used for deriving topography and bathymetry in coastal environments. Various methods were described and illustrated, with examples including stereoscopy, the waterline method, InSAR, satellite radar altimetry, inversion from aquatic color data, and inversion from wave characteristics using MSI and SAR data. The mentioned methods provide complementary data. Their combination can generate multisource bathymetry and topography products. Here, we separated the different methods in function of the coastal features that they were used for. However, many of them can be extended to other features. For instance, stereoscopy used for mapping beach topographies may be extended to intertidal areas using images acquired at low tides. The InSAR method used for intertidal topography mapping can be extended to beaches. The different methods used for nearshore bathymetry mapping may be extended to intertidal areas using images acquired at high tides. Therefore, an assessment of the potential and limitations of these different methods over different coastal features must be made. A comparison between these methods over the same study sites is also essential to obtain a concise knowledge about the difference in their performances (accuracy). The major limitation for spaceborne-based methods is meeting user requirements for vertical accuracy and further research must pursue this direction. With the advancements of remote sensing technologies and processing algorithms, better and more accurate monitoring can be expected in the future.

MONITORING SEA LEVEL AND TOPOGRAPHY OF COASTAL LAGOONS USING SATELLITE RADAR ALTIMETRY: THE EXAMPLE OF THE ARCACHON BAY IN THE BAY OF BISCAY

Radar altimetry was initially designed to measure the marine geoid. Thanks to the improvement in the orbit determination from the meter to the centimeter level, this technique has been providing accurate measurements of the sea surface topography over the open ocean since the launch of Topex/Poseidon in 1992. In spite of a decrease in the performance over land and coastal areas, it is now commonly used over these surfaces. This study presents a semi-automatic method that allows us to discriminate between acquisitions performed at high tides and low tides. The performances of four radar altimetry missions (ERS-2, ENVISAT, SARAL, and CryoSat-2) were analyzed for the retrieval of SSH and, for the very first time, of the intertidal zone topography in a coastal lagoon. The study area is the Arcachon Bay located in the Bay of Biscay. The sea level variability of the Arcachon Bay is characterized by a standard deviation of 1.05 m for the records used in this study (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017). Sea surface heights are very well retrieved for SARAL (R∼0.99 and RMSE < 0.23 m) and CryoSat-2 (R∼0.93 and RMSE < 0.42 m) missions but also for ENVISAT (R > 0.82 but with a higher RMSE > 0.92 m). For the topography of the intertidal zone, very good estimates were also obtained using SARAL (R∼0.71) and CryoSat-2 (R∼0.79) with RMSE lower than 0.44 m for both missions.

INTRODUCTION

C OASTAL regions represent only 5% of Earth's land area, yet their societal and economical importance are larger than their surface area suggests [START_REF] Agardy | Ecosystems and human well-being: current state and trends[END_REF]. The land area within 100 km from the coast accommodates about 39% of the global population according to the CIESIN -Center for International Earth Science Information Network (2005). Coastal systems are experiencing high pressures due to population growth and the overexploitation of their resources. Anthropogenic pressures exacerbated by sea level rise and the increase of global temperature lead to a rapid and threatening environmental change of these systems, which requires effective long-term coastal management initiatives.

Common features of coastal systems are coastal lagoons, occupying 13% of coastal areas worldwide [START_REF] Barnes | Coastal lagoons (Cambridge studies in modern biology 1)[END_REF]. Coastal lagoons are defined as "inland water bodies, separated from the ocean by a barrier, connected to the ocean by one or more restricted inlets which remain open at least intermittently, and have water depth which seldom exceed a few meters" [START_REF] Kjerfve | Geographic and Hydrodynamic Characteristics of Shallow Coastal Lagoons[END_REF]. They are subject to forcings from rivers, wind stress, tides, precipitation to evaporation balance, and surface heat balance [START_REF] Kjerfve | Geographic and Hydrodynamic Characteristics of Shallow Coastal Lagoons[END_REF]). These ecosystems provide important services and societal benefits (e.g., food provision, recreational, water regulation, etc.); however their subsistence is threatened by global climate change [START_REF] Chapman | Management of coastal lagoons under climate change[END_REF]. Understanding the physical dynamics of these systems is of great importance in order to direct the planning and implementation of coastal management strategies in coastal lagoons.

In the need for a better understanding of lagoons' dynamics, satellite radar altimetry measuring the variation of the surface elevation could be a very useful tool providing key information, especially for non-monitored areas. However, using altimetry in coastal regions remains a great challenge due to numerous issues including land contamination in the footprint that impacts the radar echo (or waveform), but also the lower quality of the corrections applied to the distance between the satellite and the surface (or altimeter range) than over open ocean [START_REF] Vignudelli | Coastal altimetry[END_REF]. Despite these shortcomings, recent improvements in processing techniques (e.g., careful recovering of flagged data, applying specialized retracking, improving the correction terms) extended the capabilities of altimeters in coastal areas [START_REF] Cipollini | Monitoring Sea Level in the Coastal Zone with Satellite Altimetry and Tide Gauges[END_REF].

This study analyzes the performance of radar altimetry to monitor sea level and to provide, for the very first time, topography of the intertidal zone along the altimeter tracks in the Arcachon Bay, a coastal lagoon situated in the south-west of France. The choice of this lagoon as a case study was motivated by the coverage provided by ERS-2, ENVISAT, SARAL, and CryoSat-2 altimetry missions. Our goal is to assess the evolution of measurement accuracy at Ku-band (ERS-2, ENVISAT) and the benefits of the Ka-band (SARAL) in LRM. An assessment of instrumental performance was undertaken as well for observations made by the Ku-band satellite mission CryoSat-2, the first altimeter to operate in SAR mode.

The aim of this study is threefold: (i) to investigate the limitations and potential improvements of altimetry to monitor lagoons SSH, (ii) to test the capability of altimetry to retrieve topographic variations and (iii) to optimize (time wise and accuracy wise) the processing of altimetry data in coastal lagoons environment. Tide gauge measurements and LiDAR topography datasets were used to evaluate SSHs and topography estimation made by satellite radar altimetry.

STUDY AREA

The Arcachon Bay (44 • 40 ′ N, 1 • 10 ′ W) is a mesotidal shallow semi-confined lagoon, located in the southeast of the Bay of Biscay (Figure 2.1). The total lagoon surface (174 km 2 ) is composed of channels (57 km 2 ) that drain the intertidal area (117 km 2 ). The main channels have a maximum depth around 20 m and are extended by a complex network of secondary channels [START_REF] Deborde | Role of tidal pumping on nutrient cycling in a temperate lagoon (Arcachon Bay, France)[END_REF]. The tidal cycle is semi-diurnal with a weak diurnal inequality. The tide amplitudes vary from 0.8 to 4.6 m for neap and spring tides respectively. The Arcachon Bay connects to the Atlantic Ocean through two narrow passes of 1-1.5 km width and around 12 km long. The two passes are separated by the Arguin Bank. Important seawater exchanges, reaching up to 384.106 m 3 occur during each tidal cycle [START_REF] Plus | Hydrodynamic characterization of the Arcachon Bay, using model-derived descriptors[END_REF]). Freshwater inputs from small rivers and groundwater are coming mostly from the Eyre River and the Porges Canal, located south-east and north of the Bay respectively (see Figure 2.1). They represent more than 95% (73% and 24% respectively) of the total annual freshwater inflows [START_REF] Rimmelin | Study of Annual and Seasonal Dissolved Inorganic Nitrogen Inputs into the Arcachon Lagoon, Atlantic Coast (France)[END_REF]. The intertidal area is composed of a mix of muddy and sandy material [START_REF] Deborde | Role of tidal pumping on nutrient cycling in a temperate lagoon (Arcachon Bay, France)[END_REF]. A large zone of 70 km 2 of the mudflats in the inner lagoon is covered with Zostera noltii seagrass [START_REF] Blanchet | Structuring factors and recent changes in subtidal macrozoobenthic communities of a coastal lagoon, Arcachon Bay (France)[END_REF]). . Its accuracy is expected to be about 1 cm over ocean. Over the coastal regions, it is expected to provide measurements significantly better than those from the previous Ku band missions. Improvements come from the reduced footprint of the Ka-band (about ten times smaller in surface than it is in Ku-band) and from the higher along-track sampling rate of 40 Hz (~175 km), twice that of ENVISAT [START_REF] Verron | The SARAL/AltiKa Altimetry Satellite Mission[END_REF].

DATASETS

ALTIMETRY DATA

CRYOSAT-2

CryoSat-2 mission was launched on 8 April 2010 by ESA. This mission is dedicated mainly to polar observations. However, its acquisitions can be useful for ocean and inland monitoring as it provides a global monitoring of the Earth's surface [START_REF] Nielsen | The Performance and Potentials of the CryoSat-2 SAR and SARIn Modes for Lake Level Estimation[END_REF]). The mission's main payload consists of a radar altimeter, SIRAL, operating at Ku-band (13.575 GHz) in three different modes: LRM, SAR, and SARin mode. CryoSat-2 orbits at an altitude of 717 km, with an inclination of 92°on a non-sun-synchronous orbit with a 369-day repeat cycle. The equatorial ground-track spacing is about 7.5 km shifting every 30 days. The short inter-track distance increases the sampling over the study area during one cycle [START_REF] Wingham | CryoSat: A mission to determine the fluctuations in Earth's land and marine ice fields[END_REF]. For this study region and period, CryoSat-2 operated in SAR mode.

All altimetry data used in this study come from the Geophysical Data Records (GDR) made available by the Centre of Topography of the Oceans and the Hydrosphere (CTOH-http://ctoh.legos.obs-mip.fr/). They are sampled along the altimeter track at 18 Hz for ENVISAT, 20 Hz for ERS-2 and CryoSat-2, and 40 Hz for SARAL (high-frequency mode commonly used over land and coastal areas where the surface properties are changing more rapidly than over the open ocean).

ANCILLARY DATA

ARCACHON-EYRAC TIDE GAUGE

The Arcachon-Eyrac tide gauge is managed by the French hydrographic service (SHOM) and the Gironde sea and land state office (DDTM). It is operating since November 1967. The tide gauge (Figure 2.1) (1.163550021 • W and 44.66500092 • N) is a non-contact radar sensor providing sea level measurements at 1-min time intervals since June 2000. These data are made available by REFMAR (available online: http://refmar.shom.fr/, accessed on 10 February 2018). Altimetry and tide gauge data timeline is shown in Figure 2.2.

LIDAR-DERIVED TOPOGRAPHY OF THE INTERTIDAL ZONE

The LiDAR data is extracted from RGE ALTI ® product provided by the IGN. Arcachon Bay raw data have been acquired by airborne topographic LiDAR at low tide, on 25 June 2013, and interpolated on a regular 1 × 1 m grid for RGE ALTI ® product. The controlled altimetric precision for this data is 0.2 m. For the convenience of the study, these data have been subsampled on a 10 × 10 m grid.

METHODS

The flowchart in Figure 2.3 exhibits the different steps of the methodology. All steps are described in the corresponding sections.

ALTIMETRY DATA PROCESSING

The principle of radar altimetry is the following: the altimeter emits a radar pulse and measures the two-way travel-time from the satellite to the surface. The distance between the satellite and the Earth surface-the altimeter range (R)-is thus derived with a precision of a few centimeters. The satellite altitude (H ) referred to an ellipsoid is also accurately known from orbitography modeling. Taking into account propagation delays due to interactions of EM wave in the atmosphere and geophysical corrections, the height of the reflecting surface (h) with reference to an ellipsoid or a geoid can be estimated as [START_REF] Frappart | Satellite Altimetry: Principles and Applications in Earth Sciences[END_REF]:

h = H -R + ∆R pr opag at i on + ∆R g eoph y si c al (2.1)
where H is the height of the center of mass of the satellite above the ellipsoid, R is the nadir altimeter range from the center of mass of the satellite to the sea surface taking into account instrumental corrections, ∆R pr opag at i on and ∆R g eoph y si c al are the sums of the environmental and geophysical corrections to apply to the range and respectively given by Equations 2.2 and 2.3.

∆R pr opag at i on = ∆R i on + ∆R d r y + ∆R wet + ∆R SSB (2.2)

∆R i on is the atmospheric refraction range delay due to the free electron content associated with the dielectric properties of the ionosphere, ∆R d r y is the atmospheric refraction range delay due to the dry gas component of the troposphere, ∆R wet is the atmospheric refraction range delay due to the water vapor and the cloud liquid water content of the troposphere, ∆R SSB is the range correction due to the interaction of the electromagnetic pulse emitted by the altimeter with the scatterometers within the footprint. It is known as SSB and is the sum of the EM, skewness, and tracker biases.

∆R g eoph y si c al = ∆R ocean + ∆R sol i d E ar t h + ∆R pol e + ∆R at m (2.3) where ∆R ocean is the value of the ocean tide, ∆R sol i d E ar t h and ∆R pol e are the corrections respectively accounting for crustal vertical motions due to the solid Earth and polar tides, ∆R at m is the dynamic atmosphere correction. 2. SATELLITE RADAR ALTIMETRY Altimetry-derived heights are automatically obtained from the GDR data using the MAPS software that is commonly used for the selection of valid altimetry data and their processing over land and ocean [START_REF] Biancamaria | Satellite radar altimetry water elevations performance over a 200 m wide river: Evaluation over the Garonne River[END_REF]Frappart et al. 2015a,c). More details on MAPS can be found in [START_REF] Frappart | Preliminary Assessment of SARAL/AltiKa Observations over the Ganges-Brahmaputra and Irrawaddy Rivers[END_REF]. As the ∆R SSB values were most of the times flagged in the GDR, they were not applied for the consistency of the series of observations. ∆R SSB corresponds to cm-level correction applied to the range as it varies typically from -1% to 4% of the Significant Wave Height (SWH) (e.g., [START_REF] Gaspar | Estimating the sea state bias of the TOPEX and POSEIDON altimeters from crossover differences[END_REF]).

In the Arcachon Bay, SWH is generally lower than 0.2 m but can exceptionally reach 0.5 to 0.7 m for wind intensities greater than 20 m•s -1 [START_REF] Parisot | Modélisation des agitations dans le bassin d'Arcachon[END_REF]. ∆R ocean and ∆R at m were not applied as they also affect the measurements from the Arcachon-Eyrac tide-gauge. Due to the width of the altimeters and radiometers footprints of several kilometers and several tenths of kilometers, radar echoes are a mix of returns from ocean, intertidal zone, and from the surrounding environment (forests, cities, roads, etc.) and microwave brightness temperatures are the combination of emissions from a very inhomogeneous environment. The same set of corrections used for land hydrology will be applied in this study.

The geophysical corrections applied to the range are derived from the Global Ionospheric Maps (GIM) and Era Interim model outputs from the European Centre Medium-Range Weather Forecasts (ECMWF) for the ionosphere and the dry and wet troposphere range delays respectively. The environmental corrections are obtained from the solid Earth tide [START_REF] Cartwright | Corrected Tables of Tidal Harmonics[END_REF] and polar tide [START_REF] Wahr | Deformation induced by polar motion[END_REF] tables for SARAL, and using the IERS (International Earth Rotation and Reference Systems) convention for ENVISAT. Ranges used to derive altimeter heights were those processed with the Ice-1 retracking algorithm [START_REF] Bamber | Ice sheet altimeter processing sheme[END_REF][START_REF] Wingham | New Techniques in Satellite Altimeter Tracking Systems[END_REF]) (formulation in Appendix A) because they are present in the ERS-2, ENVISAT and SARAL GDRs and were shown to be more suitable for hydrological studies in terms of accuracy of water levels and availability of the data (e.g., Frappart et al. (2006a,b)). For CryoSat-2, altimeter heights were those processed by the Sea-Ice retracker [START_REF] Laxon | Sea ice altimeter processing scheme at the EODC[END_REF]).

LEVELING TO A COMMON DATUM

The datasets used in this study are referenced to various datums. ENVISAT and CryoSat-2 altimetry data are referenced to WGS84 ellipsoid, SARAL altimetry data to the T/P ellipsoid, the LiDAR-based topography of the intertidal zone to the French reference system NGF/IGN69, and the Arcachon-Eyrac tide-gauge to the French chart datum. A datum conversion from T/P ellipsoid to WGS84 is automatically performed for SARAL measurements using Equation 2.4 adapted from [START_REF] Jekeli | Geometric reference system in geodesy[END_REF] in the new version of MAPS implemented for this study:

∆h = a ′ 1 -e ′2 1 -e ′2 si n 2 ϕ - a 1 -e 2 1 -e 2 si n 2 ϕ (2.4)
where ∆h is the variation of height at latitude ϕ due to the change of ellipsoid from T/P to WGS84 datum, a = 6,378,137 m and e = 0.081819190842621 are the semi-major axis and the eccentricity of the WGS84 datum, a' = 6,378,136.3 m and e' = 0.081819221456 are the semi-major axis and the eccentricity of the T/P datum. For comparison purposes, they were all referenced to the Mean Sea Level (MSL). Datum conversion for all data (altimetry, topography, and tide gauge data) were made 2 65 using the French maritime altimetry references (SHOM 2016b) giving the vertical differences between the different datum (-44.8 m between WGS84 and the French chart, -1.98 m between the French chart and the French reference system, and -2.48 m between the French chart and the MSL).

EXTRACTION OF THE TOPOGRAPHY OF THE INTERTIDAL ZONE UNDER THE ALTIMETER TRACKS

For comparison purposes, the topography of the intertidal zone was extracted along the altimeter ground tracks. For each altimetry measurement, the closest topography point was selected. The maximum distance obtained between an altimetry measurement and its corresponding topography point is 10 m, which is consistent with the spatial resolution of the LiDAR-derived topography (10 m). This extraction was performed for every ERS-2, ENVISAT, SARAL, and CryoSat-2 cycle as the orbit of the satellites is not exactly repetitive and generally varies within 1 km around the nominal track (Figure 2.1).

MANUAL CLASSIFICATIONS OF ALTIMETRY MEASUREMENTS AND CYCLES

Two types of classification based on ancillary data were made. The first one consists of separating altimetry measurements between submerged and emerged measurement points. This classification was made in order to use submerged points for SSH estimation, and emerged points for topography measurements. The resulting altimetry levels were compared to Arcachon Eyrac in-situ gauge measurements and LiDAR topography data respectively. To discriminate between land and water, the topography along the altimeter tracks is filled with the water levels measured at the Arcachon-Eyrac tide gauge. For each gridpoint of the LiDAR-based topography, the gridpoint is considered submerged if the water level is greater than the topography, emerged if not (see Figures 2.6 and 2.7 in section 2.5).

The second type is a classification by cycle and it was made to separate cycles with emerged land from completely submerged cycles. The cycle is considered as an emerged cycle if more than 20% of the altimeter ground track flew over land. This classification was performed to assess the performance of the automatic classification presented in section 2.4.5.1.

AUTOMATIC SELECTIONS OF VALID ALTIMETRY MEASUREMENTS

A method to automatically select the altimetry measurements (used for SSH estimation) over emerged and submerged areas was tested. It is composed of the following steps.

CLASSIFICATION OF CYCLES BETWEEN SUBMERGED AND EMERGED CYCLES

This first step discriminates submerged from emerged cycles using intrinsic altimetry parameters in order to be completely independent of in-situ data. The rationale behind this step is the use of different selection criteria for submerged and emerged cycles. The classification was made using the unsupervised k-means clustering algorithm [START_REF] Hartigan | A K-Means Clustering Algorithm[END_REF]. The number of clusters (k) was chosen to be two for submerged and emerged classes and the distance measure technique used is the cityblock (Manhattan) technique [START_REF] Craw | Manhattan Distance[END_REF]. In contrast to the Euclidean distance (straight line distance 66

2. SATELLITE RADAR ALTIMETRY between two points in Euclidean space), the cityblock distance is calculated as the distance in x plus the distance in y (in 2D). The backscattering coefficient and the peakiness (the average of these parameters per cycle) are the two parameters used to perform the clustering technique (peakiness formulation can be found in Appendix B). Before data clustering, the latter parameters were normalized and centered in order to unify their influence on distance. The use of these two parameters is based on a priori knowledge that they present significant descrepancies between water-dominated footprints and water-land-mixed footprints.

GROUPING OF CYCLE'S MEASUREMENTS INTO FOUR EQUAL PARTS

In this step, the altimetry measurements made during a given cycle were separated into four equally-sized groups. The four groups were separated by the following scores: Quartile 0 (the minimum), Quartile 1 (larger than 25% of the data points), Quartile 2 (the median), Quartile 3 (bigger than 75% of the data points), and Quartile 4 (the maximum). For each group, the standard deviation is computed to assess its dispersion.

DATA AUTOMATIC SELECTIONS

For cycles classified as submerged cycles, the groups with the least standard deviation (least dispersion) are preserved. For cycles classified as emerged cycles, the first groups with the lowest 25% of values (values between Quartile 0 and Quartile 1) are preserved because these groups are the only groups able to reach the water when land emerges.

The results of the two types of selections are compared in section 2.5.2.

PASSING-BABLOK REGRESSION FOR METHOD COMPARISONS

Passing-Bablok is the regression method used to account for agreement and systematic bias between two methods (altimetry/tide-gauges or altimetry/LiDAR). We opted for Passing-Bablok method instead of ordinary linear regression because it is not sensitive to the outliers or the distribution of errors and because the independent variable (water level from tide gauge records or bathymetry from LiDAR) is not free of error. This robust, non-parametric method consists of fitting a line describing the relationship between the two variables (X and Y) and testing whether the slope is 1 and the intercept is 0. In-depth details on the method can be found in [START_REF] Passing | A new biometrical procedure for testing the equality of measurements from two different analytical methods[END_REF]. The results are presented as a scatter plot between X (method 1) and Y (method 2), a regression line, and a linear regression equation where the slope and the intercept represent proportional and constant systematic bias respectively. A statistical test of the assumption of linearity is performed using cumulative sum linearity test. Non-linear samples are not suitable for concluding on method agreement. Furthermore, a 95% CI is also computed for the slope and the intercept to test the hypothesis that the slope is equal to 1 or the intercept is equal to 0. These hypotheses are accepted if 1 corresponds to the slope's 95% CI (if not, there is a proportional difference between the two methods) and if 0 corresponds to the intercept's 95% CI (if not, there is a constant difference or bias between the two methods).

ABSOLUTE CALIBRATION OF ALTIMETRY MISSIONS OVER THE INTERTIDAL ZONE

Comparisons between altimetry-based and in situ SSH from tide gauge were performed. They require simultaneous in situ and altimetry measurements in the same terrestrial 2.5. RESULTS

2

67 reference frame at the exact same location or comparison point (e.g., [START_REF] Cancet | Regional in situ validation of satellite altimeters: Calibration and cross-calibration results at the Corsican sites[END_REF]).

The absolute altimeter bias (Bi as al t i met er ) is estimated as follows [START_REF] Ménard | Calibration of the TOPEX/POSEIDON altimeters at Lampedusa: Additional results at Harvest[END_REF]):

Bi as al t i met er =< h al t i met er -h i nsi t u > (2.5)

where h al t i met er and h i nsi t u are the height of the reflecting surface estimated from altimeter and in situ measurements respectively. In this study, an absolute calibration is performed for estimating the bias of ERS-2, ENVISAT, SARAL and CryoSat-2 for sea level measurements and topography of the intertidal zone in the Arcachon Bay.

