# Les variations du niveau de la mer : de la moyenne globale aux échelles régionales et côtières et vers les services climatiques

Angélique Melet

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## To cite this version:

Angélique Melet. Les variations du niveau de la mer: de la moyenne globale aux échelles régionales et côtières et vers les services climatiques. Océan, Atmosphère. Université de Toulouse - Toulouse III - UPS, 2022. Français. NNT: . tel-04141514

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UNIVERSITÉ TOULOUSE III - PAUL SABATIER

HABILITATION À DIRIGER DES RECHERCHES - HDR

# Sea-level rise: from global to coastal scales and towards climate services

Presented by Angélique MELET

Defended on Nov 14, 2022

Jury:

Reviewer

Mme Sylvie Joussaume

Reviewer

Mr Markus Meier

Reviewer

Mr Ivan Haigh

Examiner

Mr Matt Palmer

Examiner

Mr Pierre Brasseur

Invited

Mme Anny Cazenave

Invited

Mr Pierre-Yves Le Traon
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# Abstract

Angélique MELET

## Les variations du niveau de la mer : de la moyenne globale aux échelles régionales et côtières et vers les services climatiques

Lorsque j'ai commencé à travailler sur l'élévation du niveau de la mer en 2014, les projections climatiques pour le 21<sup>me</sup> siècle étaient principalement disponibles pour la moyenne globale; les projections régionales de la hausse du niveau de la mer n'étant alors qu'émergentes. Un des grand défis du programme mondial de recherche sur le climat (WCRP) venait d'être mis en place sur les variations régionales du niveau de la mer et les impacts côtiers associés. Dans quelle mesure le niveau de la mer s'est élevé et s'élèvera au même rythme dans l'océan hauturier et sur les côtes restait une question ouverte. En raison des implications sociétales de la hausse du niveau de la mer, j'ai donc décidé très tôt de concentrer mes recherches sur les variations du niveau de la mer à la côte. Cela dit, les variations du niveau de la mer à la côte dépendent directement des variations du niveau de la mer aux échelles globale et régionale, et j'ai donc également travaillé sur ces échelles.

Ma démarche scientifique a consisté (i) à caractériser les différences entre les tendances du niveau de la mer et la variabilité interannuelle entre l'océan profond, au large, et l'océan côtier, (ii) à comprendre les processus pertinents à l'origine des changements du niveau de la mer, et plus particulièrement à la côte, des tendances à long-terme aux variations interannuelles et jusqu'aux extrêmes, et (iii) à régionaliser les tendances projetées du niveau de la mer et à mieux caractériser les changements projetés des niveaux extrêmes de la mer. Pour cela, j'ai analysé les données existantes et développé des outils dédiés tels que l'altimétrie côtière, des expériences de sensibilité à la représentation de différents processus dans des modèles numériques (de climat, d'océan ou de vagues), des descentes d'échelle statistiques et dynamiques pour étudier les variations du niveau de la mer à la côte, y compris en projection climatique.

Les principales questions auxquelles je me suis intéressée sont les suivantes :

* Les projections de la hausse du niveau de la mer sont essentiellement basées sur les modèles de climat. La confiance que l'on accorde à ces projections dépend donc de la capacité des modèles de climat à simuler les différentes composantes de la hausse du niveau de la mer et à reproduire les changements passés. Des questions essentielles qui se posent en matière de modélisation du climat sont donc les suivantes : les modèles de climat peuvent-ils reproduire correctement les variations passées du niveau de la mer ? Comment expliquer la dispersion de la représentation des variations du niveau de la mer dans les différents modèles de climat ?

* Dans quelle mesure la hausse régionale du niveau de la mer issue des modèles de climat est-elle représentative de la hausse du niveau de la mer à la côte, là où les impacts se produisent ? En d'autres termes, comment la variabilité du niveau de la mer dans les zones côtières diffère t'elle de la variabilité à grande échelle dans l'océan du large ? Dans quelle mesure les
projections de la hausse du niveau de la mer obtenues par descente d'échelle dans un modèle régional différent-elles de celles du modèle global de climat parent ? Dans quelle mesure l'inclusion de processus contribuant aux variations du niveau de la mer en zone côtière et non pris en compte dans les modèles globaux de climat modifie t'elle la représentation des variations du niveau de la mer à la côte ?

* Quelle est l'importance relative des différents processus et facteurs contribuant aux variations du niveau de la mer à la côte à différentes échelles de temps ?

* Les vagues contribuent fortement aux niveaux d'eau extrêmes atteints à la côte lors de tempêtes. Mais étant donné que les régimes de vent changent également aux échelles interannuelles et en réponse au changement climatique, les vagues contribuent-elles également aux variations du niveau de la mer à la côte aux échelles interannuelles et aux tendances du niveau de la mer à la côte d'ici la fin du 21<sup>me</sup> siècle ?

Au cours des sept dernières années, j'ai développé mes activités de recherche sur le niveau de la mer en parallèle de mes activités sur la définition, la coordination et la gestion du programme de recherche d'accompagnement du Service Marin du programme européen d'observation de la Terre, Copernicus, bien que ces deux activités se soient également mutuellement alimentées. Le Service Marin de Copernicus répond aux besoins des utilisateurs y compris pour la mise en oeuvre de politiques concernant l'environnement marin. En tant que tel, il fournit des données, des informations et de l'expertise scientifiques qui bénéficient à la société, ouvrant ainsi la voie d'une science avec et pour la société. Cette voie de la "science au service de la société" est à développer pour l'élévation du niveau de la mer. En effet, l'atténuation du changement climatique et la mise en place de mesures d'adaptation peuvent considérablement réduire les risques induits par l'élévation du niveau de la mer. Toutefois, sur cette thématique, les services climatiques faisant autorité et orientés vers la prise de décision pour venir en aide à l'adaptation n'en sont encore qu'à leurs débuts à travers le monde. En Europe, les inondations côtières ont été identifiées comme l'un des quatre principaux risques induits par le changement climatique vu les impacts qu'elles ont sur la population, les infrastructures et l'économie. Plus de 50 millions de personnes vivent actuellement dans des zones côtières de faible élévation en Europe, et les pertes économiques annuelles dues aux inondations côtières marines y sont estimées à 1,25 milliard d'euros. Or, l'élévation du niveau de la mer en réponse au changement climatique a été identifiée comme le principal facteur d'augmentation des pertes économiques dues aux inondations côtières en Europe d'ici la fin du siècle (par rapport à l'augmentation de l'exposition et de la vulnérabilité), ce qui souligne la nécessité de mieux comprendre et caractériser la hausse à venir du niveau de la mer.

Bien que j'aie choisi de travailler sur la hausse du niveau de la mer à la fois par motivation scientifique et à cause des implications de cette thématique pour la société, je me suis surtout concentrée sur l'aspect purement scientifique au cours des dernières années. Dans mes activités en cours et dans mes perspectives de recherche, j'accorde plus d'attention à la dimension sociétale en tirant parti de la convergence de mes recherches sur le niveau de la mer et du développement de services climatiques et du Service Marin de Copernicus.

Mes activités de recherche actuelles et futures ont donc un double objectif. Premièrement, elles visent à améliorer les connaissances sur les variations passées, actuelles et futures du niveau de la mer le long des côtes européennes et en étendant mes recherches aux événements extrêmes. Cela passera par une descente d'échelle dynamique de modèles de climat avec une représentation plus complète des facteurs physiques responsables des variations du niveau de la mer à la côte. Deuxièmement, elles visent à développer des informations scientifiques sur le niveau de la mer exploitables par la société. À cet égard, je contribuerai au développement de services climatiques dédiés à la hausse niveau de la mer à la côte et aux risques associés, tant pour les systèmes d'alerte précoce basés sur des prévisions à court terme que pour la hausse du niveau de la mer sur le 21<sup>me</sup>
siècle. Ce faisant, j'étendrai mes recherches à d'autres échelles de variabilité du niveau de la mer, plus axées sur les changements du niveau de la mer sur les côtes et vers les évènements extrêmes, et avec une ouverture vers les risques à grande échelle, en Europe.