RESULTS

Depending on their overflight time, radar altimetry missions acquired observations of the Arcachon Bay all over the tidal cycle. During low tide, they provide observations of the surface topography of the intertidal zone whereas, at high tides, they monitor the sea surface height. These changes in the nature of the reflecting surface, from wet sand and mud to sea water, modify the radar echo acquired by the altimeter. LiDAR-based topography profiles were extracted along the altimetry ground tracks in the intertidal zone of the Arcachon Bay. They were filled with water using the record from Arcachon-Eyrac tide-gauge corresponding to the altimeter overflights. They were compared to the along track profiles of altimeter height, backscattering coefficients and waveform peakiness (not available for ERS-2 in the CTOH GDR and only available at 1 Hz for ENVISAT) estimated using the Ice-1 retracking algorithm for ERS-2, ENVISAT and SARAL and the SeaIce retracking algorithm for CryoSat-2 (see [START_REF] Bamber | Ice sheet altimeter processing sheme[END_REF]) for details about the computation of these two latter parameters that are available in the altimeter GDRs). Examples for high and low tides using SARAL and CryoSat-2 data are respectively presented in Figures 2.4 ). SSH estimated using altimetry data was given by the median of submerged points' altimeter heights. For high and low tides, SARAL and CryoSat-2 missions show relatively good correspondence with in situ measurements while ERS-2 and ENVISAT show low accuracy, especially at low tides. ERS-2 is unable to accurately retrieve topography variations due to both, the coarse resolution of its footprint and changes in the range resolution between ocean (bandwidth of 300 MHz) and ice modes (bandwidth of 20 MHz). As for ENVISAT, despite the important bias obtained, altimetry measurements follow the topography variations and give an acceptable correlation coefficient as a result (see sections 2.5.2 and 2.5.3). We observe a significant increase in the backscattering coefficients and waveform peakiness values between high and low tide (Figure 2.4.c,d,and Figure 2.5.c,d). This is due to the contribution of the emerging land to the received signal. A slight variation of these parameters is observed as well at the extreme sides for high tides where land and water fall together in the altimeter footprint.

2.5. RESULTS 2 69

AUTO-CLASSIFICATION USING THE K-MEANS ALGORITHM

Using the k-means algorithm, the altimetry cycles were classified between emerged and submerged cycles. The evaluation of the auto-classification was made using the classification based on in-situ data as explained in section 2.4.4. It should be noted that the clustering technique was made using two parameters (the backscattering coefficient and peakiness) for SARAL and CryoSat-2 (Figure 2.6), and using only the backscattering coefficient for ERS-2 and ENVISAT. SARAL showed the best classification results with 100% accordance with manual classification. A good consistency was shown also by CryoSat-2 and ENVISAT with ~80% accordance and ERS-2 with 82%.

WATER LEVELS COMPARISON

For the selections made using MAPS, SSH estimation was given by the median of submerged altimetry measurements made during one crossing (cycle). An automatic selection of altimetry data was performed in addition to the manually refined data selections in MAPS. The automatic technique uses the less dispersive quartile of measurements in each cycle for cycles classified as submerged by the clustering technique, and the lowest quartiles for cycles classified as emerged. The SSH was given by the median of the chosen quartile without eliminating measurement points classified as emerged by the classification based on ancillary data. Figure 2.7 presents the comparisons made between SSHs acquired by altimetry and tide gauge measurements for MAPS manual selections (left) and for automatic selections (right) for ERS-2 (a and b), ENVISAT (c and d), SARAL (e and f), and CryoSat-2 (g and h). Linearity exists between altimetry and the tide gauge measurements, for ERS-2, SARAL, and CryoSat-2 data for the two types of selections and for the automatic selections made for ENVISAT (Table 2.2).

ERS-2 showed the most unsatisfactory results with slopes lower than 0.64 and intercepts higher than 1 (Table 2.2). The results obtained by the Passing-Bablok method could not be interpreted for ENVISAT MAPS selections since no linear relationship exists with the tide gauge measurements (a break is observed in the slope at 0 m (Figure 2.7.c)). Low accuracy for MAPS selections made for ENVISAT could be inferred from the RMSE and the mean bias obtained (1.04 m and 0.88 m respectively). The automatic selections significantly improved the estimation of SSH obtained using ENVISAT data and rendered the linearity test positive. The slopes given by ENVISAT increased from 0.60 to 0.74 and were accompanied by an improvement of R (from 0.82 to 0.86) and RMSE that remains important (RMSE~0.92 m) (Table 2.2). As explained in section 2.4.6, the method does not show proportional or constant biases if 1 belongs to the slope CI (slope(LB) < 1 < slope(UB)) and 0 belongs to the intercept CI (intercept (LB) < 0 < intercept (UB)) respectively. For SARAL, a better result is obtained using the automatic selection showing only constant bias with no proportional bias (the confidence interval of the slope contains the value 1). Slight proportional and constant biases are obtained for MAPS selections. MAPS selections present better results for CryoSat-2 that shows slight constant biases with no proportional biases for the two types of selections. For topography comparisons all measurements from every cycle were used along with the corresponding LiDAR topography measurements. Table 2.3 lists all regression models obtained. Linearity was rejected only for ENVISAT data. Therefore, the slope and the intercept obtained for ENVISAT could not be interpreted. Good comparison results are obtained for SARAL giving a slope of 1.06 and an intercept at 0.01 with no proportional or constant bias observed for topography monitoring. CryoSat-2 provides as well acceptable results with slight systematic and proportional biases. Showing a positive linearity test, ERS-2 slope and intercept showed large differences from 1 and 0. 1.93 0.90 0.17 0.25 1 Lower Bound. 2 Upper Bound. 3 1 for accepted linearity and 0 for refused linearity.

TOPOGRAPHY COMPARISON

DISCUSSION

For each altimetry cycle of ERS-2, ENVISAT, SARAL, and CryoSat-2, the water level of the Arcachon Bay was estimated by computing the median of submerged points, and compared to tide gauge measurements carried out at the same time (in a 5 min interval). Altimetry measurements above emerged points were considered as topography measurements and were compared to the nearest LiDAR bathymetry points. Over coastal areas, the altimeter footprint is contaminated by signals from different surface types which reduce the accuracy of the measurements [START_REF] Vignudelli | Coastal altimetry[END_REF]. For water levels estimation, SARAL operating at Ka-band frequency shows significant improvement in the measurement accuracy (vertical resolution) comparing to the ERS-2 and ENVISAT Ku-band altimeters, allowing better observations in coastal areas like lagoons [START_REF] Bonnefond | The Benefits of the Ka-Band as Evidenced from the SARAL/AltiKa Altimetric Mission: Quality Assessment and Unique Characteristics of AltiKa Data[END_REF][START_REF] Vu | Multi-Satellite Altimeter Validation along the French Atlantic Coast in the Southern Bay of Biscay from ERS-2 to SARAL[END_REF]. This improvement comes from the reduced footprint area (~6 km) of SARAL which reduces the impact of land on SARAL waveforms. It should be noted that the use of Ka-band is not the only factor that governs the size of the footprint, the larger bandwidth (~480 MHz) used by SARAL has an impact on the footprint size as well. According to [START_REF] Vignudelli | Coastal altimetry[END_REF], SARAL AltiKa's footprint is ~0.8 times smaller than a Ku-band altimeter for a given bandwidth. CryoSat-2 shows as well major improvements in the accuracy for water levels estimation comparing to ERS-2 and ENVISAT. Operating in the same band (Ku) as the latter missions, the better performance of CryoSat-2 comes from the use of the SAR mode of acquisition. The processing of CryoSat-2 SAR data is based on the delay Doppler technique that reduces the footprint size in the along-track direction which makes CryoSat-2 more suitable for coastal monitoring. The lower consistency with in-situ measurements was obtained using data from LRM missions operating at Ku-band (ERS-2 and ENVISAT) especially at low tides where its spatial resolution could not resolve the complex water-land mixture of the bay. Figure 2.7 shows that above mean sea level ENVISAT was capable of estimating the water level of the bay with a relatively low bias.

The results also show a great potential for radar altimetry to retrieve the topographic variation of the intertidal zone. SARAL and CryoSat-2 show a large consistency with the LiDAR measurements. ENVISAT was able to follow the variation of the intertidal zone bathymetry producing a correlation coefficient (R) of 0.57 but with an important bias (due 74

2. SATELLITE RADAR ALTIMETRY to the large footprint of ENVISAT). CryoSat-2 was the only mission that flew over the "ile aux oiseaux" sandbank (Figure 2.1.b). Some altimetry measurements made by CryoSat-2 underestimated the elevation of topography in this area. It is very likely that the cause of the high discrepancy is due to the penetration of the electromagnetic wave in the dry soil (long time after high water). We calculated the maximum penetration depth that corresponds to the electromagnetic wave frequency and the dielectric properties of the sand (Appendix D). The differences obtained between the underestimated measurements made by altimetry and the corresponding LiDAR measurements are lower than the maximum penetration depth of 1.35 m which is consistent with our hypothesis. We eliminated the underestimated points from CryoSat-2 measurements and we observed an improvement in terms of slope (from 0.96 to 0.98), intercept (from -0.09 to -0.08), and R (from 0.79 to 0.89).

In this study, an automatic classification of cycles was performed to discriminate between submerged and emerged cycles. An automatic process was also envisaged to classify each measurement point, using the backscattering coefficient that tends to increase for land-dominated areas. However, an important limitation was encountered during the automating process. During low tides, some altimetry points above water showed as well high backscattering coefficients, which complicated the separation of emerged and submerged points using the backscattering coefficient parameter. The high values of the backscattering coefficient obtained for water at low tides is most likely due to smoother water surfaces in the channels than in the bay, caused by the reduced wave activity. This reduced roughness increases the specular reflection and thus the power received by the sensor (the backscattering coefficient). An example is shown in Figure 2.9 (left) for the cycle 20 of SARAL. The backscattering coefficient of water in large channels (zone 5 and zone 3) is lower than the backscattering coefficient of water in narrow channels (zone 4 and zone 2) showing values that match land-dominated areas (zone 1).

Figure 2.9, Figure 2.10, Figure 2.11, and Figure 2.12 show the spatial variation of the backscattering coefficient for a given cycle and the waveforms corresponding to different points in the bay. Figure 2.10 and Figure 2.12 correspond to cycles crossing the bay at high tides for SARAL and CryoSat-2 respectively (same type of figures is available in Appendix C for ENVISAT (Figures C.3 and C.4)). For SARAL (Figure 2.10) and CryoSat-2 (Figure 2.12), we observe at the middle of the bay (zone 3 and zone 4) that the waveforms look like typical ocean waveforms. However, the waveforms at the edges of the bay (zones 1, 2, 5, and 6 for SARAL and zones 1 and 6 for CryoSat-2) show a sharp rise. It is not the case for ENVISAT at high tides (Figure C.3). The waveforms of ENVISAT in the middle of the bay (zone 3 and zone 4) differ from the typical ocean waveforms due to the larger footprint of ENVISAT. It should be noted that the waveforms of CryoSat-2 at high tides maintain typical ocean waveforms closer to the coastline than SARAL due to the SAR mode of CryoSat-2 that increases the resolution in the along-track direction of the satellite. Another consequence of the SAR mode is the highly energetic waveforms.

Figure 2.9 and 2.11 correspond to cycles crossing the bay at low tides for SARAL and CryoSat-2 respectively. At low tides, SARAL (Figure 2.9) shows peak shaped waveforms (relatively similar to ENVISAT waveforms at low tides (Figure C.4)) while CryoSat-2 (Figure 2.11) shows mixed shaped waveforms. Typical ocean waveforms were not observed for low tides even in areas dominated by water. The use of satellite radar altimetry to monitor SSH and topography has the potential to be applied in any tidal zone especially in remote areas where no tide gauge record or topography data are available. Radar altimetry parameters (SSH, σ 0 , and peakiness) can be used to discriminate between high (parameter values almost constant for a given cycle) and low (larger variability) tides. Until now, only large submerged and emerged areas can be discriminated during low tides. Analyses of the radar echoes (waveforms) can provide valuable information to improve the characterization of the nature of the surface (emerged or submerged).

The new-era coastal altimetry satellites contribute to the advancement of coastal ocean observing systems [START_REF] Liu | Coastal Ocean Observing Systems[END_REF]. The launch of the SWOT mission in 2021 will offer new opportunities for monitoring of coastal lagoons topography and changes in time thanks to (i) the acquisitions of elevation along two swaths of 60 km of width that will provide 2D maps, (ii) its better vertical accuracy, (iii) its shorter repeat period, (iv) the use of the Kaband that has a smaller penetration depth.

CONCLUSIONS

This study is the first to demonstrate the capabilities of altimetry to retrieve the SSH and the topography of the intertidal zone in a coastal lagoon. Data from four altimetry missions were analyzed over Arcachon's Bay coastal lagoon located in the South-East of the Bay of Biscay: (i) ERS-2, (ii) ENVISAT, (iii) SARAL, and (iv) CryoSat-2. The two first missions were operating at Ku-band in low resolution mode whereas SARAL is the first mission to operate in Ka-band in LRM and CryoSat-2 is the first mission to operate at Ku-band in SAR mode. Altimetry measurements were validated using tide gauge and LiDAR bathymetry datasets.

Considering data from the classical LRM missions operating at Ku-band (ERS-2 and ENVISAT), SSH and topography retrievals from ERS-2 are inaccurate whereas ENVISAT measurements provide better results for SSH (R > 0.82 and RMSE < 1.04 m) than for topography (R~0.54 and RMSE~0.95 m). However, SARAL and CryoSat-2 showed very satisfying correspondence with ancillary data with correlation coefficient (R) higher than 0.93 and RMSE lower than 0.42 m for SSH estimations and R higher than 0.71 for topography with RMSE lower than 0.44 m. It should be noted that the standard deviation of the whole sea level records is 1.05 m.

Furthermore, a successful and simple statistical method (based on a combination of a non-supervised clustering technique and grouping altimetry data into quartiles) was introduced in order to select valid altimetry data. The purpose of this method is to accelerate the processing phase of altimetry data and to optimize the accuracy of SSH estimation. This selection method showed very satisfying results with similar accuracy performance as the manual selections made using MAPS software.

The most important limitation lies in the large footprint of altimeters. This coarse resolution prevented us from automatically discriminating land from water using intrinsic altimetry parameters like the backscattering coefficient or waveforms peakiness. However, we were able to discriminate acquisitions made during low tides from the ones made during high tides, because at the scale of the bay good contrast between low and high tides was obtained by the backscattering coefficient and the peakiness.

While altimetry was able to monitor the topography of the bay, caution must be taken when using altimetry data to retrieve topographic variations in similar environments. Dry sandy features are most likely problematic due to the important penetration depth of 2. SATELLITE RADAR ALTIMETRY electromagnetic waves in such mediums. It is recommended to use this approach in areas exposed frequently to water.

INTERTIDAL TOPOGRAPHY MAPPING USING THE WATERLINE METHOD FROM

SENTINEL-1 & -2 IMAGES: THE EXAMPLES OF ARCACHON AND VEYS BAYS IN FRANCE

Intertidal flats lying as a buffer zone between land and sea provide critical services including protection against storm surges and coastal flooding. These environments are characterized by a continuous redistribution of sediment and changes in topography. Sea level rise, anthropogenic pressures, and their related stressors have a considerable impact on these areas and are expected to put them under more stress; hence the increased need for frequent and updated topography maps. Comparing to traditional surveying approaches, spaceborne remote sensing is able to provide topography maps more frequently with a lower cost and a higher coverage. The latter is currently considered as an established tool for measuring intertidal topography. In this study, an improved approach of the waterline method was developed to derive intertidal Digital Elevation Models (DEMs).

The changes include a faster, more efficient and quasi-automatic detection and post-processing of waterlines. The edge detection technique consists in combining a k-means based segmentation and an active contouring procedure. This method was designed to generate closed contours in order to enable an automatization of the post-processing of the extracted waterlines. The waterlines were extracted from Sentinel-1 and Sentinel-2 images for two bays located on the French Coast: the Arcachon lagoon and the Bay of Veys. DEMs were generated for the Arcachon Bay between 2015 and 2018, and for the Bay of Veys between 2016 and 2018 using satellite acquisitions made during summer (low storm activity period). The comparison of the generated DEMs with LiDAR observations showed an error of about 19 to 25 cm. This study also demonstrated that the waterline method applied to Sentinel images is suitable for monitoring the morpho-sedimentary evolution in intertidal areas. By comparing the DEMs generated between 2016 and 2018, the Arcachon Bay and the Bay of Veys experienced net volume losses of 1.12 × 10 6 m 3 and 0.70 × 10 6 m 3 respectively. The generated DEMs provide useful and needed information for several scientific applications (e.g., sediment balance, hydrodynamic modelling), but also for authorities and stakeholders for coastal management and implementation of ecosystem protection policies.

INTRODUCTION

I NTERTIDAL flats are gently sloped areas located between the high and low water spring tide marks, inundated and exposed periodically due to the ebb and flood tides. These widely spread coastal ecosystems occur primarily in tide-dominated environments and sheltered coastal embayments [START_REF] Gao | Geomorphology and sedimentology of tidal flats[END_REF]. They are highly productive and diverse areas [START_REF] Levin | The Function of Marine Critical Transition Zones and the Importance of Sediment Biodiversity[END_REF]) that provide habitat for a large community of migratory shorebirds [START_REF] Agardy | Ecosystems and human well-being: current state and trends[END_REF], supports millions of people worldwide, stabilize the coastline, defend from storm surges, and provide protection against coastal flooding (Millennium Ecosystem Assessment 2005;Nicholls et al. 2007). Human interventions (e.g., coastal development, land claim, dredging, upstream dams, etc.) accompanied by sea level rise due to climate change have put these regions under high pressure. A recent study conducted by [START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF] showed that intertidal flats have declined by 16% between 1984 and 2016. A continuous monitoring of intertidal flats, especially of the intertidal topography, is thus of high ecological, economical, and societal importance. An accurate mapping of the topography in intertidal flats is fundamental for coastal flood forecasting, coastal defense, identification of shoreline erosion or accretion, navigation, fishing, economic exploitation, and tourism [START_REF] Benveniste | Requirements for a Coastal Hazards Observing System[END_REF][START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF][START_REF] Mason | Remote sensing of intertidal morphological change in Morecambe Bay, U.K., between 1991 and 2007[END_REF].

Intertidal topography is also an essential parameter for shallow waters hydrodynamic modelling (many forcing terms in the hydrodynamic equation of motion are depth dependent, e.g. the resistance term and the wind stress) and unreliable intertidal topographies limit the accuracy of such models [START_REF] Bergsma | Video-based depth inversion techniques, a method comparison with synthetic cases[END_REF][START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF].

Nowadays, a wide variety of topography mapping techniques have been developed. Conventional techniques such as ground-based and airborne (e.g. stereo-photogrammetry, LiDAR, and InSAR) surveying provide very accurate measurements of the surface elevation. Ground-based techniques are usually dedicated to small study sites as they are constrained by logistical difficulties and high costs. Airborne techniques can cover larger areas and in short time while covering inaccessible and hazardous regions. However, the latter techniques are also expensive and unable to map the full tidal range in relatively large areas [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF]. Spaceborne-based techniques provide a viable alternative for intertidal topography mapping due to their synoptic nature. The continuous monitoring that they provide enables a regular and frequent updating of the topographic maps in these highly dynamic environments.

A variety of spaceborne-based techniques for intertidal topographic mapping and DEM generation exist now [START_REF] Salameh | Monitoring Beach Topography and Nearshore Bathymetry Using Spaceborne Remote Sensing: A Review[END_REF]. The Interferometric Synthetic Aperture Radar (InSAR) technique traditionally used for inland DEM generation has been proven to be reliable for DEM generation over intertidal areas by using images acquired at low tides. InSAR is a method with high potential for intertidal areas, but for multi-pass interferometry systems (e.g. Sentinel-1), the temporal lag between the two acquisitions with different angle is still an issue (i.e., low coherence due to long baseline, decorrelation caused by incidence angles impacting the backscattering, and changes in surface roughness from a tidal cycle to another [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF]). This limits the use of this method to the single-pass interferometry systems for which there is no temporal decorrelation [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF]. [START_REF] Catalão | Multitemporal Backscattering Logistic Analysis for Intertidal Bathymetry[END_REF] proposed a pixel-based algorithm to estimate intertidal topography based on the correlation between the temporal variation of pixels' backscattering coefficients and the tide height. Salameh 2018) showed that satellite radar altimetry is another approach that can be used to derive topographic profiles of intertidal areas along the altimeter ground tracks. The major drawback of this technique is the inability to produce gridded-DEMs as the ground tracks coverage is not dense enough. The most common technique used for DEM generation of intertidal flats is the waterline method introduced by [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]. This method uses a time series of remotely sensed images acquired at different tidal stages. The waterline (shoreline) for each image is extracted and height is assigned to it using in situ or modelled sea level information. Then the waterlines are assembled and interpolated to produce a gridded-DEM. For research purposes, the waterline method proved to be one of the best methods that provides a good trade-off between technical performance (accuracy) and cost-effectiveness [START_REF] Mason | Beach topography mapping -a comparison of techniques[END_REF].

The waterline method was used to generate intertidal DEMs in several regions. First attempts were made over the English Coasts at the Humber/Wash area [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF], the Morecambe Bay [START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF], and the Holderness coast [START_REF] Lohani | Construction of a Digital Elevation Model of the Holderness Coast using the waterline method and Airborne Thematic Mapper data[END_REF]. It was then applied for the intertidal flats of the Wadden Sea in northern Europe [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF][START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF][START_REF] Niedermeier | Topography and morphodynamics in the German Bight using SAR and optical remote sensing data[END_REF], the intertidal flats of the Gomso Bay in Korea [START_REF] Ryu | Detecting the intertidal morphologic change using satellite data[END_REF], the Macouria Amazon-derived mud bank in French Guiana [START_REF] Anthony | Nearshore intertidal topography and topographic-forcing mechanisms of an Amazon-derived mud bank in French Guiana[END_REF], the Yangtze Delta [START_REF] Zhao | A simple waterline approach for tidelands using multitemporal satellite images: A case study in the Yangtze Delta[END_REF], and the Sea Radial Sand Ridges in the Southern Yellow Sea [START_REF] Kang | Topographic mapping on large-scale tidal flats with an iterative approach on the waterline method[END_REF][START_REF] Liu | Quantitative Analysis of the Waterline Method for Topographical Mapping of Tidal Flats: A Case Study in the Dongsha Sandbank, China[END_REF][START_REF] Wang | Evolution of the topography of tidal flats and sandbanks along the Jiangsu coast from 1973 to 2016 observed from satellites[END_REF]). The waterline method was also used to generate time series of DEMs to study the morphological evolution and the development of intertidal flats [START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF][START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF][START_REF] Mason | Remote sensing of intertidal morphological change in Morecambe Bay, U.K., between 1991 and 2007[END_REF][START_REF] Ryu | Detecting the intertidal morphologic change using satellite data[END_REF][START_REF] Wang | Evolution of the topography of tidal flats and sandbanks along the Jiangsu coast from 1973 to 2016 observed from satellites[END_REF][START_REF] Xu | Estimation of seasonal topographic variation in tidal flats using waterline method: A case study in Gomso and Hampyeong Bay, South Korea[END_REF][START_REF] Zhao | A simple waterline approach for tidelands using multitemporal satellite images: A case study in the Yangtze Delta[END_REF].

Images acquired from radar (SAR) and optical systems can be used by the waterline method. The major difference in terms of methodology is the edge detection techniques that can be applied to extract waterlines. SAR data are more suited for this method due to their ability to acquire images in all weather conditions, including in presence of clouds, and during day and night [START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF]) which enables a better sampling of the tidal range. However, the edge detection (waterline extraction) for the SAR images are more problematic due to the speckle noise [START_REF] Niedermeier | Topography and morphodynamics in the German Bight using SAR and optical remote sensing data[END_REF]. For SAR images, several approaches were implemented to extract waterlines such as the multi-scale edge detection algorithm proposed by [START_REF] Mason | Accurate and efficient determination of the shoreline in ERS-1 SAR images[END_REF] using the Touzi edge operator [START_REF] Touzi | A Statistical and Geometrical Edge Detector for SAR Images[END_REF] combined with an active contouring model, wavelet-based edge detection methods adapted to SAR images [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF][START_REF] Niedermeier | Detection of Coastlines in SAR Images using Wavelet Methods[END_REF], region based level-sets [START_REF] Silveira | Separation Between Water and Land in SAR Images Using Region-Based Level Sets[END_REF], and k-means clustering [START_REF] Soares | Using K-Means and morphological segmentation for intertidal flats recognition[END_REF].

Previous studies used remote sensing images acquired by a wide variety of SAR (e.g., ERS-1/2, RadarSat-1/2, ENVISAT, JERS-1, COSMO-SkyMed, TerraSAR-X) and optical sensors (e.g., Landsat, IRS, SPOT, IKONOS, Quickbird, MOS-1). The main difficulty was to obtain a sufficient number of images during a short time period (to avoid morphological changes) that covers the whole tidal range. The solution was either to increase the period of acquisition taking the risk of major morphological evolution or to use a small number of images. Nowadays, owing to the deployment of the ESA's Sentinel-1 SAR constellation (Sentinel-1A and Sentinel-1B) launched in April 2014, the revisit time over the same area can reach 2 days. Therefore, the acquisition period needed for sampling the whole tidal range can be highly reduced. In this study, we used Sentinel-1 images to generate digital elevation models using the waterline method. We used as well cloud-free Sentinel-2 MSI 3. THE WATERLINE METHOD Images to improve the sampling of the tidal range.

As mentioned above, this method consists in three major steps: waterline edge detection, waterlines levelling, and interpolation. Those three steps can be performed by following different approaches. Previous studies used and adapted different approaches according to their needs and to the studied sites. In the present study, we aim to achieve the following objectives: (i) generate intertidal DEMs using the waterline method for two intertidal bays located on the French Coast: the Arcachon lagoon and the Bay of Veys; (ii) identify the best approaches to use for the three major steps of the method for the latter study sites; (iii) develop a unique edge detection method to extract waterlines from both Sentinel-1 (SAR) and Sentinel-2 (MSI) images; (iv) estimate the accuracy of the generated DEMs using Sentinels data over the study sites; (v) and determine the morphological changes and the associated sediment balance. It should be noted that the choice of the two study sites was motivated by the contrasted characteristics they present in order to prove the applicability of the presented methodologies in different intertidal environments. The Arcachon Bay is a sheltered lagoon with extensive muddy flats where tides enter the system through two tidal inlets while the Bay of Veys is an exposed embayment with a mix of muddy and sandy material, with abundant presence of sand.

STUDY SITES

ARCACHON BAY

The Arcachon Bay is a shallow, mesotidal coastal lagoon located in the southeastern part of the Bay of Biscay and connects to it through two narrow passes separated by the Arguin Bank (Figure 3.1.c). The tides in the bay are semi-diurnal with a weak diurnal inequality and the water exchange with the Bay of Biscay can reach up to about 384 km 3 during each tidal cycle [START_REF] Plus | Hydrodynamic characterization of the Arcachon Bay, using model-derived descriptors[END_REF]. Freshwater enters the bay from rivers, canals, and groundwater. The major two tributaries are the Eyre River and the Porges Canal contributing about 73% and 24% of the total annual freshwater inputs, respectively [START_REF] Plus | Hydrodynamic characterization of the Arcachon Bay, using model-derived descriptors[END_REF]. The lagoon has a total surface area of 180 km 2 with 115 km 2 corresponding to intertidal flats. The intertidal flats are drained by tidal creeks and tidal channels with a maximum depth around 20 m [START_REF] Deborde | Role of tidal pumping on nutrient cycling in a temperate lagoon (Arcachon Bay, France)[END_REF]. They are composed of a mix of muddy and sandy material, and a large area (70 km 2 ) of the flats are vegetated by Zostera noltii seagrass [START_REF] Blanchet | Structuring factors and recent changes in subtidal macrozoobenthic communities of a coastal lagoon, Arcachon Bay (France)[END_REF][START_REF] Proença | Potential of High-Resolution Pléiades Imagery to Monitor Salt Marsh Evolution After Spartina Invasion[END_REF].

BAY OF VEYS

The Bay of Veys is a shallow estuarine embayment located in the southern shore of the English Channel, in the western part of the Bay of Seine (Figure 3.1.b). The bay receives freshwater input from several coastal streams and four main rivers: the Aure, the Douve, the Taute, and the Vire, draining a catchment area of 3500 km 2 [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF][START_REF] Lafforgue | Modelling of enterobacterial loads to the Baie des Veys (Normandy, France)[END_REF]). The Vire is the largest river flowing directly into the bay and provides 40% of the freshwater input [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF]). It should be noted that the main four rivers flow into the bay through sluice gates that open at ebb tide and close at flood tide [START_REF] Lafforgue | Modelling of enterobacterial loads to the Baie des Veys (Normandy, France)[END_REF]). The bay is located in a semidiurnal macrotidal environment with a tidal range that reaches 8 m at spring tides [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF]. At low tides, the surface of the uncovered intertidal flats is about 37 km 2 [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF][START_REF] Timsit | Évolution du macrozoobenthos intertidal de la baie des Veys de 1985 à 2000[END_REF]). These flats extend to 5 km offshore. The lower part is devoid of vegetation and covered by 3.3. DATASETS 3 83 muddy and sandy sediments, while the upper part near the land is colonized by halophytic species dominated by Spartina anglica [START_REF] Deroin | Combining ALOS and ERS-2 SAR data for the characterization of tidal flats. Case study from the Baie des Veys, Normandy, France[END_REF][START_REF] Timsit | Évolution du macrozoobenthos intertidal de la baie des Veys de 1985 à 2000[END_REF]). The bay is surrounded by polders protected by dikes [START_REF] Deroin | Combining ALOS and ERS-2 SAR data for the characterization of tidal flats. Case study from the Baie des Veys, Normandy, France[END_REF]. The intertidal area can be separated into three major parts: the central part bounded by Carentan Channel (the Douve and the Taute confluence) from the west and by Isigny-Sur-Mer Channel (the Vire and the Aure confluence) from the east, and the eastern and western flanks.

DATASETS

Three different types of data were used in this study. Satellite images were used to extract the waterlines, tide gauge and ocean-circulation model output to determine the height (elevation) of the extracted waterlines, and LiDAR-derived DEMs to validate the DEMs generated by the waterline method. All types of data used and generated in this study are referenced or converted to the French Reference System NGF/IGN69.

SENTINEL-1 AND SENTINEL-2 SATELLITE IMAGES

ESA is currently putting into orbit the Sentinel satellite series as part of the Copernicus program (formerly known as the Global Monitoring for Environment and Security (GMES) program) (ESA 2019) developed for a long-term monitoring of the Earth surface (ocean, land, ice caps) and of its surrounding environment (atmosphere) at high spatial and 3. THE WATERLINE METHOD temporal resolutions to provide high quality information for scientific and operational purposes [START_REF] Malenovský | Sentinels for science: Potential of Sentinel-1, -2, and -3 missions for scientific observations of ocean, cryosphere, and land[END_REF].

Sentinel-1 mission is a two-satellite constellation (Sentinel-1A and Sentinel-1B) with the same reference orbit [START_REF] Torres | GMES Sentinel-1 mission[END_REF]. Sentinel-1A and -1B were respectively launched on 3 April 2014 and on 25 April 2016. Each of the Sentinel-1 satellites orbit at an altitude of 693 km, on a near polar sun-synchronous orbit, an inclination of 98.18°, and a local solar time of 18:00 at its ascending node with 12-day repeat cycle [START_REF] Torres | GMES Sentinel-1 mission[END_REF]. The major interest of this constellation composed of two satellites put in a 180-degree phase difference is to increase the temporal coverage [START_REF] Torres | GMES Sentinel-1 mission[END_REF]. Owing to this configuration, the revisit time is at least six days and can reach 4 and even 2 days between two satellite acquisitions with increasing latitudes and especially over high priority areas such as Europe, Canada and the Northern Atlantic region [START_REF] Torres | GMES Sentinel-1 mission[END_REF]). The following information has been extracted from [START_REF] Fletcher | Sentinel-1: ESA's Radar Observatory Mission for GMES Operational Services[END_REF]. The main payload instrument onboard Sentinel-1A and Sentinel-1B is a C-band SAR called C-SAR, operating at a frequency of 5.405 GHz. Sentinel-1 operates in 4 modes: Interferometric Wide-swath (IW) mode, Extra Wide-swath (EW) mode, Wave mode (WV), and Strip Map (SM) mode. The IW mode acquires data in 3 sub-swaths using the TOPSAR (Terrain Observation with Progressive SAR) technique. The combination of the three sub-swaths provides a large swath of 250 km of width, with a high ground resolution of 5 m × 20 m. The EW mode uses the TOPSAR technique as well but over 5 sub-swaths rather than 3, enabling an ultra-wide swath coverage of 400 km at the expense of the ground resolution (20 m × 40 m). The WV mode acquires data over small stripmap scenes of 20 km × 20 km size called vignettes. These vignettes are acquired every 100 km on two different incidence angles with 5 m × 5 m ground resolution over the ocean. The SM acquisition mode provides continuous coverage over a narrow swath of 80 km of width with a ground resolution of 5 m × 5 m. This latter mode offers the continuity with ERS-1&2 (1993ERS-1&2 ( -2011) ) and ENVISAT (2002ENVISAT ( -2012) ) acquisitions. Dual (HH + HV, VV + VH) and single (HH or VV) polarization modes are provided for IW, SM, and EW modes and only single polarization mode is provided for WV. Slant range, Single-Look Complex (SLC) and Ground Range, Multi-Look, Detected (GRD) level-1 products are generated in the four acquisition modes. The SLC products consist of complex images containing amplitude and phase information, provided by 3 and 5 images for each sub-swath in IW and EW modes. For the GRD products, SAR data are multi-looked to reduce speckle noise at the expense of spatial resolution, and in contrast to SLC products, the sub-swaths bursts of IW and EW modes are merged to form a single GRD image. It should be noted that for GRD products the phase information is lost.

The data used in this study are GRD products acquired in IW mode with VV polarization. The GRD products are used in full resolution with a ground resolution of 23 m × 23 m and pixel spacing of 10 m × 10 m in range × azimuth. In this study, the GRD products were chosen instead of SLC products because they are more convenient for automatic edge detection due to their reduced speckle noise and their smaller volume of data. The merged sub-swaths are also more suited for reducing the processing time. The VV polarization was used rather than the other available VH polarization because of the better contrast obtained using the former polarization.

Sentinel-2 mission is also a two-satellite constellation (Sentinel-2A and Sentinel-2B) acquiring multi-spectral observations in 13 spectral bands. Sentinel-2A and -2B were respectively launched on 23 June 2015 and on 7 March 2017. They both orbit on a 3 85 Sun-synchronous quasi-polar orbit with a 10-day repeat cycle each (5-day with 2 satellites at the equator resulting in 2-3 days at mid-latitudes) [START_REF] Drusch | Sentinel-2: ESA's Optical High-Resolution Mission for GMES Operational Services[END_REF]). The following information has been extracted from the Sentinel-2 user handbook [START_REF] Esa | SENTINEL-2 User Handbook[END_REF]. The average orbital altitude is 786 km with an inclination of 98.62°and a 10:30 a.m. descending node. It provides observations over land and coastal areas from 56°latitude South to 84°latitude North. The main payload on-board Sentinel-2 satellite is a Multi Spectral Instrument (MSI) measuring the radiance reflected by the Earth in 13 spectral bands in the visible (VIS), the Near Infra-Red (NIR), and the Short-Wave Infra-Red (SWIR). The data are acquired on a wide swath of 290 km width with 4 bands at 10 m of spatial resolution, 6 bands at 20 m of spatial resolution, and 3 bands at 60 m of spatial resolution. Two data products are made available: the level-1C Top-Of-Atmosphere (TOA) geocoded reflectance and the level-2A Bottom-Of-Atmosphere (BOA) geocoded reflectance. Both products are composed of tiles of 100 km × 100 km ortho-images in UTM/WGS84 with 10, 20, and 60 m of spatial resolution depending on the spectral band. For edge detection purposes both products showed similar performances. The level-1C product was used in this study because of its smaller data volume.

SEA LEVEL INFORMATION FROM ARCACHON-EYRAC TIDE GAUGE AND THE HYCOM OCEAN-CIRCULATION MODEL

Sea level records from the Arcachon-Eyrac tide gauge (1.163550021°W and 44.66500092°N) were used in this study. The tide gauge is operating since November 1967 and managed by the French hydrographic service (SHOM) and the Gironde sea and land state office (DDTM). Since February 2010, the tide gauge is equipped with an Optiwave 7300C sensor and a MARELTA acquisition unit (REFMAR 2012). Sea level measurements are provided at 1-minute time interval. The data are made available by REFMAR and can be found online on the SHOM data website: https://data.shom.fr. The sea level (tide and surge) model outputs from the HYbrid Coordinate Ocean Model (HYCOM) [START_REF] Bleck | An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates[END_REF], in barotropic configuration [START_REF] Baraille | Modèle shallow-water multicouches isopycnal de Miami[END_REF], with a curvilinear grid and a resolution that ranges between 2 km and 500 m when approaching the French coast were also used over our two study sites. This ocean circulation model is a joint effort between the SHOM and Météo-France in the framework of the History, Observation and Modeling of sea level (HOMONIM) project, that aims to improve the coastal flood warning system in metropolitan France and overseas (SHOM 2016a). It is forced by tides predicted by the SHOM and by wind and atmospheric pressure obtained from Météo-France meteorological models [START_REF] Pasquet | Implémentation d'un nouveau modèle opérationnel de prévision des vagues et surcotes marines[END_REF]. Different configurations of this model exist depending on the geographic domain of the region. In this study we used the data obtained by the ATL (Atlantic) configuration that covers the French Atlantic façade and the English Channel between 43°N 9°W and 62°N 10°E. At high surge the model underestimates the total sea level of about 10 cm with a phase difference of about 12 minutes [START_REF] Pasquet | Implémentation d'un nouveau modèle opérationnel de prévision des vagues et surcotes marines[END_REF]. Archived hourly forecasts of sea level (tide and surge) over Arcachon and Veys Bays respectively were provided by SHOM at https://data.shom.fr.

These forecasts were interpolated to a 1-minute interval.

LIDAR-DERIVED TOPOGRAPHY FOR INTERTIDAL AREAS

A LiDAR-derived topography of the intertidal area of the Arcachon Bay is a subset of the RGE ALTI ® product provided by the IGN at http://professionnels.ign.fr/rgealti.

Airborne LiDAR acquisitions were acquired on 25 June 2013 at low tide. The dataset is provided on a regular 1 × 1 m grid and interpolated on a 10 × 10 m grid to match the resolution of remote sensing data (Figure 3.2.a). The vertical precision for this dataset is 0.2 m.

The validation topography for the Bay of Veys was also derived from an airborne LiDAR acquisitions. The intertidal topography of the bay was extracted from the NHDF (lidar Normandie Hauts-De-France) 2016-2017 V.20180501 product provided by the SHOM (SHOM-ROLNP 2018). The data were acquired during campaigns conducted from 5 May 2017 to 26 June 2017 and led by the SHOM in partnership with the Normand Picard Coastal Observation Network (Réseau d'Observation du Littoral Normand Picard (ROLNP)). The product provides DEMs of 1 × 1 m and 5 × 5 m resolutions. In this study the 5 × 5 m DEM was used after interpolation on a 10 × 10 m grid (Figure 3.2.b) to be consistent with pixels size of the remote sensing images.

METHODS

In this study, the DEMs were generated using the waterline method. A detailed description of this method can be found in [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF] and [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF]. Before applying the waterline method on the Sentinel-1 and Sentinel-2 data, a pre-processing step was performed first to produce filtered backscattering coefficient images from Sentinel-1 scenes and Normalized Difference Water Index (NDWI) images from Sentinel-2 scenes. The aim of the pre-processing steps is to enhance the contrast of the images in order to detect the edges of the tidal flats. In this section, the pre-processing of Sentinel data using SentiNel Application Platform (SNAP) software (developed by ESA) is presented first, then a detailed summary of the waterline method is given along with the changes applied in this study.

SNAP PRE-PROCESSING

Sentinel-1 SAR and Sentinel-2 MSI images were pre-processed using the SNAP toolbox. The pre-processing workflows were designed using the SNAP graph builder tool. For SAR images, the pre-processing workflow consisted of four steps to obtain the geo-corrected backscatter images: (i) thermal noise removal using the "Thermal Noise Removal" operator of SNAP Sentinel-1 ToolBoX (S1TBX) that removes the thermal noise calculated by the operational ESA Instrument Processing Facility (IPF) [START_REF] Bourbigot | Sentinel-1 Product Definition[END_REF]) and stored in a Look Up Table (LUT) within the Sentinel-1 Level-1 products (Weiß 2019), (ii) calibration to derive radar backscattering coefficient (σ 0 ) values [START_REF] Miranda | Radiometric Calibration of S-1 Level-1 Products Generated by the S-1 IPF[END_REF]; this process convert the radar reflectivity stored as Digital Numbers (DN) in Sentinel-1 Level-1 products to backscattering coefficients, (iii) speckle-filtering using Refined Lee filtering [START_REF] Lee | Refined filtering of image noise using local statistics[END_REF], and (iv) orthorectification using the range Doppler terrain correction operator with SRTM 3" DEM [START_REF] Small | Guide to ASAR Geocoding[END_REF].

For the MSI images, the workflow consisted of the three following steps: (i) resampling of the different spectral bands to 10 m using a bilinear interpolation method, (ii) computation of the Normalized Difference Water Index (NDWI) [START_REF] Mcfeeters | The use of the Normalized Difference Water Index (NDWI) in the delineation of open water features[END_REF]; NDWI is defined as:

N DW I = ρ g r een -ρ N I R ρ g r een + ρ N I R (3.1)
where ρ g r een and ρ N I R are the reflectances of the green and the NIR bands; For Sentinel-2 images spectral bands 3 and 8 were respectively used for the green and NIR bands, and (iii) reprojection of pixels into WGS84 Coordinated Reference System (CRS).

ELIMINATION OF NOISY SAR IMAGES

Prior to edge detection, noisy SAR images must be eliminated in order to extract only accurate waterlines. In this study, we opted for an automatic elimination of noisy images to reduce the manual interventions. The elimination was based on information extracted from the histograms of SAR images. By examining the histograms of the images, we noticed that the histograms can be divided into 6 classes. An automatic classification of the images was performed using the k-means algorithm based on the following steps: (i) histograms of 1000 bins were generated for each image, (ii) then each bin was considered as a dimension for the k-means clustering. Figure 3.4 shows the averaged histograms obtained for each class. Histograms showing approximately one peak (class 5 and class 6) are noisy images with low contrast between different surface types. SAR images corresponding to these classes (5 and 6) are eliminated from further processing.

WATERLINE METHOD

The method consists in detecting the waterline (shoreline) edge of remotely sensed images using image processing techniques. Then heights are assigned to waterlines using water level information obtained either by using a hydrodynamic tide/surge model outputs over the observed area at the time of acquisition of the image or by tide gauge measurements [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]. From a series of images providing an adequate sampling of the tidal range, a set of waterlines is assembled and then interpolated to form a gridded-DEM. An edge detection method was developed to extract waterlines from Sentinel-1 (SAR) and Sentinel-2 (MSI) images. The method can be divided into eight steps described below and illustrated in Figure 3.6 using the Sentinel-1B SAR image acquired the 04/07/2017 as an example:

1. Pre-processing of Sentinel-1 & -2 images using the SNAP toolbox as explained in section 4.1 to obtain backscattering coefficient or NDWI images (Figure 3.6.a).

2. Performing the image segmentation process using k-means clustering technique [START_REF] Arthur | k-means++: The advantages of careful seeding[END_REF]. The image is divided into three different groups of pixels depending on their backscattering coefficient or NDWI values (Figure 3.6.b).

For SAR images, open water surfaces exhibit low backscattering coefficients than other features due to the lack of penetration of the EM wave in the water, the side looking geometry of the sensor, and the smoothness of the surface responsible for low power return to the sensor. Therefore, the group with the lowest centroid is composed of the pixels corresponding to water. The other groups correspond to tidal flats or inland areas. For MSI images, the pixels corresponding to water are the pixels of the group with the highest centroid (high NDWI values correspond to water).

3. Isolating the water pixels by merging the pixels of the other groups together which will produce a water mask (Figure 3.6.c).

4. Extracting the perimeter of the water mask as an initial k-means-derived edge (Figure 3.6.d).

5. Removing small areas that usually corresponds to noisy features (Figure 3.6.e) 6. Filling holes that correspond to sediments, with backscattering coefficients close to the water pixel values, or to water ponds unconnected to the water of the bay for which elevation cannot be assigned using sea level information (Figure 3.6.f).

7. Preparing the original image to the active contouring step. In this step, the pixels of the groups with the third centroid value are replaced by the centroid value of the second group. This will turn off (reduce high backscattering coefficients) the highly energetic pixels that may attract the edge towards them in the final active contouring step (Figure 3.6.g).

8. Active contouring [START_REF] Chan | Active Contours Without Edges[END_REF] applied on the modified image to obtain the final edge (Figure 3.6.h)

The edge detection method was developed in order to extract waterlines in the form of continuous and closed polygons (or many polygons for a waterline). The purpose behind this approach is to enable the automatization of the post-processing of waterlines, more specifically in removing redundant waterlines (section 3.4.3.3) and in removing the intersections between the different waterlines prior to interpolation (section 3.4.3.4).

DETERMINATION OF WATERLINES HEIGHTS

In this step, heights are associated to the extracted waterlines from water level information. As mentioned in the datasets section, water level information comes from either tide gauge records (Arcachon-Eyrac in the case of the Arcachon Bay) or from the SHOM operational sea level ocean-circulation model outputs. For the Arcachon Bay, DEMs were created based on waterlines with heights extracted from the tide gauge. The water level assigned to each waterline was the closest measurement made within 1-minute interval of the satellite passage (otherwise the waterlines were discarded). DEMs were also created for the Arcachon Bay using the model simulation outputs by considering the time series of the nearest model grid-point to the tide gauge for comparison purposes. This comparison provided a quality-check of the simulated data inside the bay, in order to use the model simulations for the Bay of Veys where no tide gauge measurements are available. For the Bay of Veys sea level time series were extracted from a grid-point at the mouth of the Bay. Assembling all the waterlines produced DEM point clouds that will be interpolated on a grid of 10 × 10 m resolution.