Enfin, même si mon activité de recherche principale sera axée sur la hausse du niveau de la mer, les connaissances étendues que j'ai acquises en océanographie (physique, biogéochimique, et glace de mer) grâce à la gestion du programme de recherche d'accompagnement du Service Marin de Copernicus, pourraient m'amener à définir, coordonner et superviser, en collaboration, des activités de recherche sur un spectre de thématiques plus large que la hausse du niveau de la mer. A plus long terme, le développement de projections coordonnées multidécennales à centennales dédiées à l'environnement marin, pourrait soutenir de nombreux utilisateurs et politiques pour diverses applications. Ces nouvelles activités pourraient s'appuyer sur les capacités développées dans le cadre du Service Marine de Copernicus, en collaboration avec le Service sur le Changement Climatique de Copernicus et d'autres programmes, et être intégrées à long terme dans le Service Marin de Copernicus.
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# Contents

Abstract iii

1 Foreword 1

2 General Introduction 5

2.1 Drivers of sea level changes 5

2.1.1 Drivers of sea level changes at the global scale 5

Thermal expansion 7

Mass loss of glaciers and ice sheets 8

Land water storage 10

2.1.2 Drivers of sea level changes at regional scales 10

2.1.3 Drivers of sea level changes in the coastal zone 12

2.2 Sea level changes from climate models 14

2.3 Organization of the manuscript 17

3 Sea Level Variations at Global Scale 19

3.1 Introduction 19

3.2 Ability of climate models to reproduce global mean sea level changes 19

3.2.1 Comparing simulated and observed global mean steric sea level rise 20

3.2.2 Comparing simulated and observed global mean sea level rise 23

3.3 Understanding the spread of global mean steric sea level in climate models 24

3.4 Ocean mixing and global mean steric sea level 27

4 Sea Level Variations at Regional Scale 33

4.1 Introduction 33

4.2 Ability of climate models to reproduce regional sea level changes 33

4.2.1 Over the world ocean in CMIP5 models 33

4.2.2 A regional focus with one CMIP6 model 35

4.3 Detection of a forced signal in SLR over 1993-2015 37

4.4 Ocean mixing and regional steric sea level 38

5 Sea Level Variations in the Coastal Zone 41

5.1 Introduction 41

5.2 From regional, offshore sea level to coastal sea level 42

5.2.1 Spatial altimetry 42

5.2.2 Statistical downscaling 49

5.3 Contribution of wind-waves to coastal sea level changes 53

5.3.1 Local scale study, from extreme events to interannual timescales 53

5.3.2 Global scale study, interannual timescales 54

Relative contributions of coastal sea level components to its interannual variability 54

Influence of climate modes on coastal sea level components interannual variability 56
<table><tr><td>5.3.3</td><td>Global scale study, projected trends</td><td>59</td></tr><tr><td>6</td><td>From Science to Society: The Copernicus Marine Service</td><td>63</td></tr><tr><td>6.1</td><td>Introduction</td><td>63</td></tr><tr><td>6.2</td><td>The Copernicus Programme</td><td>63</td></tr><tr><td>6.3</td><td>The Copernicus Marine Service</td><td>64</td></tr><tr><td>6.4</td><td>My Role in the Copernicus Marine Service</td><td>66</td></tr><tr><td>6.4.1</td><td>Scientific evolutions of the Copernicus Marine Service: strategy</td><td>66</td></tr><tr><td>6.4.2</td><td>The Copernicus Marine Service Evolution R&amp;D programme</td><td>67</td></tr><tr><td></td><td>Long-term R&amp;D activities</td><td>67</td></tr><tr><td></td><td>Mid-term R&amp;D activities</td><td>68</td></tr><tr><td></td><td>Short-term R&amp;D activities</td><td>68</td></tr><tr><td>6.4.3</td><td>Research-to-operations management</td><td>68</td></tr><tr><td>6.4.4</td><td>Dissemination activities</td><td>69</td></tr><tr><td>6.4.5</td><td>Concluding remarks</td><td>69</td></tr><tr><td>6.5</td><td>Copernicus Marine, Sea Level Changes and Coastal Zones</td><td>70</td></tr><tr><td>6.5.1</td><td>Earth observations for monitoring marine coastal hazards and their drivers</td><td>70</td></tr><tr><td>6.5.2</td><td>The Copernicus Coastal Roadmap and envisioned evolutions for sea level and coastal zones</td><td>71</td></tr><tr><td></td><td>A core, pan-European monitoring of the coastal environment</td><td>71</td></tr><tr><td></td><td>Regional climate projections of the marine environment</td><td>72</td></tr><tr><td>6.5.3</td><td>The Copernicus Coastal Thematic Hub</td><td>72</td></tr><tr><td>6.5.4</td><td>Copernicus Services for sea level rise adaptation</td><td>73</td></tr><tr><td>7</td><td>Perspectives: Sea Level Change at the Coast and Climate Services</td><td>75</td></tr><tr><td>7.1</td><td>Introduction</td><td>75</td></tr><tr><td>7.1.1</td><td>Risks induced by sea level rise</td><td>76</td></tr><tr><td>7.1.2</td><td>Adaptation and mitigation</td><td>77</td></tr><tr><td>7.1.3</td><td>Sea level information to guide adaptation and climate services</td><td>78</td></tr><tr><td>7.2</td><td>Toward a pan-European early warning system for marine coastal floods</td><td>80</td></tr><tr><td>7.2.1</td><td>ECFAS in brief</td><td>80</td></tr><tr><td>7.2.2</td><td>Forecasts of water level at the coast: quality assessment</td><td>81</td></tr><tr><td>7.2.3</td><td>Wave-ocean coupling effects on water level at the coast</td><td>83</td></tr><tr><td>7.2.4</td><td>Transfer to core services and perspectives</td><td>84</td></tr><tr><td>7.3</td><td>Projected European coastal water level changes</td><td>85</td></tr><tr><td>7.3.1</td><td>First regional projections of sea level changes: methodological considerations</td><td>86</td></tr><tr><td></td><td>Regional projections of the ocean and sea level changes</td><td>87</td></tr><tr><td></td><td>Regional projections of the wave climate and sea-level / wind-waves coupling effects</td><td>89</td></tr><tr><td></td><td>Regional projections in extreme total water levels</td><td>91</td></tr><tr><td>7.3.2</td><td>Toward an ensemble of regional sea level projections</td><td>93</td></tr><tr><td>7.4</td><td>A European assessment report on sea level rise for stakeholders</td><td>94</td></tr><tr><td>7.5</td><td>Towards coordinated regional ocean climate predictions and projections</td><td>95</td></tr><tr><td>A</td><td>List of 5 selected publications</td><td>99</td></tr><tr><td>B</td><td>List of publications</td><td>101</td></tr><tr><td>B.1</td><td>Submitted or in preparation</td><td>101</td></tr><tr><td>B.2</td><td>Publications in peer-review international journals</td><td>101</td></tr></table>
<table><tr><td>C Supervision</td><td>107</td></tr><tr><td>C.1 PhD students</td><td>107</td></tr><tr><td>C.2 Postdocs, research engineers</td><td>107</td></tr><tr><td>C.3 Internships (M2, L3, gap year)</td><td>108</td></tr></table>
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List of Abbreviations

<table><tr><td>AR4/5/6</td><td>IPCC's 4<sup>th</sup>/5<sup>th</sup>/6<sup>th</sup> / Assessment Report (2007/2014/2022)</td></tr><tr><td>C3S</td><td>Copernicus Climate Change Service</td></tr><tr><td>CEMS</td><td>Copernicus Emergency Management Service</td></tr><tr><td>CLMS</td><td>Copernicus Land Monitoring Service</td></tr><tr><td>CMEMS</td><td>Copernicus Marine Environment Monitoring Service (aka Copernicus Marine Service)</td></tr><tr><td>CMIP</td><td>Coupled Model Intercomparison Project</td></tr><tr><td>CNES</td><td>Centre National d'Etudes Spatiales (French Space Agency)</td></tr><tr><td>CNRM</td><td>Centre National de Recherches Meteorologiques</td></tr><tr><td>COCLICO</td><td>Coastal CLImate COre services</td></tr><tr><td>CORDEX</td><td>COordinated Regional climate Downscaling EXperiment</td></tr><tr><td>CTH</td><td>Copernicus Thematic Hub</td></tr><tr><td>ECFAS</td><td>European Coastal Flood Awareness System</td></tr><tr><td>EO</td><td>Earth Observation</td></tr><tr><td>ESA</td><td>European Space Agency</td></tr><tr><td>ETWL</td><td>Extreme Total Water Level</td></tr><tr><td>EVA</td><td>Extreme Value Analysis</td></tr><tr><td>DSL</td><td>Dynamic Sea Level</td></tr><tr><td>GCM</td><td>General Circulation Model</td></tr><tr><td>GIA</td><td>Glacial Isostatic Adjsutement</td></tr><tr><td>GFCS</td><td>Global Framework for Climate Services</td></tr><tr><td>GFDL</td><td>Geophysical Fluid Dynamics Laboratory (Princeton, USA)</td></tr><tr><td>GHG</td><td>GreenHouse Gases</td></tr><tr><td>GMSLR</td><td>Global Mean Sea Level Rise</td></tr><tr><td>GMTSLR</td><td>Global Mean Thermosteric Sea Level Rise</td></tr><tr><td>IBI</td><td>Iberian Biscay Ireland regional seas (northeastern Atlantic)</td></tr><tr><td>IPCC</td><td>Intergovernmental Panel on Climate Change</td></tr><tr><td>IS</td><td>Ice Sheet</td></tr><tr><td>ISSI</td><td>International Space Science Institute</td></tr><tr><td>LEGOS</td><td>Laboratoire d'Etudes en Geophysique et Oceanographie Spatiales (Toulouse)</td></tr><tr><td>LWS</td><td>Land Water Storage</td></tr><tr><td>MFC</td><td>Monitoring and Forecasting Center of CMEMS</td></tr><tr><td>MOi</td><td>Mercator Ocean International</td></tr><tr><td>SL</td><td>Sea Level</td></tr><tr><td>SLR</td><td>Sea Level Rise</td></tr><tr><td>SMB</td><td>Surface Mass Balance</td></tr><tr><td>SROCC</td><td>IPCC Special Report on Ocean and Cryosphere in a Changing Climate (2019)</td></tr><tr><td>SSP</td><td>Shared Economic Pathways</td></tr><tr><td>STAC</td><td>Scientific and Technical Advisory Committee of CMEMS</td></tr><tr><td>TAC</td><td>Thematic Assembly Center of CMEMS</td></tr><tr><td>TOA</td><td>Top Of the Atmosphere</td></tr><tr><td>TWL</td><td>Total Water Level</td></tr><tr><td>VLM</td><td>Vertical Land Motion</td></tr><tr><td>WCRP</td><td>World Climate Research Programme</td></tr></table>
**WL** Water Level