In reality, each waterline has a range of heights. This range is not taken into consideration when using a single sea level height measurement. The assumption made is that the surface water slope is negligible which can be the case. To account for surface water slopes, DEMs over the Arcachon and Veys Bays were also generated from waterlines with heights extracted from the whole water level grid-points provided by the simulations over the study areas. The height was assigned to each point of the waterlines according to the closest water level point.

REDUNDANCY REMOVAL

The redundancy removal consists in eliminating waterlines with very close heights. Due to the abundance of images provided by the Sentinel missions, many redundant waterlines were present. For instance, in a range of 15 cm, 1 to 6 waterlines can be found. For each 15 cm interval, one waterline is considered to be enough. The choice of 15 cm is arbitrary and larger intervals could be used if the number of images is low. As mentioned in sub-section 3.4.2, the edge detection technique allowed to extract each waterline as closed polygons (or objects). This step permits to automatically choose the waterline by keeping in each 15 cm interval the waterline with the least number of objects. For different waterlines with very similar heights, the waterline with the least number of objects is the waterline that corresponds to the image with the least noisy features. Figure 3.7 shows an example of three images in a 15 cm range that have different number of objects. Image number 2 possessing the least number of objects is the one which was kept for further processing. This step allows a second-degree removal of intermediate-quality images presenting some noisy features, that were not eliminated in the elimination process (section 3.4.2).

WATERLINES POST-PROCESSING

Waterlines with different heights may intersect due to the variable quality of images that impact the edge detection process or, less likely, due to changes in topography between the acquisitions of the images. The extraction of waterlines as closed polygonal regions, thanks to the edge detection method used, helps with the automatic removal of these intersections. For each waterline, its intersections with all the previous higher waterlines were identified then removed.

INTERPOLATION

The DEM point clouds were then interpolated to obtain continuous gridded-DEMs. In this study two interpolation methods widely used in geo-statistics were employed and compared: IDW [START_REF] Shepard | A two-dimensional interpolation function for irregularly-spaced data[END_REF]) and kriging [START_REF] Matheron | Principles of geostatistics[END_REF]. The point cloud was interpolated on grids of 10-meter resolution covering the study area. Kriging was performed using the Gstat software [START_REF] Pebesma | Multivariable geostatistics in S: the gstat package[END_REF][START_REF] Pebesma | Gstat: a program for geostatistical modelling, prediction and simulation[END_REF].

TOPOGRAPHIC CHANGES

Topographic changes were analyzed by subtracting the waterline-derived DEMs (creating DEM of Difference (DoD) maps) of simultaneous years. The inherent uncertainty of the generated DEM considerably affects the estimation of the volume changes. In order to detect real changes, we adopted the approach introduced by several studies [START_REF] Brasington | Monitoring and modelling morphological change in a braided gravel-bed river using high resolution GPS-based survey[END_REF][START_REF] Lane | Estimation of erosion and deposition volumes in a large, gravel-bed, braided river using synoptic remote sensing[END_REF][START_REF] Wheaton | Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets[END_REF]) that consists in specifying a Level of Detection (LoD) threshold. Absolute differences lower than this threshold will be excluded as they are considered as measurement errors rather than actual changes. The uncertainty of the DoD (δ d ) can be estimated by standard independent error propagation [START_REF] Brasington | Monitoring and modelling morphological change in a braided gravel-bed river using high resolution GPS-based survey[END_REF]:

δ d = (δh DE M 1 ) 2 + (δh DE M 2 ) 2 (3.2)
where δh DE M 1 and δh DE M 2 are the uncertainties of the DEMs used for DoD generation. The LoD can be computed using the following equation [START_REF] Schimel | Accounting for uncertainty in volumes of seabed change measured with repeat multibeam sonar surveys[END_REF]:

LoD(k) = k.δ d (3.3)
where k is a dimensionless threshold factor. In this study, we opted for k = 1 that corresponds to a confidence level of 68%. An estimation of the uncertainty of the waterline-generated DEMs is presented in section 3.5.3. After the determination of the LoD, the eroded and deposited volumes were computed using the following equations:

V er od ed = i [h 2 (i ) -h 1 (i ) < -LoD].R 2 (3.4) V d eposi t ed = i [h 2 (i ) -h 1 (i ) > LoD].R 2 (3.5)
where i denotes a grid cell, h 1 and h 2 are heights corresponding to the first and second DEMs, and R is the DEM resolution (R 2 is the surface of a grid cell). The volumetric uncertainties are computed with the following equations:

δV er od ed = R 2 .δ d .n [h 2 (i )-h 1 (i )<-LoD] (3.6) δV d eposi t ed = R 2 .δ d .n [h 2 (i )-h 1 (i )>LoD] (3.7)
where n is the number of grid cells presenting erosion or deposition. Finally, the net volume change is given by the sum of the eroded and deposited volumes:

V net = V er od ed + V d eposi t ed (3.8)

RESULTS

DEMs were generated for the Arcachon Bay and the Bay of Veys using the waterline method that can be summarized by the following steps: (i) extracting the waterlines from a series of remote sensing images that provide an adequate sampling of the tidal range, (ii) associating heights to the points of each waterline using water level information simulated or observed at the exact time of the satellite passage, (iii) assembling all the waterlines to form a point cloud DEM, (iv) and interpolating the point cloud to construct the final gridded-DEM.

Sentinel-1 and Sentinel-2 images were used to create the DEMs. Annual DEMs were generated every year from 2015 to 2018 for the Arcachon Bay, and every year from 2016 to 2018 for the Bay of Veys. The images time series used for each DEM were acquired between the first of June and the end of September. Limiting the images to the latter calm season will help us avoid the eventual major morphological changes that could occur during a more dynamic period. Table 3.1 lists the number of Sentinel-1 and Sentinel-2 images acquired for each year during the June-September period for both study sites, and the number of images eliminated due to unavailable sea level information, noisy images, and redundant waterlines heights. Heights were associated to waterlines following the three different approaches mentioned earlier in the method section: (i) using the tide gauge records, (ii) using the sea level values extracted from a single point-grid of the ocean-circulation model outputs, (iii) and using the sea level distribution over the study areas from the gridded model outputs (each waterline point is given the height of its closest grid-point in space and at the exact time of satellite passage). Finally, the assembled waterlines (DEM point clouds) were interpolated using the IDW and the kriging interpolation techniques.

In the following, we will first present the method validation performed by comparing the waterline generated DEMs to the LiDAR-derived DEMs. Then, we will show the final intertidal DEMs obtained by the waterline method followed by an estimation of the DEMs accuracy. Finally, volume changes between the observed years will be computed from the DoD maps. 3.8 presents the comparisons for the Arcachon Bay between the LiDAR-derived DEM and the 2016 six waterline-derived DEMs obtained by combining the three waterlines levelling approaches with the two interpolation techniques. Another aim of this comparison is to evaluate the best combination of levelling approach and interpolation technique. For this reason, the DEM of 2016 were chosen instead of 2015 (closer to the LiDAR acquisitions) for which no model simulation was performed by the SHOM. As indicated in Figure 3.8, the kriging interpolation method (Figure 3.8.b,3.8.d,and 3.8.f) produced slightly more accurate DEMs than IDW method (Figure 3.8.a,3.8.c,and 3.8.e) showing a lower Mean Absolute Error (MAE) and a lower RMSE for all cases. Tide gauge levelling showed better results (MAE = 0.19 m) than the two other approaches based on the model simulations. However, reliable DEMs were also obtained for the latter cases with MAEs and RMSEs equal to 0.25 m and 0.32 m respectively. In contrary to expectations, the DEMs with heights assigned using the complete model grid produced the same results as the DEMs with heights assigned using the single-grid point.

The comparisons corresponding to the Bay of Veys are presented in Figure 3.9. DEMs of 2017 were used in this case since the LiDAR observations were acquired between May and June 2017. The interpretations made for the Arcachon Bay DEMs are valid for the Bay of Veys. A decrease in the MAEs and RMSEs is observed between the two interpolation techniques.

The final DEMs were thus generated using the kriging interpolation method with heights assigned using tide gauge records for the Arcachon Bay and using the kriging interpolation method and heights assigned with the single-grid point model for the Bay of Veys. The DEMs generated for the Bay of Veys are presented in Figure 3.12. The topography shape and height are consistent with the LiDAR-derived DEM. Figure 3.12 shows a net improvement with time in terms of details. The tidal creeks in the 2018 DEM are evident comparing to the DEM generated for 2016. The 2017 DEM shows an intermediate performance. The relatively large features of the intertidal zone are well detected. These large features are stable in time, which is consistent with the sedimentary characteristics of the Arcachon Bay [START_REF] Allard | A synthesis of morphological evolutions and Holocene stratigraphy of a wave-dominated estuary: The Arcachon lagoon, SW France[END_REF]. Some smaller features that can be found in a given DEM are sometimes missed in others. This depends on the temporal sampling of the tidal range. For instance, the 2018 DEM shows more details than the 2015 DEM, smaller tidal flat features and tidal creeks were detected. This was majorly due to the finer sampling provided by the Sentinels in 2018 where the four satellites (Sentinel-1A, Sentinel-1B, Sentinel-2A, and Sentinel-2B) were in orbit. Despite the better sampling for the years 2017 and 2018, the detection of the very small tidal creeks was limited by the sensor horizontal resolution. A simple visual 3. THE WATERLINE METHOD comparison between the LiDAR-derived DEM and the waterline-derived DEMs shows that the latter features are not detected or not fully detected by the waterline method over the Arcachon Bay. It should be noted that the DEMs were interpolated over the intertidal area specified by an intertidal mask. This mask was created manually according to the satellite image acquired at the lowest tide (-1.53 m) during the 2018 June-September period. The DEMs of the other years may present some errors near the intertidal area's borders due to a missing waterline. This can be well observed for the DEM of 2015 for which the lowest waterline was extracted at -0.78 m.

INTERTIDAL DEMS

DEMS ACCURACY

The accuracy of the generated DEMs is governed by the following factors: (i) horizontal resolution of the remote sensing images (sensor-dependent), (ii) the geometric corrections, (iii) horizontal accuracy of the edge detection technique, (iv) the slope of the intertidal zone topography, (v) the accuracy of sea level information, and (vi) the slope of the surface water. The first three factors are related to horizontal inaccuracies that will lead to a height (vertical) uncertainty depending on the fourth factor. These three factors are also sensor-dependent, and their inaccuracies are determined by the SAR images since they have the lower spatial resolution (23 m × 23 m). The accuracy of the geometric corrections of the SAR images is within one pixel, therefore a horizontal uncertainty of 23 m. The edge detection technique (taking into account the speckle filtering) yielded an uncertainty of 2 pixels in the shoreline positions, therefore an uncertainty of 46 m. The latter was determined by a visual assessment of detected waterlines. The average intertidal slope obtained from the LiDAR-derived DEMs for the Arcachon Bay and the Bay of Veys are 0.17% and 0.13%, respectively. This results in a height error of 0.12 m (23 × 0.17/100 + 46 × 0.17/100) for Arcachon and 0.09 m (23 × 0.13/100 + 46 × 0.13/100) for the Bay of Veys. The fifth and sixth factors have a direct impact on the height accuracy. The combined uncertainties coming from the tide gauge and the slope for the case of Arcachon and from the model and the slope for the Veys Bay don't exceed 0.15 m. The uncertainty is thus 0.27 m (0.12 + 0.15) for Arcachon Bay and 0.24 m (0.09 + 0.15) for the Bay of Veys. These uncertainties are considered as conservative, and they are close to the observed MAEs. The estimated uncertainties allow an estimation of δ d (same as the LoD by taking k = 1) for both study sites: 0.38 m for Arcachon Bay and 0.34 m for the Bay of Veys. 3.2. Net volume changes are higher for 2017/2018 in the case of the Arcachon Bay and the Bay of Veys. For the whole period (2016/2018), both sites showed significant erosion and deposition volumes (comparing to errors) with total changes showing net losses of 1.12 × 10 6 m 3 and 0.70 × 10 6 m 3 for Arcachon and Veys Bays respectively. It should be noted that the lower net changes observed over the Veys Bay is due to the net deposition observed for 2016/2017. However, the amount of the occurring changes was higher for the Bay of Veys despite its smaller intertidal flat area.

DISCUSSION

The waterline method has traditionally faced problems with the insufficient number of satellite images acquired during a short period of time, the subjective satellite-image thresholding required in the edge detection process, and the long post-processing (sometimes manual) of the extracted waterlines prior to interpolation. In this study, we demonstrated the ability of the waterline method to generate accurate DEMs in two different intertidal areas located on the French coast (the Arcachon Bay and the Bay of Veys) while trying to overcome the limitations (mentioned above) encountered by this method.

THE NUMBER OF IMAGES

The major approximation made by the waterline method is considering a morphological stability in the intertidal area during the acquisition period of the images. These images acquired during a specified period need also to cover at best the tidal range. Thus, the use of an insufficient number of images or expanding the period of acquisition may lead to inaccuracies. To our knowledge, the shortest period (5 months) was adopted by [START_REF] Kang | Topographic mapping on large-scale tidal flats with an iterative approach on the waterline method[END_REF] using 18 HJ-1A/B CCD and 3 Landsat TM/OLI images over an exposed area of 2000 km 2 of intertidal flats. Comparing to previous studies, the use of Sentinel-1 and Sentinel-2 data provided a finer and more complete sampling of the tidal range with images acquired during a relatively short period (4 months). Figure 3.14 shows the improvement of tidal cycle sampling provided by the Sentinels between 2015 and 2018. 2017 and 2018 provide finer sampling of the tidal cycle (comparing to 2015 and 2016) with Sentinel-1A, -1B, -2A, and -2B in orbit. For instance, 80 Sentinel-1 images and 13 cloud free Sentinel-2 images are available for the 2018 June-September period over the Arcachon Bay. However, the total number of 93 images can be considered too high for generating a DEM using the waterline method. The manual selection of images is one of the important issues which limits the complete automatization of the waterline method. In this study, noisy images and images 3 107 with similar sea level were automatically removed. However, these two aspects should be further addressed in future studies, especially the determination of the optimal number of waterlines needed (that may depend on a prior knowledge of the intertidal slope) and the estimate of more adequate criteria for images selection in case of redundancy. It should also be noted that the acquisitions made by Sentinel-1 and Sentinel-2 constellations, which provide a huge number of images (every 12 days on the same swath owing to that the study zone can be completely comprised in several swaths), can provide a complete sampling of the tidal range for periods of less than 4 months.

WATERLINES EXTRACTION AND POST-PROCESSING

The first step of the waterline method is to extract the waterlines from the remote sensing images (pre-processed here with SNAP software). An edge detection method based on a combination of k-means segmentation and active contouring was proposed in this study to extract waterlines from Sentinel-1 and Sentinel-2 images. The k-means segmentation technique was employed to overcome two difficulties: the subjective thresholding decisions, and to create closed object to facilitate the post processing of the extracted waterlines. The manual post-processing may achieve slightly better results comparing to the automatic processing performed in this study. However, the high number of images render this work overwhelming and time consuming. With the unprecedented amount of data available, the automatic post-processing should be always prioritized, and future studies must focus on developing complete automated processing methods. Improvements of the edge detection method might be achieved by using other parameter (such as the backscattering ratio derived from VV and VH polarizations) or by adding another dimension to the k-means clustering (such as the backscattering coefficients derived from the other available polarization).

WATERLINES HEIGHT ASSIGNMENT AND INTERPOLATION

Another factor that impacts the accuracy of the generated DEMs is the water level information associated to the extracted waterlines. As mentioned earlier, a waterline is composed of a range of heights and the use of the tide gauge does not take into consideration this reality. However, the use of the complete grid didn't improve the results. This means that either the slope is too low, or the model is incapable of providing very accurate sea level heights over the intertidal area. For interpolation, the major problem encountered was the difference in distance between the lowest waterline from the adopted mask. This can be solved by adding the lowest waterline measured during the whole period to all DEMs or by adding an image acquired at lower tide outside the 4 months period. 3.3. For the Arcachon Bay, the three 2016 profiles showed lower MAEs (#1: 0.17 m, #2: 0.16 m, #3: 0.14 m) than the one obtained by the complete gridded-DEM (0.19 m) and the estimated accuracy (0.27 m) in section 3.5.3. A smaller error for profiles is expected because a transect can miss an eventual extensively biased region. However, it shows that a better accuracy can be achieved with more careful processing. The good accuracy provided by this method is also reflected in the MAEs and RMSEs obtained for the 2015 waterline-derived DEM with a MAE reaching 0.13 m for the third transect. Even with this good accuracy, the error is expected to be smaller since the LiDAR measurements were acquired in 2013. In contrast to transects 1 and 2, small errors barely changing with the years are observed over the third transects crossing the "île aux Oiseaux" island. This could mean that this area is undergoing less modifications than the rest of the flats. IN THE INTERTIDAL AREAS Repeat DEM surveys and DoD maps are very useful for monitoring morphological changes. However, the inherent uncertainty of the DEMs can considerably affect the computation of volume changes over large areas even for DEMs with very high accuracy [START_REF] Schimel | Accounting for uncertainty in volumes of seabed change measured with repeat multibeam sonar surveys[END_REF][START_REF] Wheaton | Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets[END_REF]. In this study we opted for the LoD thresholding approach to account for the uncertainty of the estimated volumes of erosion and deposition. The major issue of this technique is the consideration of every change within -LoD and LoD values as a noise which is not always the case. Therefore, care must be taken when interpreting the estimated volume changes. These changes are considered as a lower bound of the volume displaced at a given confidence interval (which is 68% in this study for k = 1) rather than the actual changes [START_REF] Schimel | Accounting for uncertainty in volumes of seabed change measured with repeat multibeam sonar surveys[END_REF]. Computing volume changes without LoD thresholding (k = 0) is possible. However, for intertidal flat areas experiencing small height changes comparing to their large surfaces, the summation of the volumetric error over the whole area will yield very large uncertainties. Smaller uncertainties could be obtained by using a standard independent error propagation (i.e., considering each grid-cell has an independent height error), but this is hardly the case for DEMs and can produce statistically invalid uncertainties for volume changes [START_REF] Schimel | Accounting for uncertainty in volumes of seabed change measured with repeat multibeam sonar surveys[END_REF].

DEMS ACCURACY

Considering an LoD thresholding approach, the quantification of sediment surface and volume changes (Table 3.2) performed here showed that the Arcachon Bay is more stable than the Bay of Veys. 96.00% of stable area was obtained for the Arcachon Bay against 63.44% for the Bay of Veys. The erosion-deposition balance showed a net erosion for all years and for both sites. Between 2016 and 2018 the Arcachon Bay recorded a deficit of sediments of 1.12 × 10 6 m 3 . A net erosion was also obtained for the Bay of Veys with an observed deficit of 0.70 × 10 6 m 3 . We believe that seasonal variation effect is reduced to a minimum because of the use of images acquired during the same season for the DEMs generation.

As we do not have access to sedimentation rate data, we were not able to evaluate the precision of the measured morphological changes. Similar studies performed over different environments showed also net losses. [START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF] observed a loss of (16.1 ± 4.5) × 10 6 m 3 between 1992 and 1997 over the intertidal flats of the Morecambe Bay. Erosion was also observed over the Gomso Bay (Korea) by [START_REF] Ryu | Detecting the intertidal morphologic change using satellite data[END_REF] at a rate of -3.1 × 10 m 3 /year (-9 cm over 9 years) between 1991 and 2000. It should be noted that the Morecambe Bay and the Gomso Bay have intertidal flats with surface areas of 350 km 2 and 4,500 km 2 respectively. Comparing to these latter, our two study sites have relatively small area surfaces (115 km 2 and 37 km 2 for Arcachon and Veys Bays respectively). Detecting significant (comparing to the errors) changes over these study sites demonstrates that the methods and datasets used are suited for the monitoring of morphological changes in relatively small-scale environments.

Furthermore, the inspection of Veys profiles (Figure 3.16) suggests that a detection of channel migrations is possible. For instance, transect 2 shows that the location of the channels detected by the 2017 waterline-derived DEM fits the location detected by the LiDAR. Whereas, 2016 and 2018 waterline-derived DEMs shows different locations. This can also be seen in Figure 3

CONCLUSIONS

This study presents a first attempt for intertidal DEM generation of the Arcachon and Veys Bays using the waterline method by analyzing Sentinel-1 and Sentinel-2 images. The major modification to the waterline method comparing to previous studies is the edge detection technique proposed here accompanied by an automatic elimination of noisy SAR images. This edge detection technique of 8 steps based on a combination of k-means segmentation and active contouring provided an accurate, fast, and simple edge detection procedure with faster automatic post-processing of waterlines. A combination of waterlines height assignment approaches and interpolation methods were used to generate the DEMs. The heights were assigned to waterlines using tide gauge records, single point-grid of the ocean-circulation model outputs, and the sea level distribution over the study areas from the gridded model outputs while the interpolation methods used were the IDW and kriging. On these relatively small-scale sites, the best DEMs were generated by combining tide gauge levelling with kriging interpolation. No improvements were observed by taking the surface water slope into account. A vertical accuracy better than 0.27 m and 0.24 m is obtained for Arcachon Bay and Veys Bay respectively (based on gridded-DEMs and profiles comparisons with high accuracy LiDAR data along with a methodological estimation of the method accuracy). The use of Sentinels data rendered the generated DEMs more reliable due to the high revisit time provided by its two constellations (Sentinel-1 and Sentinel-2) and thus to the finer and complete sampling of the tidal range. The success of the used methodologies and datasets over the two study sites with contrasted characteristics prove their ability to provide accurate and reliable DEMs over similar environments.

A quantitative assessment of morphological changes over the intertidal areas was also performed. Both study sites experienced between 2016 and 2018 a net loss of 1.12 × 10 6 m 3 for the Arcachon Bay and 0.70 × 10 6 m 3 for the Bay of Veys, with the Arcachon Bay showing more stable behavior. This study focused on the use of the waterline method with Sentinels images to generate accurate DEMs. However, the significant changes detected by comparing the consecutive DEMs showed that the presented methodologies and datasets are suitable for monitoring the morphological and sedimentary changes of these relatively small-scale intertidal areas. Future work will involve extending of the DEMs time series in order to estimate the morphological changes occurred during the last decade by employing the waterline method using datasets that cover this period. Furthermore, the short period of acquisition (4 months; that can be reduced) might also enable seasonal 3 113 monitoring of morphological and sedimentary variations. The monitoring of the seasonal and interannual sediment budget of intertidal areas is of great importance for effective management policies. The derived DEMs and the morphological changes measured in this study can also be assimilated to morphodynamic and hydrodynamic models to generate more precise predictions [START_REF] Mason | Remote sensing of intertidal morphological change in Morecambe Bay, U.K., between 1991 and 2007[END_REF].

With more available data and better spatiotemporal resolution, the waterline method can be pushed to its limits. The next-generation wide swath altimetry mission SWOT can generate very useful data to be used by this method. It will provide water masks that can be used as waterlines, and it will measure sea surface height which will render the waterline method independent from ground-based measurements (tide gauges) or hydrodynamic models.

MONITORING INTERTIDAL TOPOGRAPHY USING THE WATERLINE METHOD WITH THE

SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT) MISSION.

Intertidal flats are very dynamic environments pressured by anthropogenic activities and climate change. There is an increasing need for updated intertidal topography maps for scientific and coastal management purposes. The waterline method is one of the most commonly used spaceborne methods for mapping intertidal topography. This method uses a combination between a series of satellite images acquired at different tidal stages (radar or optical) and sea level information (tide gauge records or models output). The future wide-swath altimetry mission SWOT (Surface Water and Ocean Topography) will be very beneficial for the waterline method with its expected ability to provide highly accurate 2D sea level measurements in coastal areas.

INTRODUCTION

C OASTAL areas are very complex systems with diverse morphology and landforms.

The hydro and morphodynamics in coastal systems are governed by the interactions between three elements: coastal processes (i.e. waves, tides, currents, wind, river outflow, weathering in rocky coasts, and other biological, biophysical, and biochemical processes), sediment transport (erosion and deposition), and morphology (morphodynamic feedback due to the strong links between form and process [START_REF] Cowell | Morphodynamics of coastal evolution[END_REF]) [START_REF] Masselink | Introduction to Coastal Environments and Global Change[END_REF]. Over time, the morphological changes alter the hydrodynamic and the sediment transport patterns of the system. Therefore, the continuous monitoring of the topography is fundamental for hydrodynamic and morphodynamic modelling in coastal systems [START_REF] Catalão | Multitemporal Backscattering Logistic Analysis for Intertidal Bathymetry[END_REF].

Intertidal zones alternately exposed and covered by water due to the tidal regime are amongst the most logistically challenging coastal landforms for ground-based or airborne-based monitoring of their topography.

Spaceborne-based monitoring is therefore, the only viable and cost-effective approach able to provide updated intertidal topography maps [START_REF] Benveniste | Requirements for a Coastal Hazards Observing System[END_REF][START_REF] Salameh | Monitoring Beach Topography and Nearshore Bathymetry Using Spaceborne Remote Sensing: A Review[END_REF]. Various methods exist nowadays for generating intertidal DEMs from remote sensing data including SAR interferometry [START_REF] Choi | Optimum Baseline of a Single-Pass In-SAR System to Generate the Best DEM in Tidal Flats[END_REF][START_REF] Lee | High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data[END_REF], stereoscopy [START_REF] Tateishi | Relative DEM production from SPOT data without GCP[END_REF] and the waterline method [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]. The waterline method is the most commonly used technique and was introduced by [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]. It consists in extracting the waterlines (shorelines) from a series of remote sensing images acquired at different tidal stages. Then, heights are assigned to the waterlines using sea level information measured by tide gauges or extracted from hydrodynamic models. Finally, the leveled waterlines are assembled and interpolated to produce a gridded-DEM. Intertidal DEMs were generated using the waterline method in various regions especially over the English coasts [START_REF] Lohani | Construction of a Digital Elevation Model of the Holderness Coast using the waterline method and Airborne Thematic Mapper data[END_REF][START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF][START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF], the Wadden Sea in northern Europe [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF][START_REF] Li | Intertidal Topographic Maps and Morphological Changes in the German Wadden Sea between 1996-1999 and 2006-2009 from the Waterline Method and SAR Images[END_REF][START_REF] Niedermeier | Topography and morphodynamics in the German Bight using SAR and optical remote sensing data[END_REF], the Macouria Amazon-derived mud bank in French Guiana [START_REF] Anthony | Nearshore intertidal topography and topographic-forcing mechanisms of an Amazon-derived mud bank in French Guiana[END_REF], the Sea Radial Sand Ridges in the Southern Yellow Sea [START_REF] Kang | Topographic mapping on large-scale tidal flats with an iterative approach on the waterline method[END_REF][START_REF] Liu | Quantitative Analysis of the Waterline Method for Topographical Mapping of Tidal Flats: A Case Study in the Dongsha Sandbank, China[END_REF][START_REF] Wang | Evolution of the topography of tidal flats and sandbanks along the Jiangsu coast from 1973 to 2016 observed from satellites[END_REF], and more recently in the Bay of Bengal delta [START_REF] Khan | High-Resolution Intertidal Topography from Sentinel-2 Multi-Spectral Imagery: Synergy between Remote Sensing and Numerical Modeling[END_REF]) and the Arcachon and Veys Bays (Salameh et al. accepted) located on the Atlantic Façade of the French coast.

Images acquired from radar (SAR) and optical systems can be used as inputs of the waterline method. The main difference between these two types of data is the edge detection technique that is applied to extract waterlines. Waterlines extracted from optical images can be more easily extracted [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF]). However, SAR data are more suited for this method due to the ability of SAR sensors to acquire images in all weather conditions, and during day and night [START_REF] Mason | Measurement of Recent Intertidal Sediment Transport in Morecambe Bay using the Waterline Method[END_REF]) which enables a finer sampling of the tidal range. Previous studies used remote sensing images acquired by a wide variety of SAR (e.g., ERS-1/2, RadarSat-1/2, ENVISAT, JERS-1, COSMO-SkyMed, TerraSAR-X, Sentinel-1 etc.) and optical sensors (e.g., Landsat, IRS, SPOT, IKONOS, Quickbird, MOS-1, Sentinel-2 etc.) to generate intertidal DEMs using the waterline method.

As the waterline method relies on detecting the water/flats interface and on sea level information, it is worthwhile to investigate the performance of the forthcoming SWOT mission to generate intertidal DEMs using this method. SWOT will be the first wide-swath interferometric altimeter that, unlike conventional altimeters, will measure the surface water elevation in 2 dimensions (in wide swaths), providing surface water elevation 4 117 together with water extents (water masks) [START_REF] Durand | The Surface Water and Ocean Topography Mission: Observing Terrestrial Surface Water and Oceanic Submesoscale Eddies[END_REF]. Such measurements allow the extraction of waterlines directly from water masks. Since SWOT will provide SSH information at high accuracy [START_REF] Morrow | Global Observations of Fine-Scale Ocean Surface Topography With the Surface Water and Ocean Topography (SWOT) Mission[END_REF]), height will be associated to waterlines without the need of ground-based measurements or modelling of water elevation which will make this method completely independent from in-situ measurements. In this study, SWOT intertidal DEMs will be generated using SWOT-type observables simulated by the SWOT hydrology toolbox developed by the CNES. The SWOT hydrology toolbox is one of many SWOT simulators developed to help scientists and SWOT data users get familiar with SWOT products and to help them explore and test new methodologies. Such simulators are the SWOT LR (Low Rate mode) ocean simulator and the SWOT HR (High Rate mode) hydrology simulator. The latter was used by [START_REF] Chevalier | High-Resolution SWOT Simulations of the Macrotidal Seine Estuary in Different Hydrodynamic Conditions[END_REF] to assess the accuracy of future SWOT data in the Seine Estuary characterized by a strong hydrodynamic variability. Dealing with SSH-related or dependent measurements in coastal areas using satellite data can lead to sampling and aliasing related difficulties. [START_REF] Turki | On the Investigation of the Sea-Level Variability in Coastal Zones Using SWOT Satellite Mission: Example of the Eastern English Channel (Western France)[END_REF] have investigated the capabilities of SWOT measurements to infer the temporal variability of the sea level along the English Channel coasts (NW France) using statistical approaches. The synthetic SWOT samples simulated from the temporal measurements of water levels and SWOT's orbit showed some problems related to the aliasing frequency which increase with the number of overpasses per repeat orbit. As the waterline method require an adequate sampling of the tidal range, tidal aliasing is expected to present some difficulties for this method as well.

The major issue encountered by the waterline method is the availability of remote sensing images that covers the tidal range in a short period of time. This is crucial in order to avoid the morphological changes that could occur during the period of acquisition. With an observation frequency of 2-3 times within a 21-day period, SWOT has a great potential to provide reliable intertidal DEMs. In this context, SWOT-derived intertidal DEMs were generated for two intertidal bays located on the French Coast: the Arcachon lagoon and the Bay of Veys. In an attempt to study the potential of SWOT to monitor the intertidal topography using the waterline method, the present study focused on examining the impact of the SWOT sampling scheme (orbit) and the acquisition period on the accuracy of the generated DEMs, and the ability of SWOT to detect intertidal topographic changes.

SWOT MISSION

Recommended by the National Research Council decadal survey "Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond" (National Research Council 2007), SWOT mission projected for launch in 2021 will last for at least 3 years. SWOT is a collaboration between NASA and CNES with contributions from the CSA and the UKSA. Its main objectives are to provide surface water topography measurements with a higher coverage and a higher spatiotemporal resolution than conventional altimeters in order to resolve the oceanic mesoscale and submesoscale circulation, and to extend the altimetric coverage to continental surface waters [START_REF] Fu | SWOT : the Surface Water and Ocean Topography Mission : wide-swath altimetric elevation on Earth[END_REF]). SWOT will orbit at an altitude of 890.5 km, on a non-Sun synchronous orbit, and an inclination of 77.6°with 20.86-day repeat cycle [START_REF] Biancamaria | The SWOT Mission and Its Capabilities for Land Hydrology[END_REF]. The mission's main instrument will be a Ka-band Radar Interferometer (KaRIn) operating at a frequency of 35.75 GHz (wavelength of 8.6 mm) [START_REF] Biancamaria | The SWOT Mission and Its Capabilities for Land Hydrology[END_REF]. KaRIn is a bistatic SAR 4. SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT ) system with two antennas at opposite ends separated by a 10-m boom with near nadir look angles between 0.6°and 3.9° [START_REF] Fjortoft | KaRIn on SWOT: Characteristics of Near-Nadir Ka-Band Interferometric SAR Imagery[END_REF]. The two antennas transmit the radar signal and receive the backscattered signal providing observations in a 120 km wide swath (50 km from each side with 20 km gap) [START_REF] Fjortoft | KaRIn on SWOT: Characteristics of Near-Nadir Ka-Band Interferometric SAR Imagery[END_REF]). SWOT's payload includes as well a conventional altimeter that will be used for validation and calibration of the interferometric measurements and will also allow to fill the gap between the swaths [START_REF] Srinivasan | Engaging The Applications Community of The Future Surface Water and Ocean Topography (SWOT) Mission[END_REF]. In contrast to conventional altimetry missions intended to ocean surfaces only, SWOT mission will provide high precision measurements of water surface elevation over oceans, coastal, and inland water surfaces. Rivers larger than 100 m width and lakes (wetlands and reservoirs) of areas greater than 250 km 2 will be resolved with a vertical precision of 10 cm. Over terrestrial and coastal waters, SWOT will provide water elevation, slope, and water mask measurements [START_REF] Biancamaria | The SWOT Mission and Its Capabilities for Land Hydrology[END_REF]).

STUDY SITES

The current study was executed by generating SWOT-derived DEMs over two intertidal bays located on the French Coast (Figure 4.1): the Arcachon Bay and the Bay of Veys. The former is a shallow mesotidal coastal lagoon located in the southeastern part of the Bay of Biscay and the latter is a shallow estuarine embayment located on the southern shore of the English Channel.

ARCACHON BAY

The tides in the Arcachon Bay are semi-diurnal with a weak diurnal inequality and a tidal range that can reach up to 4.6 m during spring tides. The bay receives freshwater from rivers, canals, and groundwater. The Eyre River and the Porges Canal are the major freshwater tributaries contributing about 73% and 24% of the total annual freshwater inputs, respectively [START_REF] Plus | Hydrodynamic characterization of the Arcachon Bay, using model-derived descriptors[END_REF]). The surface of the intertidal area uncovered at low tides is about 115 km 2 . These intertidal flats are composed of a mix of muddy and sandy material and a large area (70 Km 2 ) of the flats are vegetated by Zostera noltii seagrass [START_REF] Blanchet | Structuring factors and recent changes in subtidal macrozoobenthic communities of a coastal lagoon, Arcachon Bay (France)[END_REF][START_REF] Proença | Potential of High-Resolution Pléiades Imagery to Monitor Salt Marsh Evolution After Spartina Invasion[END_REF]. They are drained by tidal creeks and channels with a maximum depth around 20 m [START_REF] Deborde | Role of tidal pumping on nutrient cycling in a temperate lagoon (Arcachon Bay, France)[END_REF].

BAY OF VEYS

The Bay of Veys is located in a semidiurnal macrotidal environment with a tidal range that reaches 8 m at spring tides [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF]. Several coastal streams and four main rivers (the Aure, the Douve, the Taute, and the Vire) contribute to the freshwater input into the bay [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF][START_REF] Lafforgue | Modelling of enterobacterial loads to the Baie des Veys (Normandy, France)[END_REF]). The Vire is the largest river flowing directly into the bay and provides 40% of the freshwater input [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF]. At low tides, the surface of the uncovered intertidal flats is about 37 km 2 [START_REF] Grangeré | Modelling the influence of environmental factors on the physiological status of the Pacific oyster Crassostrea gigas in an estuarine embayment; The Baie des Veys (France)[END_REF][START_REF] Timsit | Évolution du macrozoobenthos intertidal de la baie des Veys de 1985 à 2000[END_REF]) with a lower part devoid of vegetation and covered by muddy and sandy sediments and an upper part (near the land) colonized by halophytic species dominated by Spartina anglica [START_REF] Deroin | Combining ALOS and ERS-2 SAR data for the characterization of tidal flats. Case study from the Baie des Veys, Normandy, France[END_REF][START_REF] Timsit | Évolution du macrozoobenthos intertidal de la baie des Veys de 1985 à 2000[END_REF]).

INTERTIDAL DEMS

The intertidal DEMs used here were generated in a recent study (Salameh et al. accepted) by the waterline method using Sentinel-1 and Sentinel-2 images. The datasets are provided on a regular 10 ×10 m grid. The DEMs were generated for each year using images acquired between the first of June and the end of September.

SEA LEVEL INFORMATION

Sea level information used in this study were recorded by the Arcachon-Eyrac tide gauge (1.163550021°W and 44.66500092°N) for the case of the Arcachon Bay.

The Arcachon-Eyrac tide gauge has been operational since November 1967 and is currently managed by the French hydrographic service (SHOM) and the Gironde sea and land state office (DDTM). Since February 2010, the tide gauge is equipped with an Optiwave 7300C sensor and a MARELTA acquisition unit (REFMAR 2012). Sea level measurements are 120 4. SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT )

provided at 1-minute intervals. The data are made available by REFMAR and can be found online on the SHOM data website: https://data.shom.fr/ For the Veys Bay and due to the lack of tide gauge records, sea level data were extracted from the HYCOM model output [START_REF] Baraille | Modèle shallow-water multicouches isopycnal de Miami[END_REF]. This ocean circulation model is a joint effort between SHOM and Météo-France as part of the HOMONIM project, which aims to improve the coastal flood warning system in metropolitan and overseas France (SHOM 2016a). Forced by tides (predicted by the SHOM), winds and atmospheric pressure (obtained from Météo-France meteorological models) [START_REF] Pasquet | Implémentation d'un nouveau modèle opérationnel de prévision des vagues et surcotes marines[END_REF]), the SHOM model simulates the sea level (tide and surge) on a curvilinear grid and a resolution that ranges between 2 km and 500 m when approaching the French coast. Different configurations of this model exist depending on the geographic domain of the region. Data used here were simulated by the ATL (Atlantic) configuration covering the French Atlantic façade and the English Channel between 43°N 9°W and 62°N 10°E. Hourly gridded forecasts of sea level are provided by the SHOM. However, sea level data were extracted from a single grid-point located at the mouth of the Bay of Veys and interpolated to a 1-minute interval.

METHODS

The current investigation aims to evaluate the performance of SWOT to generate intertidal DEMs by using the waterline method. SWOT-type observables needed for applying the waterline method were simulated by the SWOT hydrology toolbox. In this section, a brief description of the waterline method will be given, followed by a presentation of the SWOT Hydrology toolbox. Then, a step-by-step explanation of the methodology used to generate SWOT-derived DEMs using the waterline method will be provided.

THE WATERLINE METHOD

The method consists in detecting the waterline (shoreline) edge of remotely sensed images using image processing techniques. Heights are then attributed to waterlines using water level information obtained either from a hydrodynamic tide/surge model outputs over the observed area at the time of acquisition of the image or from tide gauge measurements [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF]. From a series of images providing adequate sampling of the tidal range, a set of waterlines is assembled and then interpolated to form a gridded-DEM. A detailed description of this method can be found in [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF] and [START_REF] Heygster | Topographic Mapping of the German Tidal Flats Analyzing SAR Images With the Waterline Method[END_REF]. As mentioned earlier, the waterlines are extracted from remote sensing images using edge detection techniques which is also a valid option for SWOT (by using SWOT SAR images). However, SWOT will provide water mask measurements from which waterlines can be extracted directly without prior processing. These water masks SWOT-type observables can be simulated by the SWOT Hydrology toolbox.

SWOT HYDROLOGY TOOLBOX

The SWOT hydrology toolbox is developed by the CNES to simulate, jointly with RiverObs developed by the JPL, SWOT-type virtual (HR) data. The objectives behind this software and other SWOT simulators are to provide open source tools for end-users to simulate and get familiar with SWOT products and to test or propose methodologies that could use SWOT data.

SWOT-DEM GENERATION

Different scenarios were simulated in this study. In this sub-section, we will present the methodology used to generate a SWOT-derived DEM from the waterline method, accompanied by the results obtained for the first scenario simulated for the Arcachon Bay (A01 -mission start time: 01/01/2016 00:00:00; simulation start time 01/06/2016 00:00:00; simulation end time: 01/10/2016 00:00:00). The methodology steps are the following:

• Determination of all ascending and descending orbits that have swaths containing the area of interest using the orbit selection module of the SWOT hydrology toolbox. This module takes as input the theoretical SWOT's orbit, the bounding box of the area, the mission start time, and the simulation start and end time. This first simulation will determine the SWOT's orbits and cycles that have swaths containing the study area between the simulation start and end time. The results obtained of this first step for the A01 test are shown in Table 4.1. Each run in Table 4.1 is a pass of SWOT over the study area between the simulation's start and end times.

• Assigning water elevation to SWOT's passes using sea level information extracted at the exact time of the satellite overflight of the area. Sea level heights are also shown in Table 4.1. The tidal coverage provided by SWOT during the acquisition period is shown in Figure 4.2.a.

• Generating water masks shapefiles from the DEM and the water elevation of SWOT's passes (DEM's pixels lower than the water elevation correspond to the water mask).

The approximation made here is that the water elevation in the Bay is constant.

• Simulating the pixel cloud (with realistic errors) which consists in water pixels with geolocated heights using the large-scale simulator (sisimp) of the toolbox. A simulation was made for each run in Table 4.1. This module takes as input the cropped orbits from the orbit selection module, the water mask, and the water elevation.

• Production of water masks shapefiles with their corresponding water elevation from the simulated pixel clouds (of each run) using the Lake processing module LOCNES (Lake Observation Cover aNd Extent from SWOT). The Lake processing module was convenient for usage in this study because the water elevation in the Bays was considered as constant similar to a lake, and both of our study sites are located within the SWOT's HR mask.

• Extracting the waterlines from the simulated water masks. The waterlines are the perimeters of the water masks.

• Assigning water elevation of the water masks simulated by the Lake processing module to the waterlines. Examples of three levelled waterlines are presented in Figure 4.2.b.

• Assembling (Figure 4.2.c) and interpolation of the waterlines to generate the SWOTderived DEM (Figure 4.2.d) using the kriging method [START_REF] Matheron | Principles of geostatistics[END_REF]. Kriging was performed using the Gstat software [START_REF] Pebesma | Multivariable geostatistics in S: the gstat package[END_REF][START_REF] Pebesma | Gstat: a program for geostatistical modelling, prediction and simulation[END_REF] on grids of 10-m resolution covering the study area.

RESULTS AND DISCUSSION

The general aim of this study is to investigate the performance of SWOT in generating DEMs of intertidal zones using the waterline method. In section 4.5, we presented the methodology for generating a SWOT-derived DEM using the SWOT Hydrology Toolbox. As stated earlier, the assessment of SWOT's performance relies on studying the impact of the SWOT sampling (i.e. SWOT's orbit), the acquisition period, and SWOT's measurement error (vertical error), on the accuracy of the SWOT-derived DEMs. The sampling of the waterlines depends on the repeat orbit patterns of the satellite which varies with the mission start time. Therefore, in order to examine the impact of SWOT's sampling on the accuracy of the generated DEMs, a set of simulations were achieved with the same acquisition period (4 months -between June and September) but with different mission start times. The generated DEMs were compared to the original DEMs by computing the MAEs and RMSEs. The DEM with the lowest error was then used to study the impact of the acquisition period. This was done by simulating other DEMs with shorter and longer acquisition periods but with the same mission start time (that corresponds to the DEM with the lowest error). Finally, the ability of SWOT to detect topographic changes was assessed by generating SWOT intertidal DEMs for 2017 and 2018 in order to create DoD maps (a qualitative comparison between Sentinel-derived and SWOT-derived DoDs is provided). Figure 4.4 shows another limitation that SWOT could face while using the waterline method. We can see that the bay is well covered on one side and waterlines are missing on the other side which is due to the swath of orbit #348 cutting the bay in half (Figure 4.1). This also implies that the unfavorable aliasing originates from the other orbits and not from orbit #348 because this orbit is covering well the other part of the bay. The SWOT-derived DEMs for tests A02 and A04 are shown in f. High errors are located in the right side of the Bay where waterlines were missing. For A02 test, high errors were observed over the "Iles aux Oiseaux" island where the topography is higher than the highest detected waterline. A higher waterline was detected for the A04 test, which explains the lower errors over the island. Figure 4.5 shows the comparison between the original DEM and the SWOTderived DEMs for tests A02 and A04.

Figure 4.6 shows the tidal coverage provided by SWOT for V01 and V06 tests. For V01, the sampling of the tidal range is almost complete and with a good regularity while for V06 a considerable water level range is not covered. This is also apparent in the and a varying simulation start times (in order to change the acquisition period from 4 months to 2, 3, 5, 6, and 7 months). By comparing to the original DEMs, we have demonstrated that SWOT mission is capable of generating accurate intertidal DEMs. However, the DEMs accuracy is strongly dependent on the mission start time (orbit) and the accuracy may decrease due to an unfavorable aliasing. MAEs varied between 5.2 cm and 19.5 cm for the Arcachon Bay and between 11.6 cm and 28.4 cm for the Veys Bay. From shortening and extending the acquisition period we also showed that (i) the acquisition period could be reduced to 3 months and still provide relatively accurate measurements and (ii) improvement in accuracy could be made by extending the acquisition periods and adding more waterlines. However, adding waterlines is preferred to be made by importing data from other sensors while keeping the same short acquisition period, rather than extending it and making the DEM more prone to errors due to topographic changes that may occur.

These findings confirm the benefits of SWOT in monitoring intertidal areas. In addition to sea surface height, SWOT will be able to generate not one but several intertidal DEMs during a year. Thus, seasonal and interannual topographic changes could be quantified. However due to unfavorable aliasing between the orbit and the tides, the best sampling within a year could occur in different periods for different years. Therefore, care must be taken when choosing the acquisition periods of SWOT to generate intertidal DEMs if no external data from other sources were used to complete the tidal range sampling. Furthermore, with SWOT providing water heights in 2D (water heights and water extents), the waterline method will be executed far more easily than before while taking into account the water slope which will improve the accuracy of the generated DEMs.