**WMO** World Meteorological Organization
# 1 Foreword

I used to be a physical oceanographer exploring the ocean circulations in a remote and interesting part of the world, the Solomon Sea. At that time, I scratched the surface of the essential role the ocean is playing in the climate system. Eager to learn more, I've joined a climate modeling center, contributed to the development of climate models and started to perform climate projections. Through the influence of the representation of internal-wave driven ocean mixing on steric sea level changes in climate models, I've opened the pandora box of the processes that are impacting sea level changes. The incredible range of processes and factors driving sea level changes, including the vast majority of ocean physics (ocean currents, mixing, density etc) but obviously also other components of the Earth climate system (atmosphere, cryosphere, hydrology) and geodesy and geophysical factors (Earth's gravity field, rotation, solid earth deformation etc) was a strong incentive for me to choose and orient my research activities towards sea level changes. What an extraordinary playground for a curious scientist! And what a thematic with concrete implications for society, given the tremendous threat sea level rise is posing to coastal communities and ecosystems worldwide. That was it, I decided to dedicate my research to sea-level variations.

When I started to work on sea level rise in 2014, 21st century projections were rather limited to global mean sea level rise (SLR); regional projections were only emerging back then. A World Climate Research Programme grand challenge was setup on regional sea-level change and coastal impacts. Whether past and future sea levels were rising at the same rate in the deep, open ocean and at the coast was an open question. Because of the societal implications of sea level rise, I've thus decided early on to focus my research on coastal sea level variations. But as sea level changes at the coast depend on sea level changes at global and regional scales, I've worked on these different scales. After providing a quick introduction on the different drivers of sea level changes at global, regional and coastal scales in Chapter 2, I dedicate one chapter on my research activities to each of these scales in Chapters 3, 4, and 5 respectively.

My scientific approach has been to (i) characterize how sea level trends and interannual variability differ from the deep, offshore ocean to the coastal ocean, (ii) to understand the relevant processes driving sea level changes, and especially so at the coast from the long-term trends to extremes, and (iii) to regionalize projected sea level trends and to better characterize projected changes in extreme sea levels. To that aim, I've analyzed existing data and developed dedicated tools such as reprocessed coastal altimetry, sensitivity model (climate, ocean or wave) experiments to the representation of different processes, dynamically downscaled climate model projections of sea level changes.

The main questions I've been interested in are:

* Projections of SLR are essentially based on climate models. Confidence in SLR projections therefore depends on the ability of climate models to simulate the various components of SLR and to reproduce SL changes over the historical period. Major questions in climate modeling are therefore: can climate models accurately reproduce past changes and can they successfully and robustly predict the future? What explains the spread in climate-model projections? These questions apply at both global and regional scales.
* How representative are regional sea level changes induced from climate models for coastal sea level changes, where impacts are occurring? In other words, how different is coastal sea level variability from the large-scale, offshore one? How different are regionally downscaled projections of sea level changes compared to that from the parent global climate model? How the inclusion of coastal sea level drivers and their interactions with mean sea level changes are altering coastal sea level change representations?

* What is the relative importance of the different processes and factors contributing to SL changes at the coast at different timescales?

* Wind-waves are a known large contributor to extreme water levels at the coast. But as wind regimes are also changing in response to climate change, are wind-wave contribution to coastal sea level change also changing at interannual-to-multidecadal timescales? What are time-mean projected changes by the end of 21st century?

Over the past 7 years, I've developed my sea-level research activities mostly in parallel to my activities on the definition, coordination and management of the Copernicus Marine Service R&D program (presented in Chapter 6), although these two streams of activities have also fed one another. The Copernicus Marine Service is user and policy driven and as such, it provides scientific data and information for the ultimate benefit of society, thereby creating a pathway for actionable science for society. This "science for society" pathway is much needed for sea level rise since mitigation of climate change and adaptation measures can reduce SLR induced risks. Yet, authoritative, consistent and decision-oriented dedicated climate services to support policies, adaptation and decision-making are still in their early development worldwide. Floods, with their impacts on people, the built environment and the economy, have been identified as one of the four key climate change induced risks for Europe. More than 50 million people currently live in European low-elevation coastal zones, and the expected annual damage of marine coastal flood is estimated at €1.25 billion euros for Europe. The increased hazards posed by SLR in response to climate change has been identified as the main driver of the future rise in coastal flood losses for Europe (compared to increased exposure and vulnerability), stressing the need to better understand and characterize projected sea level changes.

Although I chose to work on sea level changes motivated by both scientific and societal implications reasons, I've mostly focused on the former during the past years. In my on-going activities and research perspectives, presented in Chapter 7, I'm paying more attention to the latter by leveraging on the convergence of my sea-level research and of the development of Copernicus Marine and climate services.

The objectives of my current and future research activities are two-fold. First, they aim at improving knowledge of past, current and projected sea level changes along European coasts, with a focus on coastal sea level changes and with an extension of my research towards extreme events. This will notably be achieved through a regional dynamical downscaling of climate model with a more comprehensive representation of physical drivers of coastal sea level changes. Second, they aim at bridging the gap between sea level science and actionable information for society. In that regard, I'll contribute to the development of climate services dealing with sea level change at the coast and related risks, both for early warning systems based on short-term forecasts, and for long-term sea level rise and changes in water level extremes. This will extend my research towards other scales of sea level variability, more focused on coastal sea level changes, and with an opening from sea level hazards information for broad-scale, European, risk assessment.

Finally, although my main research activity will be targeted towards the aforementioned sea-level topics, the broad knowledge I've gained on blue, white and green ocean sciences through
the management of the Copernicus Marine R&D program, much wider than SLR, and the capacity to identify and prioritize needed scientific evolution could lead me to define, coordinate and supervise research activities on a wider spectrum of thematics than SLR. On longer time horizons, the development of coordinated multidecadal-to-centennial projections, or even of decadal predictions dedicated to the marine environment could support many users and policies, for various applications. "What-if" scenarios could allow to explore different mitigation and adaptation strategies, for instance. These new activities could leverage on the capabilities of the Copernicus Marine Service, in collaboration with the Copernicus Climate Change Service and other programs, and become part of the core services such as the Copernicus Marine Service in the long run.

The work presented in this manuscript would not have been possible without many enjoyable and fruitful collaborations (in the following chapters, publications that I (co-)authored appear in bold fonts). I want to warmly thank my colleagues from whom I've learnt so much. A special thank goes to B. Meyssignac, G. Le Cozannet, R. Almar, F. Birol, R. Hallberg, S. Legg, PY. Le Traon, M. Drevillon, Y. Drillet, A. Voldoire, G. Reffray, among many others. It also benefited from the work of PhD students (V. Kumar, A. Chaigneau), undergrad students (M. Nonti, B. Chide, A. Chaigneau, G. Mouttapa, M. David) and from other colleagues (S. Padilla, G. Cesbron, M. Irazoqui) I've been glad to supervise over the past years. I also thank the Copernicus Marine Service Scientific and Technical Advisory Committee members, and especially the chair/co-chairs, N. Smith, P. Brasseur and A. Pascual, for discussions shaping the future of the service. Finally, I thank my many colleagues at Mercator Ocean and the coffee machine(s), for their constant and precious support.
<figure><img src="image_6.png" /></figure>
# 2 General Introduction

*The more I learn, the more I realize how much I don't know.*

Albert Einstein

Sea level (SL) changes at the coast result from processes acting at various space and time scales, from extreme events to long-term SL rise, with the superimposition of global, regional, and more local variations (Fig. 2.1). There is a large body of literature describing key drivers of SL changes at different scales. In this section, I don't intend to give a full review but only to provide some general background information relevant for the next chapters of this manuscript. The terminology for sea level processes follow as much as possible that presented in Gregory et al., 2019.

<figure><img src="image_7.png" /></figure>

FIGURE 2.1: A schematic illustration of the climate and non-climate driven processes that can influence global (blue colours), regional (green colours), relative and extreme sea level (ESL) events (red colours) along coasts. Major ice processes are shown in purple and general terms in black. SLE stands for Sea Level Equivalent and reflects the increase in GMSL if the mentioned ice mass is melted completely and added to the ocean. From SROCC, Oppenheimer et al., 2019.

## 2.1 Drivers of sea level changes

### 2.1.1 Drivers of sea level changes at the global scale

Sea level rise (SLR) is a direct consequence of climate change, which is due to the current energy imbalance of our planet at the top of its atmosphere (e.g. Forster et al., 2021; Meyssignac et al.,
2019; Von Schuckmann et al., 2016). The Earth receives 342 W m⁻² from the Sun shortwave radia-
tion. Nearly 30% of that radiation is reflected back to space by the Earth surface and atmosphere
(Figure 2.2). The remaining radiation warms our atmosphere, ocean, land and cryosphere. In
return, these components emit long-wave radiation (black body radiation) back to space. Part of
these long wave radiation are absorbed by greenhouse gases such as water vapor and CO₂ in our
atmosphere, leading to a natural greenhouse effect without which the atmosphere would be 33
degrees colder. Yet, human activities have led to increased concentrations of greenhouse gases in
the atmosphere, increasing longwave radiations towards the Earth surface, leading to a net imbal-
ance of ~ 0.7 W m⁻² at the top of the atmosphere. The Earth energy imbalance, with our planet
reemitting less energy to space than it receives from the Sun, leads to an excess of energy, mostly in
the form of heat, in the climate system. About 91% of the excess heat stored in the climate system
has been absorbed in the oceans (Cheng et al., 2017; Levitus et al., 2012; Von Schuckmann et al.,
2020). This ocean heat uptake causes a thermal expansion of the ocean leading to a global mean
rise in sea level. The remainder of the heat excess has been absorbed by the atmosphere, land ice,
sea ice and land surfaces. As land ice (glaciers, ice sheets) melts and is dynamically discharged
to the ocean, water is added to the ocean, increasing its mass and volume and thereby rising sea
level (Figure 2.2). The contemporary global mean sea level rise on decadal timescales and longer is
therefore a direct and integrative response to the Earth energy imbalance causing climate change.
As such, global mean sea level rise has been selected as one of the seven indicators of climate
change by the World Meteorological Organization.

<figure><img src="image_8.png" /><figcaption>FIGURE 2.2: Schematic showing the Earth energy imbalance at the top of the at-
mosphere, *N*. The resulting heat excess of the climate system is uptaken at 91% in
the ocean, leading to thermal expansion of the seawater, while ~ 3% is absorbed by
icesheets and glaciers, inducing ice mass transfer from land to the ocean, adding to
the ocean mass and rising sea level. SW stands for short-wave and LW for long-
wave.</figcaption></figure>
### Thermal expansion

Oceans cover about 71% of the Earth's surface, with an average depth of nearly 4 km. Due to their large mass and heat capacity (1,000 times larger than that of the atmosphere), oceans are the largest reservoir of the anthropogenic heat excess in the climate system. As the ocean warms, its density decreases and it occupies a larger volume which is translated by a rise in sea level (e.g. positive steric sea level change). Ocean heat uptake is not spatially uniform but is rather dominated by the Southern Ocean (e.g. Morrison et al., 2016; Zanna et al., 2019), with the North Atlantic possibly uptaking more heat over the next decades (Shi et al., 2018). Over 1971-2018, thermal expansion has been the largest contributor to global mean sea level rise, explaining half of the ~11 cm rise (Figure 2.3, Fox-Kemper et al., 2021). Heat absorbed by the ocean at its surface is then exported at depth, redistributed within the ocean through advection and mixing (section 2.1.2). Globally, oceans have absorbed more than 90% of the Earth heat excess accumulated in the climate system since 1955, of which 66% is in 0-700m depth ocean layer, 24% in the 700-2000m layer and 10% below 2000m depth (Zanna et al., 2019).

Under a high-emission/ low-mitigation climate change scenario (SSP5-8.5, O'Neill et al., 2016), thermal expansion is projected to contribute to 39% of the 77 cm of GMSLR by 2100 (from the 1995-2014 baseline, Fig. 2.3).

<figure><img src="image_9.png" /></figure>

FIGURE 2.3: Observed and projected global mean sea level rise (GMSLR) over 1971-2100 under a low CO₂ emission scenario (SSP1-2.6) and a very high emission scenario (SSP5-8.5). The contributions from the major GMSLR constituents are shown for years 2018, 2050 and 2100. From IPCC AR6, Fox-Kemper et al., 2021.

As heat is exported away from the ocean surface mixed layer and isolated from contact with the atmosphere, it buffers the warming of the atmosphere over long timescales (centuries to millenia). If emissions of greenhouse gases (GHG) were to cease, the concentration of GHG in the
atmosphere would decline over the first following decade mostly due to uptake by the land car-
bon sink and dissolution and buffering of CO₂ in the ocean mixed layer. As these carbon sinks
saturate, the decline in atmospheric CO₂ slows. On longer timescales, CO₂ is removed from the at-
mosphere through buffering in the deep ocean and dissolution of calcium carbonate in sediments
(Archer et al., 1997). As a result, CO₂ has a long timelife of 5 to 200 years, so that a substantial
part of anthropogenic CO₂ will remain in the atmosphere centuries after emissions stopped, and
will keep contributing to the radiative forcing of the Earth until a new equilibrium is reached.
Hence, after cessation of CO₂ emissions, the surface air temperature and upper ocean layer warm-
ing would almost stabilize within decades (with a slight increase persisting for centuries, Zickfeld
et al., 2017), while the deep ocean would continue to warm due to thermal coupling between the
upper and lower layers of the ocean, tracking the time-integral of the radiative forcing. Due to the
large thermal inertia of the ocean, thermal expansion would therefore continue at unabated rates
for centuries after CO₂ emissions cease (Bouttes et al., 2013; Mengel et al., 2018; Zickfeld et al.,
2017).

Mass loss of glaciers and ice sheets

Water is continuously exchanged between the different reservoirs of the Earth surface (atmosphere, cryosphere, surface and ground water over continents, ocean) as part of the water cycle and in response to internal climate variability and climate change. The transfer of water between land and ocean contributes to ocean mass and volume variations, which translate in sea level changes. 362 10¹² kg (362 Gt) of land ice mass loss raises the global mean sea level by 1 mm. The current Greenland and Antarctic icesheets account for ~ 70% of freshwater on Earth. If melted completely, mountain glaciers would raise sea level by 0.5m, the Greenland icesheet by 7m, and the Antarctic icesheet by 58m (with the unstable west Antarctic icesheet holding a potential of 5m of SLR) (Figure 2.1).

Although the formation and collapse of ice sheets have been the largest contributors to multi-
millennia timescales sea level changes (Quaternary glaciations/ deglaciations in response to Mi-
lankovitch cycles), we will focus here on contemporary changes.

Glaciers

Glaciers contribute for a small fraction of the total ice surface on Earth ( 4%), which corresponds to a potential of ~ 0.3 m of SLR if all glaciers were to melt (Farinotti et al., 2019)). Yet, glaciers are highly responsive to climate change and glacier mass loss have been a dominant contributor to GMSLR during the 20th century. Over 1971-2018, glaciers have contributed to 22% (21 mm) of GMSLR (Figure 2.3, Fox-Kemper et al., 2021). The mass of a glacier is set by its surface mass balance (SMB), which is the difference between mass gained by snow accumulation and mass ablation through melting and sublimation.

It can be noted that out of the estimated 200,000 glaciers of the world (Randolph Glacier Inventory), only 300 are observed. Therefore, the contributions from glacier mass loss to GMSLR depends on regional extrapolation for the calibration of SMB models.

As glaciers are out of balance with current climatic conditions, they will continue to lose mass
in the future even without further temperature increase. Mountain glaciers are projected to con-
tribute to 23% of the 77 cm of GMSLR by 2100 (from the 1995-2014 baseline) under the SSP5-8.5
scenario (Fig. 2.3).