I NTERTIDAL flats often found in embayments, lagoons, estuaries, deltas, but also on open coasts, constitute one of the most extensive coastal ecosystems [START_REF] Fan | Open-Coast Tidal Flats[END_REF][START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF]). These environments provide highly valuable services to human society by stabilizing the shoreline, providing shelter and protection from coastal flooding (by dissipating wave energy), providing goods (mussels, bivalves and other molluscs, which are harvested as food), acting as a Carbon sink, and by naturally trapping sediments and filtering water [START_REF] Costanza | The value of the world's ecosystem services and natural capital[END_REF]Millennium Ecosystem Assessment 2005;[START_REF] Nicholls | Coastal systems and low-lying areas[END_REF]. They have as well a great ecological importance as they support coastal biodiversity providing habitat for a large community of vegetation and wildlife species [START_REF] Costanza | The value of the world's ecosystem services and natural capital[END_REF][START_REF] Martínez | The coasts of our world: Ecological, economic and social importance[END_REF].

Intertidal flats are threatened by human activities (habitat destruction, pollution, hydrological alteration, overexploitation) and climate change (sea level rise, changes in temperature, changes in rainfall patterns, increase in extreme events) [START_REF] Murray | The global distribution and trajectory of tidal flats[END_REF]. Another indirect threat is the lack of information and data measurements essential for understanding, managing, protecting, and finding optimal solutions between exploitation and preservations of these environments. This requires a continuous monitoring of the morphological evolution of these systems, which can be performed by regularly measuring the topography in intertidal areas.

Mapping the topography in intertidal areas can be performed using ground-, airborne-, and spaceborne-based techniques. However, a cost-effective large-scale continuous monitoring is only possible using spaceborne-based techniques. Different methods were developed and used for this purpose that make use of SAR and optical images. New remote sensing technologies opened the way for bringing improvements to the developed methods and for using new data sources such as satellite radar altimetry measurements. The latter is a technique intended originally to measure ocean surface topography along the nadir track of the satellite. Near the coasts, data acquisition and processing suffer from several flaws. However, new satellite radar altimetry technologies operating in ka-band and SAR mode increased the potential of this remote sensing tool in coastal areas. Monitoring coastal areas with radar altimetry will be taken to the next level with the future wide-swath SWOT altimetry mission designed to provide 2D maps of water surface topography in high resolution over ocean, coastal, and inland areas. New SAR, optical, and altimetry technologies along with SWOT are thus very valuable data sources for the monitoring of coastal intertidal areas.

With the growing demand for updated intertidal topography datasets, and for what it's worth to coastal research and coastal management, the main objectives of this thesis were to explore and improve spaceborne-based remote sensing methodologies using recent technologies, and to investigate the potential of the future SWOT mission, for monitoring the topography in intertidal areas. This thesis is part of the SWOT mission and the SWOT COTEST project (Characterization, Modeling and SWOT Potentiality to Measure Hydro-meteo-marine Phenomena in the Coastal and Estuarine Systems) in the framework of the TOSCA (Terre Solide, Océan, Surfaces Continentales et Atmosphère) program of CNES, with one of the axes of which concerns the coupling of SWOT and current satellite missions for observing coastal areas.

Methodologies developed or used in this work were applied for the intertidal zones of two bays: The Arcachon Bay and the Bay of Veys. Both bays are located on the French Atlantic Façade. The two study sites present some contrasted characteristics. The Arcachon Bay is a sheltered lagoon with extensive muddy flats where tides enter the system through two tidal inlets while the Bay of Veys is an exposed embayment with a mix of muddy and sandy material, with abundant presence of sand. First, satellite radar altimetry capabilities were explored by assessing its performance to monitor SSH and intertidal topography in the Arcachon Lagoon. Second, improvements were implemented to the waterline method, the most commonly used method for generating intertidal gridded-DEMs, by using recent SAR (Sentinel-1) and MSI (Sentinel-2) sensors (carried out in the Arcachon Bay and the Bay of Veys). Finally, the potential of SWOT to monitor topography using the waterline method was assessed for the two studied sites, which allowed us to make projections for the future, concerning the monitoring of intertidal areas' topography using spaceborne remote sensing observations. These studies allowed us to answer the research questions presented in the introduction chapter of this thesis, and they are the following:

1. Thanks to the use of ka-band and the SAR mode, Satellite radar altimetry is capable to extract intertidal topography profiles with an accuracy that can reach 0.23 m.

2. Satellite altimetry is not able yet to automatically separate emerged and submerged measurement points in intertidal areas based on altimetry intrinsic parameters (Sigma0 and Peakiness). However, an automatic separation between acquisitions made at low and high tides can be performed.

3. The waterline method produced accurate intertidal DEMs for the Arcachon and Veys Bays using Sentinel-1 and -2 images with an accuracy that reached 19 cm. The good accuracy resulted from the fine sampling provided by Sentinel-1 and -2.

4. Thanks to a new edge detection technique developed during this thesis, the amount of manual interventions using the waterline method were significantly reduced.

5. The waterline method is suitable for morphological changes monitoring over relatively small-scale intertidal environments such as the Arcachon Bay and the Bay of Veys. Arcachon and Veys Bays experienced a net erosion between 2016 and 2018.

6. Using the waterline method, SWOT is able to provide very accurate intertidal DEMs with an accuracy that can reach 5 cm. SWOT's accuracy is however dependent on the chosen period of acquisition related to SWOT's orbit characteristics.

7. With the right acquisition period that provides a complete sampling of the tidal range, SWOT has an important potential in detecting topographic changes in intertidal areas.

Detailed conclusions for these three research studies are given below.

Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay.

The study consisted in investigating, for the first time, the capability of satellite altimetry to extract intertidal topographic profiles along the altimeters ground tracks. The investigation was made with observations acquired over the Arcachon lagoon by four altimeters: ERS-2 (Ku-band; LRM mode), ENVISAT (ku-band; LRM mode), SARAL (ka-band; LRM mode), and CryoSat-2 (ku-band; SAR mode). The study also included an examination of the performance of altimetry to measure the SSH in coastal lagoons and an attempt to automatically discriminate emerged measurement points from the submerged ones, using intrinsic altimetry parameters (backscattering coefficient and Peakiness). By comparing altimetry measurements to tide gauge and LiDAR data, it is found that satellite altimetry is able to retrieve SSH and topographic variations in intertidal zones with accuracies that can reach 0.22 and 0.23 m respectively.. The use of Ka-band and SAR mode improved the measurements accuracy for SSH and enabled the monitoring of topography. This comes from the reduced footprint area (∼6 km) of SARAL (because It operates in the ka-band and it has a larger bandwidth of 480 MHz) and the reduced footprint size in the along-track direction for CryoSat-2 (due to the usage of SAR mode). However, the auto-discrimination cannot be performed, point by point, using only the backscattering coefficient and the Peakiness parameters. The most important limitation lies in the large footprint of altimeters.

Nevertheless, a successful auto-discrimination was performed between acquisitions made during low tides from acquisitions made during high tides. This is due to the good contrast obtained for the mentioned parameters at the scale of the bay between low and high tides.

Intertidal topography mapping using the waterline method from Sentinel-1 & -2 images: the examples of Arcachon and Veys Bays in France.

After exploring satellite radar altimetry capabilities in intertidal areas, we went for studying imaging systems that can acquire spaceborne-images which enables the generation of gridded intertidal DEMs rather than extracting topography profiles. For this purpose, the study consisted in improving one of the most common remote sensing-based method for intertidal topography monitoring, the waterline method, using Sentinel-1 (SAR) and Sentinel-2 (MSI) images. The waterline method consists in extracting waterlines (water/flats interface) from remote sensing images, assigning heights to the extracted waterlines using sea level information, assembling of waterlines, and interpolation. It was applied for two intertidal bays, the Arcachon Bay and the Bay of Veys. The waterline method considers the intertidal areas as static during the acquisition period. Therefore, it is very important to use images extracted during a short period of time to avoid major topographic changes. This study showed that the use of Sentinels observations enables a complete sampling of the tidal range in less than 4 months. Traditionally, the waterline method suffered not only from insufficient number of satellite images, but also from the subjective satellite-image thresholding required in the edge detection process, and the long post-processing (sometimes manual) of the extracted waterlines prior to interpolation. A new edge detection technique was developed in this study to overcome these difficulties, accompanied by an automatic procedure to eliminate noisy SAR images and excluding them from further processing. This technique which is able to extract waterlines from SAR and MSI images is based on a combination between k-means-based segmentation and an active contouring process, and it was designed to create closed contours (objects). The subjective thresholding was avoided by segmenting the image using the k-means clustering algorithm. The post-processing of waterlines was automatized thanks to the extraction of waterlines as closed contours and it enabled: (i) the automatic removal of intersecting (intertwining) part of waterlines performed manually in previous studies and (ii) the automatic selection of the most suitable waterline from a set of redundant waterlines (waterlines with similar heights). The latter was made based on the number of waterlines' objects (the waterline with least objects was kept) and thus allowed a second-degree removal of intermediate-quality images presenting some noisy features, which were not eliminated in the first elimination process. Therefore, by using this method there is no need for manual selection of images and manual modification of the extracted waterlines. Using the enhanced waterline method, intertidal DEMs were generated with an error of about 19 to 25 cm. Furthermore, the study confirmed the ability of the waterline method to measure topographic changes in the Arcachon and Veys Bays using Sentinel-1 and Sentinel-2 images where significant erosion and deposition volumes were detected.

Monitoring intertidal topography using the waterline method with the SWOT mission.

We studied the performance of the future SWOT mission to monitor intertidal topography using the waterline method. With its ability to provide water heights in 2D, SWOT will provide valuable data input for the waterline method. SWOT's performance was assessed by generating intertidal DEMs from SWOT-type observables simulated using the SWOT Hydrology Toolbox developed by the CNES. The study showed that SWOT is capable of generating intertidal DEMs with very good accuracy. However, this accuracy is dependent on the sampling scheme (SWOT's orbit) and could be ameliorated using waterlines extracted from other remote sensors. The acquisition period to generate reliable DEMs using only SWOT data can reach 3 months which indicates that several DEMs could be generated in a year. Therefore, and owing to the good accuracy provided by SWOT, this mission has a great potential to follow seasonal and interannual topographic changes in intertidal areas. It should be noted that using SWOT data, the water slope will be accounted for when sea level information will be assigned to waterlines as SWOT measures water heights in 2D.

Monitoring topographic changes.

The repeatability and the continuous monitoring provided by spaceborne-based remote sensing missions is a key point for estimating topographic changes. From the DEMs constructed for the consecutive years or seasons, DoD maps showing morpho-sedimentary evolution can be generated. These maps will show stable intertidal areas and patterns of erosion and deposition that occurred in the period that separates the compared DEMs. The intertidal zone of the Arcachon Bay showed a stable behavior with small patterns of erosion and deposition distributed in the intertidal zone. Concerning the Bay of Veys, adjacent erosion and deposition zones located along the channels were observed. This localization may indicate a migration of the channels between the observed years. The DoD maps enabled also the computation of the sediment budget between 2016 and 2018 for both Bays. Between 2016 and 2018, the Arcachon Bay and the Bay of Veys experienced net volume losses of 1.12 × 10 6 m 3 and 0.70 × 10 6 m 3 respectively. It should be noted that although the net changes observed in Veys Bay were smaller, the magnitude of the changes during the observation period was greater in Veys Bay. Regarding SWOT mission, it was also able to detect topographic changes patterns once a favorable acquisition period that provides adequate sampling of the tidal range was chosen.

OUTLOOK

This research has shown the usefulness of recent and future spaceborne remote sensing missions for monitoring the topography in intertidal areas. In this study, topographic maps were generated for the intertidal areas of the Arcachon Bay and the Bay of Veys (all previous studies were local as well). With the increasing number of free Earth observation products (e.g., Sentinel products) and the introduction of new tools that can process huge amounts of data (e.g. Google Earth Engine), it is now more than ever possible to generate intertidal topography products on a larger scale (e.g. continental). This can be done with the methods presented here but also with other satellite-based methods such as InSAR and stereoscopy. The latter methods and the ones presented in this study are all direct methods. The use of inverse methods that can retrieve topography from images acquired (SAR or optical) at high tide could bring a lot more to the table. A lot of studies investigated the capabilities of inverse methods in shallow waters but testing their abilities in intertidal areas (very shallow) is still lacking. One algorithm that is able to use all these methods depending on the available data products may be the ultimate aim. With the rapid evolution of machine learning techniques, the pixels in the acquired images can be accurately classified (water, flats, sand, rocks, etc.) which can help choosing the method, depending on the data type and its classification scheme. For instance, an automatic classification that results in dividing the image between intertidal pixels and shallow water pixels instruct the algorithm to use an inverse method for the inundated pixels and a direct method for the uncovered ones from multiple data sources provided as input.

Furthermore, the ability of spaceborne-based methods to regularly provide topographic maps open the door for a lot of scientific applications. For instance, the waterline method allows us to monitor topographic changes that occurred in the last decades by using satellite images archives and relating them to climatic factors or hydrodynamic processes. Furthermore, storms impact assessment could be made by generating intertidal DEMs before and after storm events. Knowing the topography and water levels (from altimetry acquisitions) allows also the computation of other parameters such as water exchange volumes between the ocean and intertidal bays. In the context of climate change, sea level rise, and intensification of storms, coastal zones will undergo profound changes that will need to be monitored and understood. Generating accurate intertidal DEMs by coupling various types of remote sensing data (imagery, altimetry, etc.) will be very beneficial for morphodynamic and hydrodynamic modelling. Regarding hydrodynamic modelling, accurate intertidal DEMs (that can be coupled to other bathymetric and topographic datasets) will enable the quantification of fine coastal processes such as the run up in swash zone and infragravity waves. The generated DEMs provide as well useful and needed information for authorities and stakeholders for coastal management and implementation of ecosystem protection policies.

The use of radar satellite altimetry was proven here to be able to provide valuable information for intertidal environments. [START_REF] Salameh | Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay[END_REF] is the very first study that tackled this subject and proved the ability of satellite altimetry to extract intertidal topographic profiles in the Arcachon Bay. Therefore, the next step that should be taken is to prove the quality of altimeters again in other intertidal environments, such as the Bay of Mont-Saint-Michel and the Seine Bay ("Vasière Nord") in France Normandy, and the Minas Bay in Fundy Bay Canada (highest tidal range in the world). These intertidal environments are overflown by different altimeters, and assessing the performance of altimetry over these specific study sites is very helpful for the purpose of creating a more complete understanding of altimetry's capabilities in intertidal areas due to the contrasted characteristics they present: size (3.2 km 2 for Seine; 117 km 2 for Arcachon; 242 km 2 for Mont-Saint-Michel; 400 km 2 for Minas Bay in Fundy), type of materials (mud/sand for Seine; mainly muddy for Arcachon; sand/mud for Mont-Saint-Michel and Minas Bay in Fundy Bay), and tidal regime (macrotidal for Seine, Mont-Saint-Michel and Fundy; mesotidal for Arcachon).

For topography monitoring purposes, we recommend the use of radar altimetry in areas exposed frequently to water. Therefore, dry uncovered areas of intertidal flats such as small islands that could be found inside the intertidal areas or beaches around it should be excluded because they are prone to EM wave penetration and thus erroneous elevation measurements. Otherwise, the penetration should be accounted for (see Appendix D).

Regarding the auto-discrimination between emerged and submerged measurement points (measurements over flat or over water surfaces), a focus must be made on analyzing the altimetry waveforms (rather than or in combination to the backscattering coefficient and Peakiness) in order to efficiently classify the measurement points. Radar altimetry provided relatively accurate measurements in the intertidal area of the Arcachon Bay, yet more accurate measurements may be provided by the laser altimetry mission ICESat-2.

This mission can provide data with very high spatial resolution (with measurements every 0.7 m comparing to 175 m at best for altimetry) and it must be tested because it can be useful for calibration and validation of other methods used in remote sites where there is no in situ measurements.

Since its introduction by [START_REF] Mason | Construction of an inter-tidal digital elevation model by the 'water-line' method[END_REF], the waterline method has seen a lot of improvements. Its use is now more interesting than ever with the huge amounts of available data. With this amount of data that sometimes surpass our need (for the usage of the waterline method), it is essential to tackle these questions: what is the optimal number of images? what is the best sampling rate in case of huge number of images? how the optimal number and the sampling rate change with the scale of the site and the topography slope? and on what criteria the selection of images should be based? Another important aspect that concerns the waterline method is the edge detection technique. Since 1995, several edge detection techniques were proposed and used to extract waterlines. However, no comparison studies were made between the different proposed methods. We think that this is a crucial study that should be made in order to converge towards the best accuracy-wise and time processing-wise and completely automatic approach to use. We also recommend the distribution of the developed edge detection algorithms in order to facilitate and motivate the usage of the waterline method. This will render its use more practical and will help in generating more topographic maps for scientific or comparison purposes.

The waterline method has been used for quantifying topographic changes. In this study we demonstrated its ability to detect significant changes over our study sites and using Sentinels data. Quantifying topographic changes was also performed in previous studies. However, the observed changes obtained by the waterline method were never validated using changes obtained by another more accurate method such as airborne LiDAR. This work is also essential to prove that changes observed are related to real changes and not to method deficiencies.

Certainly, SWOT will be beneficial for the waterline method as confirmed in this study. However, a focus must also be made on SWOT interferometric abilities as SWOT is an interferometer. Its ability to provide accurate interferometric measurements over tidal flats has more advantages comparing to the waterline method. One pass over a study site at low tide will be sufficient to generate a topographic map. Thus, less images will be needed, and more topographic maps could be created without the errors that could be introduced from topographic changes.

D EM WAVE PENETRATION DEPTH IN SAND

The penetration depth (δp) of an EM wave in an homogeneous medium can be expressed as a function of its dielectric permittivity. According to [START_REF] Ulaby | Microwave Remote Sensing: Active and Passive[END_REF], it can be written as follows:

δ p = λ ε′ 2πε ′′ (D.1)
where λ is the wavelength of the EM wave, ε′ and ε ′′ are the real and complex parts of the dielectric permittivity respectively. Empirical relationships between dielectric permittivity (ε) and soil nature and its water content were established. In this study, we used the empirical relationships from [START_REF] Hallikainen | Microwave Dielectric Behavior of Wet Soil-Part 1: Empirical Models and Experimental Observations[END_REF] that have the following form: 2 in [START_REF] Hallikainen | Microwave Dielectric Behavior of Wet Soil-Part 1: Empirical Models and Experimental Observations[END_REF]. Maximum penetration depth are obtained for dry soils (i.e., m v = 0). Equation D.1 becomes:

max(δ p ) = λ a 0 ′ + a 1 ′S + a 2 ′C 2π a ′′ 0 + a ′′ 1 S + a ′′ 2 C (D.3)
Over the sandbank known as "île aux oiseaux", we consider S = 100 and C = 0. This latter equation becomes:

max(δ p ) = λ a 0 ′ + 100a 1 ′ 2π a ′′ 0 + 100a ′′ 1 (D.4)

E TIDAL ALIASING

Satellites are in constant rotation around the Earth in a repetitive orbit. A satellite altimeter provides a time series (discrete sequence of values) of ocean surface level variations with a period equal to N days. This implies that a measurement of sea surface height at a given location can only be made every N days. A continuous signal of period T can only be completely reconstructed from discrete values if these values are sampled at a frequency greater than 2/T (Nyquist frequency). If the sampling interval is greater than T/2 then the signal of frequency 1/T becomes aliased. In the case of satellite altimetry, this aliasing phenomenon is therefore related to the satellite's revisit period.

How the tidal aliasing affects the SWOT generated DEM's using the waterline method? For the waterline method, we need a series of satellite images taken at different tidal stages. These images must cover the tidal range completely in order to get an accurate DEM from the extracted waterlines. The tidal aliasing affects the sampling scheme provided by the satellite. It could result in: (i) missing images (waterlines) for high tides, low tides, or both, (ii) high sampling for a given interval of the tidal range while no acquisitions are made for other intervals (Figure E.1).