Ice sheets

The Greenland and Antarctic ice sheets have the potential to be the largest contributors to sea
<figure><img src="image_10.png" /></figure>

FIGURE 2.4: Current world-wide glaciers from the Randolph Glacier Inventory, their area in km² (green/blue circles) per regions and their regional mass budget (in Gt yr⁻¹, red circles) over 2003-2009 (from Gardner et al., 2013).

level rise over the next centuries due to their large grounded water storage. Icesheets lose mass through a negative SMB and through discharge of ice stream flowing from the ice sheet to ocean (potentially through ice shelves) and iceberg calving (dynamical ice mass loss). Dynamical ice loss is influenced by different processes and can be accelerated through basal melting, ice shelf conditions (ice shelf thickness, surface crevasses, ice shelf geometry and buttressing effects) and instabilities of ice shelves (e.g. marine ice shelf instability -MISI, Ritz et al., 2015; Robel et al., 2019-, marine ice cliff instability -MICI, DeConto and Pollard, 2016; Edwards et al., 2019- see also Pattyn, 2018). Although changes in ice shelves don't really contribute to sea-level rise directly as they are already floating, they provide an important buttressing effect on the grounded ice of the main ice sheet (whose loss does contribute to SLR).

The Greenland and Antarctic ice sheets are different in many aspects, including their extent, elevation, surrounding atmospheric and ocean conditions, ice loss key processes and overall response to climate change. For instance, the Greenland ice sheet mass loss is due to both negative SMB and to dynamical ice mass loss (ice flowing into the ocean and iceberg calving) while the Antarctic ice sheet loses mass mostly dynamically. The Antarctic ice sheet also mostly loses mass in its western sector, where the bed of the ice sheet is well below sea level and instabilities are more prone to be triggered.

Over 1971-2018, the Greenland ice sheet has contributed to 13% (12 mm) of GMSLR, while the Antarctic ice sheet (including peripheral glaciers) contributed to 7% (7 mm) of GMSLR (Figure 2.3, Fox-Kemper et al., 2021). However, the ice sheets mass loss is accelerating so that their contribution to GMSLR is also increasing over more recent periods. Large uncertainties exist on projections of the Antarctic ice sheet mass loss especially, depending on the onset of processes and instabilities and their timing that could lead to high-end sea level rise projections by 2100 and later. When not accounting for processes with a low level of confidence (e.g. the marine ice sheet instability), ice sheets are projected to contribute to 32% of the 77 cm of GMSLR by 2100 (from the 1995-2014 baseline) under the SSP5-8.5 scenario, almost equally partitioned between the contribution from
the Greenland and Antarctic ice sheets (Fig. 2.3).

## Land water storage

Transfer of terrestrial water (other than ice caps and glaciers) to the ocean and vice-versa as part of the natural hydrological cycle and human interventions lead to ocean mass and sea level changes. Land water storage (LWS) changes result from two main components: groundwater depletion and artificial water impoundments on land. Additional contributions come from changes in water mass in endorheic basins, deforestation and changes in soil moisture, changes in the snow cover and permafrost.

Groundwater depletion is mostly due to groundwater pumping (to answer an increasing water demand for drinking purposes, industries and agriculture). Roughly 80% of groundwater depletion ends up in the ocean (Wada et al., 2016), leading to SLR. On the contrary, water impoundment behind dams and reservoirs leads to a sea level fall. It has been estimated that nearly 30,000 reservoirs were built during the 20^th^ century, with a sharp increase from the 1950s (Chao et al., 2008; Konikow, 2011). Although water impoundment exceeded groundwater depletion for the majority of the 20^th^ century, it has been tapering off since the 1990s due to a decline in dam and reservoir construction. On the contrary, groundwater depletion has more than doubled over the last decades, with groundwater depletion rates exceeding rates of water impoundment, leading to a positive SLR contribution of LWS. This trend is expected to continue over the 21^st^ century, with a decreasing relative contribution of water impoundment and an increasing contribution from groundwater depletion (Wada et al., 2016). However, large uncertainties are attached to LWS contribution to SLR (Cáceres et al., 2020; Frederikse et al., 2020).

Over 1971-2018, LWS has contributed to 8% (7 mm) of GMSLR (Figure 2.3, Fox-Kemper et al., 2021). By 2100, LWS is projected to contribute to 4% of the 77 cm of GMSLR (from the 1995-2014 baseline) under the SSP5-8.5 scenario (Fig. 2.3).

Before moving on to drivers of sea level changes at regional scales, it is useful to mention that although I mostly focus on 21st century sea level changes in this manuscript, GMSL is committed to rise beyond 2100. GMSL will continue rising for centuries and will remain elevated for thousands of years, even if we stabilize the Earth's surface temperature. This is due to the large ocean inertia and continuing deep-ocean heat uptake, and to the mass loss of Greenland and Antarctic ice sheets (Box et al., 2022; Clark et al., 2018; Fox-Kemper et al., 2021; Mengel et al., 2018). For instance, if a 2 degree global warming level were to be exceeded, GMSL would be committed to rise by 2 to 6 m over the next 2 millenia. If a 4 degree global warming level were to be exceeded, GMSL would be committed to rise by 12 to 16 m over the next 2 millenia (Fox-Kemper et al., 2021).

### 2.1.2 Drivers of sea level changes at regional scales

Sea level has not and will not rise uniformly over the ocean (Figure 2.5). At regional scale (O(100-1,000 km)), sea level changes can deviate substantially from GMSLR (mostly ranging within ±30% of the global rise, Slangen et al., 2014) due to a number of processes, with three key drivers. First, ocean circulations redistribute the seawater mass, heat and salinity, leading to regional dynamic sea level changes. Changes in ocean circulations are mostly driven by surface wind stress, but also by air-sea heat and freshwater fluxes (Forget and Ponte, 2015; Meyssignac et al., 2017a; Todd et al., 2020) and by intrinsic ocean variability (Llovel et al., 2018; Serazin et al., 2015). Regional dynamic sea level changes are mostly steric (ocean density changes), with a predominance of its thermosteric component.
<figure><img src="image_11.png" /></figure>

FIGURE 2.5: Regional sea level trends in mm yr⁻¹ over the period 01/1993-10/2019 from satellite altimetry. Credit: CMEMS, C3S.
Second, geographical redistribution of mass over the Earth, including contemporary or past transfers between land and ocean such as glaciers and icesheets mass loss or land water storage changes, induce change in Earth gravity and rotation as well as viscoelastic solid-Earth deformations (GRD). GRD effects induce sea level changes through changes in the geoid and vertical land movement (Tamisiea, 2011). The glacial isostatic adjustment (GIA, Peltier, 2004) causes contemporary relative sea level change due to GRD effects through ongoing viscous changes in the solid Earth caused by past changes in land ice, mostly through the last deglaciation following the Last Glacial Maximum (~20,000 years ago). GIA and contemporary GRD effects on relative sea level changes are illustrated through sea level fingerprints, a quasi-equilibrium geographical pattern associated to a given change in the geographical distribution of mass on Earth (Spada and Melini, 2019a). These sea-level fingerprints are presented in Figure 2.6, and induce substantial relative sea level changes at high latitudes close to the mass loading changes. Indeed, masses such as ice sheets exert a gravitational pull on surrounding ocean water over a distance of $O(10^6$ km) rising a bit sea level there. As icesheets lose mass, the gravitational pull they exert is reduced making sea level in the surrounding region less elevated. The added freshwater to the ocean is fastly redistributed over the ocean, raising sea level further away from the icesheet.

Third, regional changes of atmospheric pressure loading over the ocean (due to changes in atmospheric circulations and moisture content) induce regional changes in the inverted barometer effect at scales longer than $O(1$ month) (Wunsch and Stammer, 1997). For a positive regional anomaly of sea level pressure of 1 mbar, regional sea level drops by 1 cm. The inverted barometer effect is a more minor driver of regional sea level changes at seasonal and longer timescales.

<figure><img src="image_12.png" /></figure>

FIGURE 2.6: The spatial fingerprint of sea level rise expressed as a percentage of the global mean sea level contribution from the dominant terms in the sea level budget, extracted from Grinsted et al., 2015.

### 2.1.3 Drivers of sea level changes in the coastal zone

*This section discusses the contribution of Woodworth et al., 2019.*

At coastal scales, several other processes lead to substantial sea-level changes from the regional, open ocean and should be considered when estimating local SL changes at the coast
(Woodworth et al., 2019). Among these processes are tides, atmospheric surges, wind wave con-
tributions, seiches, coastal waves, effects of river discharges and vertical land motion (Figure 2.7).
Coastal sea level variability spans a wide range of timescales and spatial scales (e.g. signals from
coastal trapped waves, Hughes et al., 2019). Processes driving coastal sea level change can also
interact (e.g. Idier et al., 2019) due to their effects and dependence on water depth for instance.
In addition, relative sea level changes can be due to vertical land movements (VLM) of natural
(sediment compaction in deltas, Earth tectonics, GIA and contemporary solid Earth deformation
due to land ice mass loss) or anthropic origins (pumping of groundwater, weight of the built envi-
ronment etc.). In many coastal megacities, VLM can induce relative sea level trends similar to or
larger than trends induced by oceanic and climate factors causing absolute sea level changes (see
e.g. Figure 7 of Melet et al., 2020b, Nicholls et al., 2021, Wu et al., 2022).

<figure><img src="image_13.png" /></figure>

FIGURE 2.7: Schematic of processes contributing to total water level changes at the coast. The mean sea level derived from radar altimetry data includes contributions from ocean thermal expansion and ocean circulation, transfer of water from land to ocean due to mass loss from glaciers and the Arctic and Antarctic ice sheets, as well as from land water storage changes (pictograms on the right, top to bottom). Sea level variability from tides and coastal processes including storm surges due to air pressure effects and wind setup, as well as wave setup and swash are superimposed on the larger-scale changes. Vertical land movements are denoted by VLM. The rotation of the depression (D) applies to the northern hemisphere. Extracted from **Woodworth et al., 2019**, adapted from **Melet et al., 2018**.

Tides

In many places, astronomical tides are dominating the high-frequency (daily and half-daily) coastal
sea level changes. When propagating from the open to coastal ocean, tides are amplified and can
be in resonance depending on the coastline and water depth. Tides also vary on other frequencies,
including at low frequencies (mainly at periods of 15 days, 4.4 years -perigee precession effect-,
18.6 years -lunar nodal cycle-, Haigh et al., 2020) (Woodworth et al., 2019).

Atmospheric surge

This component represents sea level changes due to atmospheric pressure effects (including the
inverted barometer effect) and wind setup, where surface winds pile up water against the coast.
Because this contribution is larger during storms (which are characterized by atmospheric low
HOW DO WIND GENERATED WAVES IMPACT COASTAL SEA LEVEL ?

<figure><img src="image_14.png" /></figure>

FIGURE 2.8: Schematic description of wave-induced processes impacting coastal sea level for (a) infragravity waves, (b) wave setup and (c) wave runup. The horizontal dotted black line represents the still water level, which includes the mean sea level, the astronomical tide and the atmospheric surge components. Extracted from Dodet et al., 2019.

pressure and strong winds), this component is usually referred to as storm surge. Atmospheric surges are the largest in places located under storm tracks or cyclone trajectories, and facing large continental shelves (Walton and Dean, 2009).

Wave setup and runup

Wave contributions to coastal sea level changes are due to both locally generated wind waves (wind-sea waves) and remotely generated waves (swells) (Dodet et al., 2019). Wind-generated waves accumulate (during their growth) and transport momentum across ocean basins. This momentum is released to the water column when waves break in the shallow surf zone, which typical width ranges from 10m to 10km. Wave breaking in the surf zone induces a dissipation of wave energy, and a corresponding shoreward decrease of the wave energy flux. The induced
shoreward convergence of the wave-induced momentum flux (also called wave radiation stress) causes a shoreward sea level increase to compensate the decrease in momentum flux. Longuet-Higgins and Stewart, 1964 hypothesized wave setup to result from a dynamical balance between the cross-shore pressure gradient associated with a cross-shore tilt in sea level and the momentum flux convergence associated with wave breaking (Figure 2.8). Wave setup thus corresponds to the time mean dynamic elevation of SL due to wave breaking.

The waterline oscillations at the time scale of individual waves and wave groups corresponds to the swash. Together, wave setup and swash combine to achieve the wave runup, which is the maximum elevation reached by the swash.

## 2.2 Sea level changes from climate models

A range of approaches have been taken to making sea-level projections, including semi-empirical models, literature syntheses, model hybrid studies, model syntheses, probabilistic projections, expert judgement studies (see a review by Garner et al., 2018). The main approach thus far for 21st century sea level projections relies on climate models (e.g. Oppenheimer et al., 2019, Fox-Kemper et al., 2021). Climate models can directly simulate dynamic sea level change (DSL, corresponding to the variable zos in CMIP) associated with ocean density and circulation changes. Because most ocean component of climate models are Boussinesq (therefore conserving the ocean volume rather than its mass), they do not explicitly simulate the global mean thermal expansion. This contribution can however be diagnosed from the simulated 3D ocean density field and added a posteriori (Griffies and Greatbatch, 2012). The sum of the global mean steric sea level and of the DSL (corrected for the inverted barometer effect) is called sterodynamic SL (Gregory et al., 2019) and is the only contribution to SLR that is directly simulated by climate models.

At the time of the IPCC AR4 (Meehl et al., 2007), regional sea level projections only included the sterodynamic sea level component (Fig. 2.9a). In particular, ice-sheet models and the understanding of ice-sheet dynamics were not mature enough yet. Contributions from land-ice mass were accounted for GMSLR only.

Much progress has been made over the last decade in estimating past and projected regional sea level changes from climate models (Carson et al., 2019; Slangen et al., 2017a, 2014, 2012), especially regarding land ice components. Projections of regional relative sea level changes over the 21st century were developed based on CMIP3 and CMIP5 model outputs (Slangen et al., 2014, 2012) by calculating the contribution of glaciers and ice sheets changes using offline process-based regional models forced with boundary conditions derived from climate model projections (mainly temperature and precipitation) (e.g. Fettweis et al., 2013; Marzeion et al., 2012).

Land water storage changes were estimated from observations and global hydrological models (Döll et al., 2014; Konikow, 2011; Wada et al., 2016) and projections based on Representative Concentration pathways (RCPs) (e.g. Wada et al., 2016). GIA was estimated using an ice chronology and the so-called sea-level equation (Farrell and Clark, 1976; Peltier, 2004) is used to get the spatial fingerprint of the GIA contribution due to the viscoelastic response of solid Earth and changes in Earth's gravity field and rotation (referred to as GRD, Gregory et al., 2019) induced by the redistribution of mass on Earth following the melt of the last glacial maximum icesheets. GRD effects were also accounted for (with more emphasis on the elastic response of solid Earth) to get the spatial fingerprints of contemporary mass transfer between the cryosphere, land water and ocean (Spada and Melini, 2019b). The regional contributions were added together to get regional relative sea level historical and projected changes.

Following this approach, projections of regional relative SLR were presented over the 21st century in the IPCC AR5 (Church et al., 2013b) (Fig. 2.9b). As no model can currently simulate all contributions to sea level rise, these projections were constructed by adding up the individual
contributions. In AR5 and SROCC, the sterodynamic SL change from climate models was added to the contribution of (i) land-ice mass computed from offline models forced by GCM outputs, (ii) LWS changes and (iii) GIA, using their GRD fingerprints to get regional relative SL changes. Although a first attempt was made in AR5 to account for the contribution of dynamic mass loss of the Antarctic IS to SLR, modeling was still based on limited physics and the quantification of this contribution based on a few studies. In AR6 (Fox-Kemper et al., 2021), land ice contributions (ice sheets and glaciers) are based on model intercomparison projects (MIPs) and on gaussian process model calibrated emulators of these MIPs (Edwards et al., 2019). Emulators are used to make projections coherent with the assessed equilibrium climate sensitivity and projections of global surface air temperature and to populate more comprehensively climate, ice sheet and glacier modeling uncertainties. GMTSLR is also based on an emulator of CMIP6 results, while dynamic sea level change directly comes from CMIP6 models (zos, with removal of the climate drift). Global and regional sea level projections based on CMIP6 models are discussed in IPCC AR6 Fox-Kemper et al., 2021, including work from, for instance, Hermans et al., 2021; Jevrejeva et al., 2021; Palmer et al., 2020, and probabilistic projections which are notably discussed in Kopp et al., 2017; Le Cozannet et al., 2019.

Since AR5, understanding and modeling of the dynamic ice-sheet contribution to SLR have represented an area of active research. In SROCC (Oppenheimer et al., 2019), AR5 global and regional SLR projections were updated by including a new estimate of the dynamic contribution of the Antarctic IS (based on process-based studies by Bulthuis et al., 2019; Golledge et al., 2015; Golledge et al., 2019; Levermann et al., 2014; Ritz et al., 2015) (Fig. 2.9c), resulting in higher SLR projections than in AR5.

Yet, several uncertain processes were not accounted for in SROCC for sea level projections, due to a lack of science maturity or consensus. These processes relates to the Antarctic ice sheet contribution to sea level rise, which represents a large source of uncertainty under high-emission scenarios. Among them is hydrofracturing of the ice shelves due to melting at the surface and rainfall draining in crevasses, fracturing the floating ice shelf and contributing to its calving, reducing back pressure at the grounding line, higher subaerial grounded ice cliffs and possibly triggering marine ice cliff instabilities (MICI, DeConto and Pollard, 2016). Ice shelves - ocean feedbacks could also occur (Bronselaer et al., 2018). Basal melt of ice shelves freshens and stratifies the water layers below the ice shelf. In the Southern Ocean, westerly winds induce an Ekman pumping tilting isopycnals towards the surface. This Ekman pumping is responsible for the upwelling towards the surface and north of the Antarctic Circumpolar Current of relatively warmer, deep water masses such as the Circumpolar Deep Water (e.g. Talley, 2013). When the surface ocean stratifies, isopycnal surfaces are depressed and flattened, so that the transport and mixing of the relatively warmer Circumpolar Deep Water along isopycnals heads rather towards the continent, leading to a subsurface warming of water proximal to the ice shelf base and cavities and to the grounding line (Bronselaer et al., 2018). This could in turn favor basal melt and marine ice sheet instability (MISI, Pattyn et al., 2012; Ritz et al., 2015). In addition, re-stratification due to basal melting of the Antarctic ice sheet could increase the formation of sea-ice, isolating further the ocean from the atmosphere and inhibiting the densification of surface water through reduced heat lost to the atmosphere, reducing deep water convection with consequences for the global overturning circulation (Marshall and Speer, 2012; Talley, 2013). Finally, the effects of added freshwater to the ocean from grounded ice on the dynamic sea level are not yet accurately taken into account in climate models.