  )). 19 6 Global trajectory in the extent of tidal flats (Source: from Murray et al. (2019)). 20 7 Passive and active remote sensing. from lidar Remote Sensing and Applications (Source: from Dong and Chen (2018)). . . . . . . . . . . . . . . . . 21 8 A diagram illustrating the swaths of data that SWOT will collect. The interferometer will produce two parallel tracks, with a Nadir track from a traditional altimeter in the gap between the swaths. The overall width of the swaths will be approximately 120 km. . . . . . . . . . . . . . . . . . . . . . . . . 23 1.1 (a) Satellite image of Western France (source: Google Earth Pro 2018) showing the location where the Pleiades stereo pair was obtained (orange rectangle located in southwest France) on November 14, 2017; (b) Zoom in of the Pleiades mosaic showing the area where the LiDAR airborne topographic survey was carried out (green dotted line polygon) and the area where RTK-GPS topographic measurements were taken; (c) The RTK-GPS survey lines (in red) and a photograph of the surveyor with the mobile GPS unit (from Almeida et al. (2019)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.2 Three beach profiles showing the comparison between RTK-GPS, Pleiades (PL1A) and LiDAR, showing the erosion of the berm that occurred between the LiDAR survey and RTK-GPS and Pleiades (from Almeida et al. (2019)). . . 31 1.3 (a) Waterlines extracted over the German part of the Wadden Flats for 1998; (b) Intertidal topographic map obtained after interpolation. Standard deviation at each grid point through the years from 1996-1999 and 2006-2009 for (c) Tertiussand, (d) Gelbsand, and (e) Medemsand. Adapted from Heygster et al. (2010) and Li (2014). . . . . . . . . . . . . . . . . . . . . . . 33 xv 2.7 Comparisons between in-situ and altimetry-based SSH for ERS-2 (a,b), ENVISAT (c,d), SARAL (e,f), and CryoSat-2 (g,h) using two different approaches for selecting the valid measurements: MAPS manual selections (left) and automatic selections (right). . . . . . . . . . . . . . . . . . . . . . . . . 71 2.8 Comparisons between LiDAR and Altimetry-based topography measurements for: (a) ERS-2, (b) ENVISAT, (c) SARAL, and (d) CryoSat-2. . . . 72 2.9 Spatial variation of the backscattering coefficient for SARAL (cycle 20) at low tide along with the corresponding waveforms of the indicated zones. . . . . . 75 2.10 Spatial variation of the backscattering coefficient for SARAL (cycle 2) at high tide along with the corresponding waveforms of the indicated zones. . . . . . 75 2.11 Spatial variation of the backscattering coefficient for CryoSat-2 (cycle 2) at low tide along with the corresponding waveforms of the indicated zones. . . . 76 2.12 Spatial variation of the backscattering coefficient for CryoSat-2 (cycle 5) at high tide along with the corresponding waveforms of the indicated zones. . . 76 3.1 (a) An overview map with the location of the study sites: (b) the Arcachon Bay and (c) the Bay of Veys. (b) and (c) include the intertidal flats and the rivers and canals flowing into the two bays. . . . . . . . . . . . . . . . . . . . . . . . . 83 3.2 LiDAR-derived DEMs used for validation for the (a) Arcachon Bay (extracted from the RGE ALTI® product provided by the IGN) and (b) the Bay of Veys (extracted from the NHDF (lidar Normandie Hauts-De-France) 2016-2017 V.20180501 product provided by the SHOM (SHOM-ROLNP 2018). Heights are referenced to the French Reference System NGF/IGN69 datum. . . . . . . 87 3.3 A step by step overview of the methods used in this study to generate DEMs using the waterline method along with the corresponding sections. . . . . . . 88 3.4 Averaged histograms of each class obtained by classifying the images' histograms using k-means algorithm. . . . . . . . . . . . . . . . . . . . . . . . . 90 3.5 Examples of noisy SAR images acquired over the Arcachon Bay with histograms corresponding to: a) class 5 and b) class 6. . . . . . . . . . . . . . . 90 3.6 The different steps of the edge detection technique that combines a k-means segmentation process with a snake active edge contouring algorithm. . . . . . 92 3.7 Examples of redundant waterlines with quasi-same height and different number of polygons. Waterline #2 presents the least number of polygons. . . 95 3.8 Comparisons between the LiDAR-derived DEM and the 2016 waterline-derived DEMs for the Arcachon Bay generated using: (a) IDW interpolation and tide gauge levelling; (b) kriging interpolation and tide gauge levelling; (c) IDW interpolation and single point model levelling; (d) kriging interpolation and single point model levelling; (e) IDW interpolation and complete grid model levelling; (f) kriging interpolation and complete grid model levelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.9 Comparisons between the LiDAR-derived DEM and the 2017 waterline-derived DEMs for the Veys Bay generated using: (a) IDW interpolation and single point model levelling; (b) kriging interpolation and single point model levelling; (c) IDW interpolation and complete grid model levelling; (d) kriging interpolation and complete grid model levelling. . . . . . 99 LIST OF TABLES 1.1 Comparison of methods for mapping the bathymetry of shallow waters and the topography of their adjacent beaches. . . . . . . . . . . . . . . . . . . . . . 51 2.1 Main characteristics of the altimetry missions used in this study. . . . . . . . . 59 2.2 Passing-Bablok regression model and statistical results for the comparisons made between in-situ and altimetry-based SSH (ERS-2, ENVISAT, SARAL, and CryoSat-2) for manual (MAPS) and automatic selections. . . . . . . . . . . . . 72 2.3 Passing-Bablok regression model and statistical results for the comparisons made between LiDAR and altimetry-based topography estimation for ERS-2, ENVISAT, SARAL, and CryoSat-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.1 The number of available Sentinel-1 and Sentinel-2 images for Arcachon and Veys Bays between 2015 and 2018 and the number of eliminated images due to unavailable sea level information, noisy (SAR) or cloudy (MSI) images, and images with redundant water level. . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.2 Topographic changes in terms of surface (km 2 ) and volume (10 6 m 3 ) between 2016 and 2018 for the Arcachon Bay and the Bay of Veys. . . . . . . . . . . . . . 106 3.3 MAEs and RMSEs of LiDAR-and waterline-derived topography profiles of Figures 3.15 (Arcachon) and 3.16 (Veys). . . . . . . . . . . . . . . . . . . . . . . 112 4.1 The results obtained by the orbit selection module simulating SWOT's swaths covering the Arcachon Bay for the A01 test (mission start time: 01/01/2016 00:00:00; simulation start time 01/06/2016 00:00:00; simulation end time: 01/10/2016 00:00:00) and the attributed sea level obtained from the Arcachon-Eyrac tide-gauge records. . . . . . . . . . . . . . . . . . . . . . . . 122 4.2 The comparison results expressed as MAEs and RMSEs between the original DEM and the SWOT-derived DEMs simulated with various mission start time and the same acquisition period. . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.3 The comparison results expressed as MAEs and RMSEs between the original DEM and the SWOT-derived DEMs simulated with the same mission start time and various acquisition periods. . . . . . . . . . . . . . . . . . . . . . . . . 129 xxi L ES zones côtières sont des systèmes complexes situés à l'interface terre-mer.

Chapitre 1 :

 1 Suivi de la topographie et la bathymétrie des zones côtières par télédétection spatiale : une revue de la littérature[START_REF] Salameh | Monitoring Beach Topography and Nearshore Bathymetry Using Spaceborne Remote Sensing: A Review[END_REF]).

Chapitre 2 :

 2 Suivi du niveau de la mer et de la topographie des lagunes côtières intertidales à l'aide de l'altimétrie satellitaire : L'exemple du bassin d'Arcachon dans le golfe de Gascogne (Salameh et al. 2018).

Chapitre 3 :

 3 Suivi de la topographie intertidale par la méthode de la ligne d'eau à partir des images Sentinel-1 & -2 : l'exemples du bassin d'Arcachon et de la baie des Veys en France (Salameh et al. accepted).

Figure 1 :

 1 Figure 1: Spatial extent of the coastal zone, including the coastal plain, shoreface and continental shelf. Note that the widths of these zones are globally highly variable. (Source: Masselink et al. (2011). Reproduced with permission of Hodder & Stoughton Ltd.)

Figure 2 :

 2 Figure 2: Conceptual diagram illustrating the morphodynamic approach, showing the coastal morphodynamic systems and the environmental boundary conditions (sea level, climate, external forcing and static boundary conditions). (Source: Masselink and Gehrels (2015)).

Figure 3 :

 3 Figure 3: The coastal system comprises interacting natural and human sub-systems, and external terrestrial and marine influences. A range of non-climate drivers can act directly or indirectly on this system. (Source: Adapted from Nicholls et al. (2007). Reproduced with permission of IPCC).

Figure 4 :

 4 Figure 4: Bottom coverage achieved by lead lines, single beam echosounders, and MBESs.

Figure 5 :Figure 6 :

 56 Figure 5: General patterns of zonation of tidal flats (Reineck and Singh 1980). HWS: High water on springs; LWS: Low water on springs. (Source: from Gao (2019)).

Figure 7 :

 7 Figure 7: Passive and active remote sensing. from lidar Remote Sensing and Applications (Source: from Dong and Chen (2018)).

Figure 1 .

 1 3.a shows the waterlines extracted by Heygster et al. (2010) over the German part of the Wadden flats (for 1998) and Figure 1.3.b shows the DEM generated after the interpolation.

Figure 1 . 3 :

 13 Figure 1.3: (a) Waterlines extracted over the German part of the Wadden Flats for 1998; (b) Intertidal topographic map obtained after interpolation. Standard deviation at each grid point through the years from 1996-1999 and 2006-2009 for (c) Tertiussand, (d) Gelbsand, and (e) Medemsand. Adapted from Heygster et al. (2010) and Li (2014).

  .

  4.a gives an overview of the vertical nodal linear regression. The map allows for a synoptic view of the development of the region as a whole, as well as of various sandbars of the region. The dynamic sandbars Tertiussand, D-Steert, and Gelbsand are located in the front region to meet the waves and tides coming in from the open sea, while the sands Trischen, Eider, and Süderoogsand, which are not standing alone, erode eastwards[START_REF] Li | Morphological Development of the German Wadden Sea from 1996 to 2009 Determined with Waterline Method and SAR and Landsat Satellite Images[END_REF].

1 35Figure 1 . 4 :

 114 Figure 1.4: (a) Vertical nodal linear regression for the Schleswig-Holstein Wadden Sea. Temporal development of marked and named sandbars discussed in Li (2014) (from Li (2014)); (b) Turnover height (red) and net balance height (blue) of the North Frisian Wadden Sea. Black: Sea-level rise according to Wahl et al. (2013) for Hörnum (6.6 mm/yr, upper line) and Cuxhaven (3.7 mm/yr, lower line) with reference to 1996 Adapted from Li (2014).

Figure 1 .

 1 Figure 1.4.b condenses the development of the parameters mean turnover height and net balance height for the North Frisian Wadden Sea, together with their regression lines. The turnover height from 1996 to 2009 shows an overall increasing trend, with a slope of 8.2 ± 0.7 mm/yr. The main contribution is accretion (62%), as can be seen from the net balance height, which is 7.5 ± 1.1 mm/yr. These results represent the mean change in height for the whole research area. This may vary locally, as indicated by the vertical nodal linear regression map (Figure 1.4.a). The positive values of the net balance height indicate that in each single year, the accretion averaged over the research area is stronger than the erosion (Li 2014).

Figure 1 . 5 :

 15 Figure 1.5: TanDEM-X InSAR DEM for the Gomso Bay test site. The estimated DEM (color) for the tidal flat is overlaid on the TanDEM-X amplitude image (grey), scaled from -2 to 3 m. Upper left: 35.710139°N /126.46995°E. Bottom right: 35.610046°N/126.64958°E. The extent of the DEM image is 11.1 km (N-S) × 16.3 km (E-W) and the spatial resolution of the DEM is 5 m (from Lee and Ryu (2017).

Figure 1 .

 1 Figure 1.8: Aquatic color-derived bathymetry in the Arcachon inlet (southwestern France). (a) 2017-10-06 and (b) 2018-09-01 bathymetries retrieved from Sentinel-2/MSI data using the QAB (Capo et al. 2014). The parameters used or generated by QAB to inverse bathymetries are the tidal height, T (in m), diffuse attenuation coefficient of downwelling irradiance at 559 nm, K d (in m -1 ), maximum optical water depth, H max (in m), remote sensing reflectance for optically deep waters at 559 nm, r r s_d eep (sr -1 ), remote sensing reflectance of bottom substrate at 559 nm, and r r s_bot t om (sr -1 ). (c) Location of in situ acoustic bathymetry data used for evaluation of QAB (d) performances and (e) uncertainties (marks and bars are associated with the MAE and the 95% CI, respectively, calculated for 0.5 m depth intervals). Red and green colors are associated with the years 2017 and 2018, respectively.

  methodology for estimating bathymetry is based on five steps: 1. Computation of the local wave spectra based on a wavelet analysis. 2. Extraction (based on the local spectrum) of N dominant waves characterized by their wavelengths λ n and directions θ n , n ∈ [1, N ];

Figure 1 .

 1 Figure 1.9: Panchromatic image of SPOT-5: (a) Reunion Island; (b) Zoom on the area of Saint Pierre (from Poupardin et al. (2016)).

Figure 1 .

 1 Figure 1.10: The bathymetry: (a) measured; and (b) estimated by the CWB (in m) method on the area of Saint Pierre on Reunion Island. The isobaths represented in black range from 0 to 50 m depth with a step of 5 m (from Poupardin et al. (2016)).

Figure 1 .

 1 Figure 1.12: Regional bathymetry: (a) From combined echosounder surveys; (b) From Pleiades (from Almar et al. (2019a)).

Figure 1 .

 1 Figure 1.13: (a) 2D cross-correlation result clearly showing a wavy pattern; (b) The sinogram in the Radon angular space of the cross-correlation; (c) The signal along the dominant direction to compute wavelength and celerity. The black signal is the raw signal (with a ∆t lag) and the red signal is the auto-correlation with no lag. The shift between the two signals is the average distance made by the waves within ∆t (which is 8 s here) (from Almar et al. (2019b)).

4 .

 4 SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT )

2 59

 2

and 2 . 5 (

 25 same type of figures is available in Appendix C for ERS-2 (Figure C.1) and ENVISAT (Figure C.2)

Figure 2 . 6 :

 26 Figure 2.6: Comparisons between manual (left) and automatic (right) classifications (made using an unsupervised clustering technique) of cycles for SARAL (a,b) and CryoSat-2 (c,d).

Figure 2 .

 2 Figure 2.8 presents topography comparisons between LiDAR and altimetry measurements for ERS-2 (a), ENVISAT (b), SARAL (c), and CryoSat-2 (d).For topography comparisons all measurements from every cycle were used along with the corresponding LiDAR topography measurements. Table2.3 lists all regression models obtained. Linearity was rejected only for ENVISAT data. Therefore, the slope and the intercept obtained for ENVISAT could not be interpreted. Good comparison results are obtained for SARAL giving a slope of 1.06 and an intercept at 0.01 with no proportional or constant bias observed for topography monitoring. CryoSat-2 provides as well acceptable results with slight systematic and proportional biases. Showing a positive linearity test, ERS-2 slope and intercept showed large differences from 1 and 0.

72 2 .

 2 SATELLITE RADAR ALTIMETRY

Figure 2 . 8 :

 28 Figure 2.8: Comparisons between LiDAR and Altimetry-based topography measurements for: (a) ERS-2, (b) ENVISAT, (c) SARAL, and (d) CryoSat-2.

Figure 2

 2 Figure 2.9: Spatial variation of the backscattering coefficient for SARAL (cycle 20) at low tide along with the corresponding waveforms of the indicated zones.

Figure 2 .

 2 Figure 2.10: Spatial variation of the backscattering coefficient for SARAL (cycle 2) at high tide along with the corresponding waveforms of the indicated zones.

Figure 2 .

 2 Figure 2.11: Spatial variation of the backscattering coefficient for CryoSat-2 (cycle 2) at low tide along with the corresponding waveforms of the indicated zones.

Figure 2 .

 2 Figure 2.12: Spatial variation of the backscattering coefficient for CryoSat-2 (cycle 5) at high tide along with the corresponding waveforms of the indicated zones.

2 77

 2

Figure 3 . 1 :

 31 Figure 3.1: (a) An overview map with the location of the study sites: (b) the Arcachon Bay and (c) the Bay of Veys. (b) and (c) include the intertidal flats and the rivers and canals flowing into the two bays.

Figure 3 .Figure 3 . 3 :

 333 Figure 3.3: A step by step overview of the methods used in this study to generate DEMs using the waterline method along with the corresponding sections.

  Figure 3.5 shows two examples of SAR images corresponding to class 5 and class 6 respectively.

Figure 3 . 4 :

 34 Figure 3.4: Averaged histograms of each class obtained by classifying the images' histograms using k-means algorithm.

Figure 3 . 5 :

 35 Figure 3.5: Examples of noisy SAR images acquired over the Arcachon Bay with histograms corresponding to: a) class 5 and b) class 6.

Figure 3 .

 3 Figure 3.6: The different steps of the edge detection technique that combines a k-means segmentation process with a snake active edge contouring algorithm.

Figure 3 . 7 :

 37 Figure 3.7: Examples of redundant waterlines with quasi-same height and different number of polygons. Waterline #2 presents the least number of polygons.

Figure 3 .

 3 Figure 3.8 presents the comparisons for the Arcachon Bay between the LiDAR-derived DEM and the 2016 six waterline-derived DEMs obtained by combining the three waterlines levelling approaches with the two interpolation techniques. Another aim of this comparison is to evaluate the best combination of levelling approach and interpolation technique. For this reason, the DEM of 2016 were chosen instead of 2015 (closer to the LiDAR acquisitions) for which no model simulation was performed by the SHOM. As indicated in Figure3.8, the kriging interpolation method(Figure 3.8.b, 3.8.d, and 3.8.f) produced slightly more accurate DEMs than IDW method(Figure 3.8.a, 3.8.c, and 3.8.e) showing a lower Mean Absolute Error (MAE) and a lower RMSE for all cases. Tide gauge levelling showed better results (MAE = 0.19 m) than the two other approaches based on the model simulations. However, reliable DEMs were also obtained for the latter cases with MAEs and RMSEs equal to 0.25 m and 0.32 m respectively. In contrary to expectations, the DEMs with heights assigned using the complete model grid produced the same results as the DEMs with heights assigned using the single-grid point.The comparisons corresponding to the Bay of Veys are presented in Figure3.9. DEMs of 2017 were used in this case since the LiDAR observations were acquired between May and June 2017. The interpretations made for the Arcachon Bay DEMs are valid for the Bay of Veys. A decrease in the MAEs and RMSEs is observed between the two interpolation techniques.The final DEMs were thus generated using the kriging interpolation method with heights assigned using tide gauge records for the Arcachon Bay and using the kriging interpolation method and heights assigned with the single-grid point model for the Bay of Veys. Figure3.10.a and 3.10.b show respectively, the absolute difference between the 2013 LiDAR-derived DEM and the 2016 waterline-derived DEMs for Arcachon Bay (tide gauge levelling and kriging interpolation), and the absolute difference between the 2017 LiDAR-derived DEM and the 2017 waterline-derived DEM for Bay of Veys (single-grid point model levelling and kriging interpolation).The DEMs generated for the Bay of Veys are presented in Figure3.12. The topography shape and height are consistent with the LiDAR-derived DEM. Figure3.12 shows a net improvement with time in terms of details. The tidal creeks in the 2018 DEM are evident comparing to the DEM generated for 2016. The 2017 DEM shows an intermediate performance.

Figure 3 .

 3 Figure 3.11 shows the generated DEMs for the Arcachon Bay. The four DEMs reflect a good correspondence with the LiDAR-derived DEM (Figure3.2.a). The relatively large features of the intertidal zone are well detected. These large features are stable in time, which is consistent with the sedimentary characteristics of the Arcachon Bay[START_REF] Allard | A synthesis of morphological evolutions and Holocene stratigraphy of a wave-dominated estuary: The Arcachon lagoon, SW France[END_REF]. Some smaller features that can be found in a given DEM are sometimes missed in others. This depends on the temporal sampling of the tidal range. For instance, the 2018 DEM shows more details than the 2015 DEM, smaller tidal flat features and tidal creeks were detected. This was majorly due to the finer sampling provided by the Sentinels in 2018 where the four satellites (Sentinel-1A, Sentinel-1B, Sentinel-2A, and Sentinel-2B) were in orbit. Despite the better sampling for the years 2017 and 2018, the detection of the very small tidal creeks was limited by the sensor horizontal resolution. A simple visual

Figure 3 . 8 :

 38 Figure 3.8: Comparisons between the LiDAR-derived DEM and the 2016 waterline-derived DEMs for the Arcachon Bay generated using: (a) IDW interpolation and tide gauge levelling; (b) kriging interpolation and tide gauge levelling; (c) IDW interpolation and single point model levelling; (d) kriging interpolation and single point model levelling; (e) IDW interpolation and complete grid model levelling; (f) kriging interpolation and complete grid model levelling.

Figure 3

 3 Figure 3.9: Comparisons between the LiDAR-derived DEM and the 2017 waterline-derived DEMs for the Veys Bay generated using: (a) IDW interpolation and single point model levelling; (b) kriging interpolation and single point model levelling; (c) IDW interpolation and complete grid model levelling; (d) kriging interpolation and complete grid model levelling.

Figure 3 .

 3 Figure 3.10: Absolute difference between a) Arcachon LiDAR-derived DEM (2013) and the 2016 waterlinederived DEM; b) Veys Bay LiDAR-derived DEM (2017) and the 2017 waterline-derived DEM.

Figure 3 .

 3 Figure 3.11: Cont.

Figure 3 .

 3 Figure 3.11: Arcachon Bay waterline-derived DEMs for: (a) 2015; (b) 2016; (c) 2017; and (d) 2018.

Figure 3 .

 3 Figure 3.12: Cont.

  surface of the intertidal zone for each year along with the surfaces showing erosion and deposition. Eroded, deposited, and net volume changes occurring between the studied years were also computed following the formulation presented in section 3.4.4. Results are shown in Table

Figure 3 .

 3 Figure 3.13: Intertidal flats DoD maps for the Arcachon Bay between a) 2017-2016; b) 2018-2017; c) 2018-2016; and for the Veys Bay between d) 2017-2016; e) 2018-2017; f) 2018-2016.

Figure 3 .

 3 Figure 3.14: The evolution of the tidal coverage provided by Sentinel-1 and Sentinel-2 for the June-September period between 2015 and 2018 in the Arcachon and Veys Bays.

Figure 3 .

 3 Figure 3.15 and Figure 3.16 present a comparison between the LiDAR-derived DEM and the waterline-derived DEMs (of all years) over three transects of the Arcachon Bay and the Bay of Veys respectively. MAEs and RMSEs corresponding to these comparisons are listed in Table3.3. For the Arcachon Bay, the three 2016 profiles showed lower MAEs (#1: 0.17 m, #2: 0.16 m, #3: 0.14 m) than the one obtained by the complete gridded-DEM (0.19 m) and the estimated accuracy (0.27 m) in section 3.5.3. A smaller error for profiles is expected because a transect can miss an eventual extensively biased region. However, it shows that a better accuracy can be achieved with more careful processing. The good accuracy provided by this method is also reflected in the MAEs and RMSEs obtained for the 2015 waterline-derived DEM with a MAE reaching 0.13 m for the third transect. Even with this good accuracy, the error is expected to be smaller since the LiDAR measurements were acquired in 2013. In contrast to transects 1 and 2, small errors barely changing with the years are observed over the third transects crossing the "île aux Oiseaux" island. This could mean that this area is undergoing less modifications than the rest of the flats.

5 .

 5 MONITORING THE INTERANNUAL MORPHO-SEDIMENTARY CHANGES

  .13. The adjacent erosion and deposition patterns may indicate a migration of channels from pixels showing deposition to pixels showing 112 3. THE WATERLINE METHOD

4 119Figure 4 . 1 :

 441 Figure 4.1: (a) An overview map with the location of the study sites: (b) the Arcachon Bay and (c) the Bay of Veys. (a) includes the coverage provided by SWOT's orbit; (b) and (c) include the intertidal flats and the rivers and canals flowing into the two intertidal bays.

4. 4 .

 4 DATASETSTwo types of data were used in this study to generate the input for the SWOT hydrology toolbox: intertidal DEMs (for each study site for the years 2016, 2017, and 2018) and sea level information. All types of data used and generated in this study are referenced or converted to the French Reference System NGF/IGN69.

4 121

 4

122 4 .

 4 SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT ) • Comparing the SWOT-derived DEMs to the original DEMs by computing their MAE and RMSE which were respectively 9.5 cm and 14.4 cm for the A01 test. The Absolute difference map between the two DEMs for the latter test is shown in Figure 4.2.e along with a density scatter plot in Figure 4.2.f.

124 4 .

 4 SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT )

  Figure 4.4 (a and b) where waterlines of A02 and A04 are shown.

  Figure 4.4.c and Figure 4.4.d and the comparisons with the original DEM in Figure 4.4.e and Figure 4.4.

Figure 4 .

 4 7.a and Figure 4.7.b showing the extracted waterlines of these two tests. The unfavorable sampling reduced the accuracy of the DEM because a large area of the bay is not covered by waterlines. It is obvious from the DEMs shown in Figure 4.7.c and Figure 4.7.d that for V06 test the channels of the bay were not detected due to a lack of waterlines where high differences exist by comparing to the original DEM (Figure 4.7.f ).

Figure 4 .

 4 8 shows the comparison between the original DEM and the SWOT-derived DEMs for tests V01 and V06. 4. SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT )

Figure C. 3 :

 3 Figure C.3: Spatial variation of the backscattering coefficient for ENVISAT (cycle 21) at high tide along with the corresponding waveforms of the indicated zones.

Figure C. 4 :

 4 Figure C.4: Spatial variation of the backscattering coefficient for ENVISAT (cycle 9) at low tide along with the corresponding waveforms of the indicated zones.