Regional SLR projections for the end of the 21st century presented in the AR4 (Meehl et al., 2007), AR5 (Church et al., 2013b), SROCC (Oppenheimer et al., 2019) and AR6 (Fox-Kemper et al., 2021) IPCC reports are shown in Fig. 2.9. These different generations of projections exhibit robust regional patterns: regional sea level rise is projected to be larger than the GMSLR in the
<figure><img src="image_15.png" /></figure>

FIGURE 2.9: Regional sea level projections in IPCC reports since 2007. (a) In AR4 (Meehl et al., 2007), only the sterodynamic component of regional sea level rise was included. Regional relative SLR projections shown in (a) are using the SRES A1B scenario (close to the RCP6.0 scenario used in AR5), 16 CMIP3 climate models, and changes are from 1980-1999 to 2080-2099. Stippling denotes regions where the magnitude of the multi-model ensemble mean divided by the multi-model standard deviation exceeds 1.0. (b) In AR5 (Church et al., 2013b), atmospheric loading, manometric SLR and their GRD effects (from glaciers, SMB of the Greenland and Antarctic IS, LWS, GIA) were added to sterodynamic sea level to build regional sea level projections. Projections shown in panel (b) are for RCP4.5 using 21 CMIP5 models between 1986-2005 and 2081-2100 and the decomposition of the contributors is shown. (c) SROCC regional RSL median change between 1986-2005 and 2081-2100 (in m) for RCP4.5. Projections are based on updated values for Antarctica, include GIA and GRD effects, and results from AR5 for glaciers, land water storage (LWS) and the Greenland IS. (d) AR6 regional median RSL changes between 1995-2014 and 2100 for the SSP2-4.5 climate change scenario (close to RCP4.5). Global mean thermal expansion, ice sheets and glaciers contributions are derived from global surface air temperature projections from emulators consistent with the assessment of the equilibrium climate sensitivity and transient climate response. The contribution from icesheets include processes whose understanding and modeling we have medium confidence in.
Arctic (esp. in the Canada basin and over the East Siberian Shelf), a narrow meridional band around 35°S of larger SLR in the Atlantic and Indian sectors of the Southern Ocean and a smaller than the global mean SLR poleward in the Southern Ocean. This meridional dipole in the Southern Ocean is associated with a poleward shift and intensification of the westerlies in response to GHG emissions and ozone depletion (e.g. Fyfe et al., 2007).

**2.3 Organization of the manuscript**

Most projections of SLR are based on climate models. The confidence in SLR projections therefore depends on the ability of climate models to simulate the various components of SLR and to reproduce SL changes over the historical period. Major questions in climate modeling are therefore: can climate models accurately reproduce past changes and can they successfully and robustly predict the future? What explain the spread in climate-model projections?

In Chapter 3 and 4, I provide insights on these questions for the global-mean and regional sea level rise.

Climate models do not fully resolve SL changes at the coast due to their coarse resolution. A number of small-scale ocean processes that are specific to the highly dynamic coastal zone could contribute to modify sea level rise rates from the offshore, deep ocean to the coastal zone. Moreover, a number of relevant processes that are driving sea level changes at the coast are not represented in climate models (tides, atmospheric surface pressure forcing, wave setup). Consequently, sea level low-frequency changes at the coast may not just be an extrapolation of the regional sea level changes estimated with climate models and assessed in Chapter 4. This issue is explored in Chapter 5, first with dedicated altimetry products and through statistical downscaling, and then by assessing the contribution of wave-driven sea level changes to low-frequency (trends, interannual variability) total water level changes at the coast.

Chapter 6 is dedicated to my activities as head of the Copernicus Marine Service R&D program. Although it may be perceived as a digression from my sea level research activities, Chapter 6 actually also presents long-term evolutions of the Copernicus Marine Service that are relevant for my future SL research. Moreover, it provides insights on my activities in one of the world's major ocean/climate service through which authoritative scientific data and information are provided for the ultimate benefit of society, by supporting policies and user needs.

My on-going, future activities and perspectives are provided in Chapter 7. They correspond to a convergence of my activities presented in Chapters 3 to 6 as they combine (i) sea level research topics with a focus on forecasted and projected coastal sea level changes for Europe, notably based on dynamical downscaling of climate models and with an extension of my research towards extreme events, with (ii) the development of climate services dealing with sea level changes at the coast and related risks, notably by leveraging on Copernicus Marine capacities and by preparing long-term evolutions of the service.
# 3 Sea Level Variations at Global Scale

## 3.1 Introduction

This chapter describes my research activities on global mean sea level changes. While I've decided early on to focus my research on coastal sea level variations and underlying processes, these are necessarily dependent on global mean sea level changes. For instance, regional domain-limited climate projections of sea level changes require information on global-mean sea level rise, as well as on regional SLR (see Chapter 4). As climate models are the backbone of climate projections, it is essential to understand how global mean sea level can vary in climate models, and to evaluate the accuracy and reliability of climate model GMSLR projections. Indeed, for any socio-economic and greenhouse gases emission scenario, GCMs exhibit a substantial spread in historical and projected GMSLR (Melet and Meyssignac, 2015). These activities on global mean sea level changes have provided me with a good understanding of climate models and of their limitations wrt the representation of SL changes. This is a pre-requisite to use them to regionalize sea level projections, which correspond to my current and future activities (see Chapter 7).

In this context, I have conducted different research activities, presented in the sections hereafter. The first one is on the assessment of the ability of climate models from the Coupled Model Intercomparison Project Phase 5 (CMIP5) to reproduce global mean sea level changes over the 20th century and the altimetry era (i.e. since 1993). This work has been performed as part of an international team supported by the International Space Science Institute (ISSI) and focused on Contemporary Regional and Global Sea Level Rise: Assessment of Satellite, in-situ Observations and Climate Models. This team was led by Benoit Meyssignac (LEGOS), and included 15 members. My main collaborators have been B. Meyssignac (CNES/LEGOS), A. Slangen (then at CSIRO, AUS; now at NIOZ, NL), and K. Richter (then at Innsbruck Univ., AT; now at Bjerknes Center for Climate Research, NO).

My second main research thread with respect to the global mean sea level dealt with a better understanding of the CMIP5 climate model spread on the main component of sea level rise: the global mean thermosteric sea level (GMTSL).

Finally, I've also investigated how GMTSL rise is sensitive to the magnitude of vertical (also called diapycnal or isotropic) mixing in the ocean. This work has been performed during my postdoc under the framework of a Climate Process Team (CPT) on internal-wave driven mixing, funded by NOAA and the USA National Science Foundation. This CPT was led by J. MacKinnon (Scripps, USA) and was composed of researchers working on ocean mixing theory, observations, process studies, and climate modeling. My main collaborators for this work have been R. Hallberg, S. Legg (Princeton Univ, USA) and B. Samuels (GFDL, USA).

## 3.2 Ability of climate models to reproduce global mean sea level changes

*This section discusses the contribution of Melet and Meyssignac, 2015; Slangen et al., 2017b.*

As reported in Chapter 2, sea level will rise by several tens of centimeters by the end of the century, with considerable impacts on densely populated megacities, critical infrastructures and
economic activities. Decisions made by policy-makers for sea level rise adaptation will be made largely based on sea level rise projections (Abadie et al., 2020; Hinkel et al., 2019; Oppenheimer et al., 2019; Vousdoukas et al., 2018b).

Robustness and confidence in projections of future sea level changes depend on the reliability of climate models. In that regard, the ability of climate models to reproduce the components of sea level rise over the twentieth century can inform on the reliability of the models simulations of future changes across a range of emission scenarios (Church et al., 2013b; Oppenheimer et al., 2019). In this section, we therefore evaluate CMIP5 GCMs against observations of sea level rise.