ε

  = a 0 + a 1 S + a 2 C + (b 0 + b 1 S + b 2 C ) m v + (c 0 + c 1 S + c 2 C ) m v (D.2)where S and C are the sand and clay fraction of soil given in percent, m v is the volumetric water content given in percent, a 0 , a 1 , a 2 , b 0 , b 1 , b 2 , c 0 , c 1 , c 2 are the constants of the empirical relationship given in Table

Figure E. 1 :

 1 Figure E.1: SWOT sampling for test V06.

  . Reproduced with permission of Hodder & Stoughton Ltd.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Conceptual diagram illustrating the morphodynamic approach, showing the coastal morphodynamic systems and the environmental boundary conditions (sea level, climate, external forcing and static boundary conditions). (Source: Masselink and Gehrels (2015)). . . . . . . . . . . . . . . . 16 3 The coastal system comprises interacting natural and human sub-systems, and external terrestrial and marine influences. A range of non-climate drivers can act directly or indirectly on this system. (Source: Adapted from Nicholls et al. (2007). Reproduced with permission of IPCC). . . . . . . . . . . . . . . . . 18 4 Bottom coverage achieved by lead lines, single beam echosounders, and MBESs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5

  1. Est-ce que l'altimétrie satellitaire est capable d'extraire des profils topographiques intertidales à marée basse ? 2. Est-ce qu'il est possible d'effectuer une auto-discrimination entre les points de mesure émergés et submergés en utilisant des paramètres altimétriques intrinsèques (Coefficient de rétrodiffusion et Peakiness) (Annexe B).

	3. Les missions d'imagerie Sentinel (1 et 2) (open source) fournissent-elles des données
	adéquates pour le suivi de la topographie intertidale en utilisant la méthode de la
	ligne d'eau ?
	4. Quelles améliorations pourraient être apportées à la méthode de la ligne d'eau afin
	de réduire le taux du traitement manuel ?

5. L'application de la méthode de la ligne d'eau permet-elle de fournir régulièrement des MNEs intertidaux aptes à détecter des changements topographiques ?

6. Est-ce que SWOT permet de mesurer la topographie des zones intertidales à l'aide de la méthode de la ligne d'eau ?

7. Est-ce que SWOT permet le suivi des changements topographiques à l'aide de la méthode de la ligne d'eau ?

Table 1 .

 1 1 presents the strengths, limitations, and accuracies associated with the different methods used for the retrieval of coastal topography and bathymetry.

	51
	1

Table 1 .

 1 1: Comparison of methods for mapping the bathymetry of shallow waters and the topography of their adjacent beaches.

	Method	Sensors	Area	Strengths	Limitations	Accuracy or relative error (%)
	Stereoscopy	Stereo optical	Beach	High horizontal resolution	Dependence of ground control	RMSE between 0.35 and 0.48 m in
		imagery		Capable of capturing local beach	points to correct the vertical offset	Almeida et al. 2019.
				features.	of the digital elevation model
					(DEM) Almeida et al. 2019.
	Waterline	SAR and	Intertidal	Increasing number of sensors in	Assumes stable topography	Depends on vertical coverage,
		optical		orbit allow better sampling of	during data acquisition period.	0.20 m shown in Li 2014.
				intertidal depth range. Historic
				maps possible from past satellite
				data.
	InSAR	SAR	Intertidal	No field data are required.	High temporal decorrelation for	RMSE of 0.20 m in Lee and Ryu
					multi-pass interferometry.	2017.
	Radar	Radar and	Intertidal	Laser altimetry can provide very	Generate only intertidal	RMSE of 23 m in Salameh et al.
	Altimetry	Laser		accurate measurements.	topography profiles.	2018.
		Altimeters
	Aquatic Color	Multi-	Nearshore	No field data are required.	Sensitive to 1-heterogeneity of	Depend on inherent optical
	Radiometry	spectral and			optical properties of water	properties of the water column
		hyper-			column and bottom substrate. 2-	and bottom substrate.
		spectral			surface effects (sunglint,
					adjacency effect).
	Correlation-	Multi-	Nearshore	No field data are required.	The method does not take	Less than 30% in Poupardin et al.
	Wavelet-	spectral			currents into consideration.	2016.
	Bathymetry
	(CWB)
	Wave	SAR	Nearshore
	Characteristics		(between -15
	from SAR		and -30 m)

Table 2 .

 2 1 presents a summary of the main characteristics of the altimetry missions used in this study, which are described in more detail below.

Table 2 .

 2 1: Main characteristics of the altimetry missions used in this study. its nominal orbit until October 2010[START_REF] Zelli | ENVISAT RA-2 advanced radar altimeter: Instrument design and prelaunch performance assessment review[END_REF]. From November 2010 to April 2012, ENVISAT was put into the extending phase consisting of a drifting on a 30-day orbit lowered by 17 km. SARAL SARAL is a CNES-ISRO joint-mission that was launched on 25 February 2013. Its payload is composed of the AltiKa radar altimeter and bi-frequency radiometer, and a triple system for precise orbit determination: the real-time tracking system DIODE of DORIS instrument, a Laser Retroflector Array (LRA), and the Advanced Research and Global Observation Satellite (ARGOS-3). Its orbital characteristics are the same as ENVISAT (see above). The first four cycles of SARAL do not follow precisely the ENVISAT orbit. AltiKa radar altimeter is a solidstate mono-frequency altimeter that provides accurate range measurements. It is the first altimeter to operate at

	Mission	ERS-2	ENVISAT	SARAL	CryoSat-2
	Agency	ESA	ESA	CNES/ISRO	ESA
	Launch on	21/04/1995	01/03/2002	25/02/2013	08/04/2010
	End date	06/07/2011	08/06/2012	Present	Present
	Altimeter name	RA	RA-2	AltiKa	SIRAL
	Radar frequency	Ku-band	Ku and S-bands	Ka-band	Ku-band
	Altitude	785 km	790 km	790 km	717 km
	Orbit inclination	98.52°98.54°98.54°92°R
	epetitivity	35 days	35 days	35 days	369 days
	Ground-track spacing at the equator	85 km	85 km	85 km	7.5 km
	Along track sampling	20 Hz (350 m) 18 Hz (∼400 m) 40 Hz (175 m) 20 Hz (350 m)
	2.3.1.1. ERS-2
	The ERS-2 satellite was launched in 1995 by ESA. Its payload is composed of several
	sensors, including a radar altimeter (RA), operating at Ku-band (13.8 GHz). It was
	sun-synchronously orbiting at an altitude of 785 km with an inclination of 98.52°with a
	35-day repeat cycle. This orbit has a ground-track spacing about 85 km at the equator.
	ERS-2 provided observations of the topography of the Earth from 82.4°latitude north to
	82.4°latitude south. ERS-2 data are available from 17 May 1995 to 9 August 2010 but with a
	limited coverage after 22 June 2003.

Table 2 .

 2 2: Passing-Bablok regression model and statistical results for the comparisons made between insitu and altimetry-based SSH (ERS-2, ENVISAT, SARAL, and CryoSat-2) for manual (MAPS) and automatic selections.

	Mission	ERS-2	MAPS	Auto

ENVISAT SARAL CryoSat-2 ERS-2 ENVISAT SARAL CryoSat-2

	Linearity 3	1	0	1	1	1	1	1	1
	Slope Slope LB 1 Slope UB 2	0.16 -0.05 0.44	0.60 0.51 0.71	0.93 0.87 0.97	0.94 0.85 1.02	0.64 0.23 2.07	0.74 0.67 0.83	0.95 0.91 1.01	0.92 0.79 1.01
	Intercept	1.06	0.70	-0.06	0.10	1.43	0.66	-0.06	0.13
	Intercept LB	1.36	0.74	-0.09	0.10	1.68	0.69	-0.13	0.11
	Intercept UB	0.91	0.69	-0.02	0.15	1.02	0.65	-0.05	0.22
	R	0.39	0.82	0.99	0.93	0.11	0.86	0.99	0.95
	RMSE (m)	1.75	1.04	0.23	0.42	1.70	0.92	0.22	0.39
	Mean Bias (m)	1.47	0.88	0.18	0.23	1.50	0.79	0.17	0.24
	1 Lower Bound. 2 Upper Bound. 3 1 for accepted linearity and 0 for refused linearity.

2 73 Table 2 .

 732 3: Passing-Bablok regression model and statistical results for the comparisons made between LiDAR and altimetry-based topography estimation for ERS-2, ENVISAT, SARAL, and CryoSat-2.

	Mission	ERS-2	ENVISAT	SARAL	CryoSat-2
	Linearity Test 3	1	0	1	1
	Slope Slope LB 1 Slope UB 2	1.39 1.08 1.75	0.92 0.84 1.02	1.06 0.96 1.19	0.96 0.86 1.09
	Intercept Intercept LB Intercept UB R	2.09 2.31 1.92 0.17	0.83 0.89 0.77 0.54	0.01 0.08 -0.04 0.71	-0.09 -0.04 -0.13 0.79
	RMSE (m)	2.01	0.95	0.23	0.44
	Mean Bias (m)

Table 3 .

 3 1: The number of available Sentinel-1 and Sentinel-2 images for Arcachon and Veys Bays between 2015 and 2018 and the number of eliminated images due to unavailable sea level information, noisy (SAR) or cloudy (MSI) images, and images with redundant water level.

	Study Site Year	Mission	Number of available images

Number of eliminated images due to: Unavailable sea level information Noisy/cloudy images Redundant water level

	3.5. RESULTS					97
	3.5.1. DEMS VALIDATION
	Figure
							3
		2015	Sentinel-1 Sentinel-2	36 0	1 0	9 0	11 0
	Arcachon	2016 2017	Sentinel-1 Sentinel-2 Sentinel-1 Sentinel-2	37 5 79 6	3 0 3 0	9 0 20 1	13 0 38 0
		2018	Sentinel-1 Sentinel-2	87 13	15 4	26 0	32 0
		2016	Sentinel-1 Sentinel-2	24 2	0 0	13 0	2 0
	Veys	2017	Sentinel-1 Sentinel-2	58 4	0 0	34 0	7 0
		2018	Sentinel-1 Sentinel-2	49 13	0 0	33 1	10 0

Table 3 .

 3 2: Topographic changes in terms of surface (km 2 ) and volume (10 6 m 3 ) between 2016 and 2018 for the Arcachon Bay and the Bay of Veys.

	Case		Surface (km 2 )		Volume (10 6 m 3 )
		Stable	Eroded	Deposited	Eroded	Deposited Total
	Arcachon 2016/2017	91.30 (98.24%) 1.12 (1.20%)	0.52 (0.56%) -0.61 ± 0.43 0.24 ± 0.20 -0.37
	Arcachon 2017/2018	90.00 (96.85%) 2.27 (2.44%)	0.66 (0.71%) -1.09 ± 0.87 0.32 ± 0.25 -0.77
	Arcachon 2016/2018	89.22 (96.00%) 2.93 (3.15%)	0.79 (0.85%) -1.54 ± 1.12 0.42 ± 0.30 -1.12
	Veys 2016/2017	19.08 (69.51%) 3.51 (12.79%) 4.86 (17.70%) -2.27 ± 1.19 3.16 ± 1.65 0.90
	Veys 2017/2018	17.75 (64.64%) 5.96 (21.70%) 3.75 (13.66%) -4.11 ± 2.02 2.42 ± 1.27 -1.69
	Veys 2016/2018	17.42 (63.44%) 5.16 (18.79%) 4.88 (17.77%) -4.23 ± 1.75 3.53 ± 1.66 -0.70

Table 3 .

 3 3: MAEs and RMSEs of LiDAR-and waterline-derived topography profiles of Figures 3.15 (Arcachon) and 3.16 (Veys).

				Arcachon					Veys
			MAE (m)			RMSE (m)			MAE (m)		RMSE (m)
	Year/Transects	#1	#2	#3	#1	#2	#3	#1	#2	#3	#1	#2	#3
	2015	0.16 0.14 0.13 0.23 0.18 0.17	x	x	x	x	x	x
	2016	0.17 0.16 0.14 0.22 0.19 0.18 0.35 0.37 0.28 0.45 0.51 0.37
	2017	0.17 0.18 0.15 0.22 0.22 0.18 0.28 0.23 0.27 0.34 0.35 0.37
	2018	0.20 0.20 0.12 0.25 0.25 0.15 0.32 0.37 0.34 0.49 0.58 0.46

Table 4 .

 4 1: The results obtained by the orbit selection module simulating SWOT's swaths covering the

	Arcachon Bay for the A01 test (mission start time: 01/01/2016 00:00:00; simulation start time 01/06/2016
	00:00:00; simulation end time: 01/10/2016 00:00:00) and the attributed sea level obtained from the Arcachon-
	Eyrac tide-gauge records.
	Run	Cycle	Orbit	Date	Time	Sea level (m)
	c008_t348	8	348	07/06/2016	10:59:10	-1.12
	c008_t419	8	419	10/06/2016	00:18:14	-0.46
	c009_t113	9	113	19/06/2016	22:40:22	-1.18
	c009_t348	9	348	28/06/2016	07:44:07	0.15
	c009_t419	9	419	30/06/2016	21:03:11	0.03
	c010_t113	10	113	10/07/2016	19:25:19	1.47
	c010_t348	10	348	19/07/2016	04:29:05	1.80
	c010_t419	10	419	21/07/2016	17:48:09	2.42
	c011_t113	11	113	31/07/2016	16:10:17	1.42
	c011_t348	11	348	09/08/2016	01:14:02	-0.90
	c011_t419	11	419	11/08/2016	14:33:06	-0.42
	c012_t113	12	113	21/08/2016	12:55:14	-1.61
	c012_t348	12	348	29/08/2016	21:58:59	-0.71
	c012_t419	12	419	01/09/2016	11:18:03	-1.15
	c013_t113	13	113	11/09/2016	09:40:11	0.93
	c013_t348	13	348	19/09/2016	18:43:56	2.66
	c013_t419	13	419	22/09/2016	08:03:00	1.96

  SWOT SAMPLINGFor each site, 11 simulations were performed by incrementing the mission start time of 6 days starting from 01-01-2016 00:00:00 to 29-02-2016 00:00:00. For all tests, the acquisition period is 4 months with simulations starting in 01-06-2016 00:00:00 and ending in 01-10-2016 00:00:00. The simulated SWOT-derived DEMs were compared to the original DEMs. MAEs and RMSEs for all tests are shown in Table4.2. As anticipated, the accuracy of the DEMs vary with the mission start time owing to a coarse sampling or/and sometimes unfavorable aliasing. As can be seen in Table4.2, for the Arcachon Bay the MAEs vary between 5.2 cm (A02) and 19.5 cm (A04) and for the Veys Bay between 11.6 cm (V01) and 28.4 cm (V06). The better accuracy obtained for the Arcachon Bay may be due to the better coverage that SWOT provides for the Arcachon Bay. Orbit #141 is cutting the edge of the Veys Bay (Figure4.1) which makes the latter covered by 2 orbits only (#320 and #042). It should be noted that in Table4.2 and Table 4.3, orbit #141 was not counted among the number of passes.Figure4.3 shows the tidal coverage (or sampling) provided by SWOT for A02 and A04 tests. It is clear that SWOT covers better the tidal range in A02. For A04, the intermediate part of the tidal range highlighted in blue is mostly unsampled. This unfavorable sampling for A04 is also apparent in

4.6.1.

Parts of this chapter have been published in RemoteSensing 2019, 11(19) [START_REF] Salameh | Monitoring Beach Topography and Nearshore Bathymetry Using Spaceborne Remote Sensing: A Review[END_REF]).

Parts of this chapter have been published in Remote Sensing 2018, 10(2)[START_REF] Salameh | Monitoring Sea Level and Topography of Coastal Lagoons Using Satellite Radar Altimetry: The Example of the Arcachon Bay in the Bay of Biscay[END_REF]).

Parts of this chapter have been accepted for publication in isprs journal of photogrammetry and remote sensing(Salameh et al. accepted).

THE WATERLINE METHOD

3. THE WATERLINE METHOD

THE WATERLINE METHOD erosion.Figure 3.15: Topography profiles comparison between the LiDAR-derived DEM and the 2015, 2016, 2017, and 2018 waterline-derived DEMs over the Arcachon Bay along three transects.

Parts of this chapter have been submitted to isprs journal of photogrammetry and remote sensing(Salameh et al. submitted)

SURFACE WATER AND OCEAN TOPOGRAPHY (SWOT )

To analyze the change between the overall time period, DoD maps were also generated between the first year and the last year DEMs. The DoD maps are presented in Figure 3.13 for the Arcachon Bay (Figures 3.13.a,3.13.b,and 3.13.c) and the Veys Bay (Figures 3.13.d,3.13.e,and 3.13.f). These differences may result from topographic variations (erosion or deposition) but also from method deficiencies. Therefore, care must be taken when interpreting the pixels with very high differences. The 2015 waterline-derived DEM over the Arcachon Bay was excluded because the lowest waterline detected was considerably higher than the lowest waterlines of other years.

The Arcachon intertidal flats showed an overall stable behavior. The height difference values observed in Figure 3.13 for the Arcachon Bay are considerably lower than the values obtained for the Veys Bay. For the Arcachon Bay small spots of erosion and deposition distributed over the intertidal area were detected for all years, with two apparent deposition areas observed between 2017 and 2018 at the Eyre Delta. Over the Bay of Veys we observe adjacent erosion and deposition patterns. They are mostly localized along the channels but can also be found at the two sides and in the middle of the intertidal area. This localization over the channels may imply a possible migration of channels between the years.

Considering grid cells with height values between -LoD and LoD as stable, we

A ICE-1 (OCOG) FORMULATION

The Ice-1 (OCOG) retracking algorithm approach consists of replacing the waveform with a box that has the same center of gravity as the waveform. The box is defined using three measurements:

where N is the total gate number, al n is the number of eliminated gate in the starting and ending of waveform and y(n) is the power of the nth gate. The middle of the Leading Edge Point (LEP) is given by: LEP = centre of gravity -0.5 × width (A.4)

B PEAKINESS FORMULATION

Peakiness is a measure of how sharply peaked an echo is. It is the ratio of the maximum power (highest bin value) to the accumulated echo power above the retracking point. The peakiness in AltiKa GDR is given by:

where N WF is the total number of the registering gates, and N right is a number of points to the right from the tracking point (i.e., above the retracking point). For SIRAL:

C ERS-2 AND ENVISAT DATA AT LOW AND HIGH TIDE -RELATED TO CHAPTER 2 LIST OF PUBLICATIONS ABSTRACT

Intertidal flats provide essential services including protection against storm surges and coastal flooding. These environments are characterized by a continuous redistribution of sediments and topographic changes. They are under increasing pressure due to anthropogenic activities and sea level rise. The continuous monitoring of their topography is fundamental for hydrodynamic and morphodynamic modeling of coastal systems. Intertidal flats are among the most logistically challenging coastal landforms for ground-based and airborne-based topography monitoring. Spaceborne-based monitoring is the only viable and the most cost-effective approach capable of providing regularly intertidal topography maps. Recent developments in radar (altimetry and Synthetic Aperture Radar (SAR)) and optical technologies, bring new types of data and enhanced capacities for monitoring intertidal environments. This PhD dissertation investigates the use of spaceborne-based methods for monitoring the topography in intertidal areas using radar altimetry, SAR, and multispectral satellite observations. The main objective is to explore, develop, or enhance methods dedicated for intertidal topography mapping. Being a part of the preparation phase of the future SWOT (Surface Water and Ocean Topography) radar altimetry mission, first mission to operate in wide-swath SAR interferometry mode, this PhD dissertation also investigates the capability of SWOT to map intertidal topography.

Methodologies developed or/and used in this thesis were applied to two intertidal environments located on the French Coast: The Arcachon Bay and the Bay of Veys. We showed, for the first time, that recent advancements in technologies enabled satellite radar altimetry to extract intertidal topography profiles along the altimeters ground tracks. Second, we introduced an improved and quasi-automatic approach for the use of the waterline method (most common method for intertidal topography mapping) to derive intertidal Digital Elevation Models (DEMs). The changes include faster, more efficient and quasi-automatic detection and post-processing of waterlines. We also brought to light the ability of SWOT to generate highly accurate intertidal DEMs using the waterline method. The methodologies used here allow the generation of intertidal topography measurements regularly, that with careful usage, can be used for detecting topographic changes in intertidal environments. We showed that the two study areas eroded during 2016-2018, losing 1,12 × 10 6 m 3 and 0,70 × 10 6 m 3 for the Arcachon Bay and the Bay of Veys respectively. Updated DEMs provide useful and needed information for several scientific applications (e.g., sediment balance, hydrodynamic modelling), but also for authorities and stakeholders for coastal management and implementation of ecosystem protection policies.

Keywords-topography, intertidal, remote sensing, Synthetic Aperture Radar, multispectral, satellite radar altimetry, SWOT, Arcachon, Veys Bay

RÉSUMÉ

En lien avec les activités humaines et l'élévation du niveau de la mer dans le cadre du changement climatique, les zones intertidales sont soumises à de fortes pressions. La topographie de ces environnements est ainsi en évolution permanente. Le suivi de la topographie est fondamental pour la modélisation hydrodynamique et morphodynamique des systèmes côtiers. Ce suivi fait face à des importantes difficultés, surtout sur le plan logistique, vu la localisation des zones intertidales entre les limites des plus hautes et des plus basses marées. La télédétection spatiale est une des meilleures approches pour assurer des mesures topographiques intertidale à jour dans l'espace et dans le temps. Cette thèse porte ainsi sur l'utilisation de la télédétection spatiale pour le suivi de la topographie des zones intertidales par des capteurs radar (altimétrie et Radar à Synthèse d'Ouverture (RSO)) et multispectrales. L'objectif principal est d'explorer, de développer ou d'améliorer des méthodes dédiées à la cartographie de la topographie intertidale. Cette thèse étudie également la capacité de la future mission SWOT (Surface Water and Ocean Topography), première mission altimétrique à fournir des élévations au sein d'une fauchée au moyen de la technique d'interférométrie SAR (RSO), à cartographier la topographie dans les zones intertidales. Les méthodologies développées et utilisées dans cette thèse ont été appliquées à deux baies intertidales situées sur la façade Atlantique de la côte française : Le Bassin d'Arcachon et la Baie des Veys. Nous avons d'abord montré que les améliorations techniques des nouvelles missions satellitaires permettaient, pour la première fois, à l'altimétrie satellitaire de fournir des profils topographiques intertidaux le long des traces des altimètres. Deuxièmement, nous avons introduit une approche améliorée de la méthode de la ligne d'eau (méthode la plus courante pour la cartographie de la topographie intertidale) qui sert à générer des Modèles Numériques d'Élévation (MNEs) intertidaux à l'aide des images satellitaires (RSO et multispectrales). Grâce à cette nouvelle approche, la détection des lignes d'eau et leurs post-traitements sont maintenant plus rapides, plus efficaces et quasi-automatiques. Nous avons également mis en évidence la capacité de SWOT à générer des MNEs intertidaux précis en utilisant la méthode de la ligne d'eau. Les méthodologies développées et utilisées au cours de cette thèse sont capables de mesurer régulièrement la topographie dans les zones intertidales et permettre la détection des changements topographiques dans ces environnements et proposer des bilans morpho-sédimentaire. Ainsi, les deux zones intertidales étudiées sont en érosion sur la période de 2016 à 2018 avec des pertes en volume de 1,12 × 10 6 m 3 et 0,70 × 10 6 m 3 pour le bassin d'Arcachon et la baie des Veys respectivement. Ces informations sont utiles et nécessaires pour plusieurs applications scientifiques (par exemple, le bilan sédimentaire, la modélisation hydrodynamique), mais aussi pour les autorités et les acteurs du littoral dans le but de la mise en oeuvre des politiques d'utilisation et de protection de ces environnements.

Mots-clés-topographie, intertidale, télédétection, Radar à Synthèse d'Ouverture, multispectrale, altimétrie satellitaire, SWOT, Arcachon, Baie des Veys