In recent decades, a major question in sea level research has been the closure of the 20th century GMSLR budget (Church et al., 2011; Gregory et al., 2013b; Jevrejeva et al., 2017). Assessing the GMSLR budget closure comes with issues. The first issue relates to observations. Before the advent of the altimetry era, estimates of GMSL changes are mainly based on tide-gauge reconstructions (Church and White, 2011; Dangendorf et al., 2017; Hay et al., 2015; Jevrejeva et al., 2014; Ray and Douglas, 2011). These estimates vary substantially because of the uneven space and time coverage of tide gauge records (Marcos et al., 2019b; Thompson et al., 2016). Observational estimates of the components of GMSL are also uncertain over the 20th century as we lack observations of glaciers and ice-sheet mass balance and of ocean temperature, especially before 1970 and in the Southern Hemisphere, sea-ice covered regions, marginal seas and the deep ocean (Abraham et al., 2013). Another difficulty is that the sum of model-based SL components tend to underestimate the total observed global SLR (e.g. Gregory et al., 2013b).

### 3.2.1 Comparing simulated and observed global mean steric sea level rise

Steric sea level changes represent the main contribution to SLR over the past decades. When averaged over the global ocean, halosteric sea level change (salinity-change induced ocean water density changes) is negligible (see Gregory et al., 2019, for a demonstration) so that global mean steric sea level change reduces to its thermosteric component. Although the global mean thermosteric sea level (GMTSL) is often provided from CMIP models as the variable *zostoga*, we recomputed it directly from available CMIP5 climate models (Melet and Meyssignac, 2015) for different reasons. First, comparisons of observed and simulated GMTSLR are more meaningful over the 0-700m layer as observational estimates of thermal expansion are more accurate and sometimes available only for the 0-700 m layer (observations of the ocean in situ temperature and salinity are sparse below 700 m, especially before the 2000s, Abraham et al., 2013). Second, we wanted to use the same ocean mask for climate models, excluding marginal seas and lakes (such as the Mediterranean Sea, Red Sea, Black Sea, Caspian Sea, Baltic Sea, Persian Gulf, Hudson Bay, and Great Lakes) from the global mean as the temperature and salinity fields tend to be less reliable in these regions in climate models, and can deteriorate the global mean. Finally, we found issues with the *zostoga* variable in some climate models. GMTSLR was thus computed from monthly 3D temperature (potential temperature was converted to in situ temperature) and salinity fields of the CMIP5 models, using the model native grid and excluding marginal seas and lakes.

Climate models need to be spun up for a quasi-equilibrium to the forcing and model settings to be reached. In the deep ocean, the timescales of equilibrium are of thousands of years. Spinup integrations of climate models are usually (much) shorter than the equilibrium timescales due to numerical cost issues. As a result, most historical and piControl (using pre-industrial forcing) simulations, which are initialized with the spinup integration, are still drifting, in particular in the ocean deepest layers. The non-closure of the global mass and energy budget can also contribute to the drift of climate models (Hobbs et al., 2016; Irving et al., 2020). Thermosteric sea level being a depth-integrated variable, the long-term climate drift can have a large effect on this variable in climate models (Sen Gupta et al., 2013). To remove this drift and avoid capturing natural and
physical oscillations, we estimated the long-term climate drift by an order-2 polynomial fit of the piControl run over the period corresponding to the historical simulation.

<figure><img src="image_16.png" /></figure>

FIGURE 3.1: Thermosteric sea level (mm) relative to year 2005 for the 0-700-m layer over (a) 1900-2005, (b) 1961-2005. Observational estimates are the mean of Domingues et al., 2008; Ishii and Kimoto, 2009; Levitus et al., 2009. An uncertainty related to the observational estimates is shown as the purple shaded area. Thermosteric sea level trend (mm yr⁻¹) is shown for the 0-700-m layer over (c) 1900-2005, (d) 1961-2005. In (c-d), spacing along the x axis is used to separate the different climate models (the model ensemble mean is shown as a black dot at the right end of the x axis). The color scheme is identical in each panel: CMIP5 models are shown with thin grey and thick color lines in (a-b) and dots and diamonds in (c-d). Adapted from Melet and Meyssignac, 2015.

These estimates of CMIP5 simulated GMTSL were then compared to observations in **Melet and Meyssignac, 2015**. The comparison is shown in Fig. 3.1 over the 20^th^ century and over 1961-2005 as the amount of ocean temperature observations have significantly increased since the 1960s (Abraham et al., 2013), and over the altimetry era (1993-2005 here to overlap with historical simulations of CMIP5 models). This comparison showed that the ensemble mean of the GMTSL of CMIP5 models is within the observation uncertainty, both for the annual mean time-series and the trends (Fig. 3.1). Over 1900-2005, the model ensemble global mean thermal expansion of the upper 700m of the ocean is 29 mm at a rate of 0.21 mm yr⁻¹, while over 1961-2005, GMTSL rose by 19 mm (700 upper meters) at a faster rate of 0.45 mm yr⁻¹. However, individual models show a substantial spread over the ensemble mean, and a significant number of models simulate thermal expansion that is not within the uncertainty of observations. Some models consistently overestimate thermal expansion over the 20^th^ century, while other models consistently underestimate it. In section 3.3, we explain this spread in CMIP5 GMTSLR.

Related to the need to correct the historical simulations and projections for the long-term drift in climate models is the issue of volcanic forcing. Explosive volcanic eruptions inject aerosols in the stratosphere that reflect incident solar radiation and weaken the solar radiation at the ocean surface. After major volcanic eruptions, a drop in GMTSL is reproduced in climate models (Fig. 3.1, see years 1883-Krakatau, 1902-Santa Maria, 1912-Mt Katmai, 1963-Mt Agung, 1982-El Chichon, 1991-Pinatubo volcanic eruptions). The ocean then recovers the following decades with an
enhanced heat uptake (Church et al., 2005; Gregory et al., 2006). In historical simulations, climate models use a volcanic forcing with historical eruptions. However, volcanic forcing was omitted in the piControl experiments of some CMIP models while volcanic forcing is prescribed in historical simulations, resulting in a spurious time-mean negative forcing in the historical experiment relative to the piControl experiment for these models, a significant spurious negative bias in ocean heat uptake and an up to 40% underestimate of GMTSLR (Gregory, 2010; Gregory et al., 2013a). To overcome this bias, the previous cited studies suggested adding a correction of 0.1 ± 0.1 mm yr⁻¹ to the thermal expansion rate of climate models that imposed volcanic forcing in their historical experiment but omitted it in their piControl experiment. Church et al., 2013a suggested that thermal expansion rates of CMIP5 models may be similarly under-estimated, depending on the details of the individual model control runs, and therefore applied the same correction of 0.1 mm yr⁻¹, a correction also used in the 5th Assessment Report of the IPCC (Church et al., 2013b).

<figure><img src="image_17.png" /><figcaption>FIGURE 3.2: (a) Top-to-bottom GMTSL (mm) relative to year 2005 over 1850-2005. CMIP5 models prescribing volcanic forcing in the piControl experiment (piC-V group) are shown in green, while models omitting volcanic forcing in the piControl experiment (non-piC-V group) are shown in black. (c) 0-700m GMTSL referenced in 2005 for the ensemble mean of models prescribing volcanic forcing in the piControl experiment (piC-V group; green) and ensemble mean of models omitting volcanic forcing in the piControl experiment (non-piC-V group; black). The observational estimates of Domingues et al., 2008; Ishii and Kimoto, 2009; Levitus et al., 2009 are shown with purple lines. An uncertainty related to the observational estimates is shown as the purple shaded area. The years and names of major volcanic eruptions are indicated with black vertical lines. Adapted from Melet and Meyssignac, 2015.</figcaption></figure>

We revisited the impact of volcanic forcing on thermal expansion rates in CMIP5 models before
applying the same correction in **Melet and Meyssignac, 2015**. We splitted the ensemble of models in two groups: models prescribing volcanic forcing in both their piControl and historical experiments (piC-V group) and models prescribing volcanic forcing only in their historical experiments (non-piC-V group) (Fig. 3.2). Although it was expected from the physical arguments presented inGregory et al., 2013a that models of the non-piC-V group would exhibit weaker rates of thermal expansion than models of the piC-V group, no clear separation of the two groups was found (Fig. 3.2). Applying a correction of 0.1 mm yr⁻¹ to the thermal expansion rate of the non-piC-V models would thus result in a larger thermal expansion rate of the non-piC-V group than of the piC-V group, which would be contradictory to the purpose of the correction in the first place. Given the spread of the thermal expansion in piC-V and non-piC-V models (Fig. 3.2a) and the lack of separation between the two groups (Fig. 3.2b), we considered that differences in thermal expansion between the piC-V and non-piC-V groups were not a signature of different volcanic forcing protocols but rather the signature of the spread of models due to other sources of uncertainty, or tuning of model historical simulations to reproduce key metrics such as the surface temperature. Based on this analysis, we decided to apply no correction to the thermal expansion rates simulated by models omitting volcanic forcing in their piControl experiments. The correction for volcanic forcing was revisited in **Slangen et al., 2017b**, and this new correction was used in the IPCC SROCC (Oppenheimer et al., 2019).

### 3.2.2 Comparing simulated and observed global mean sea level rise

Estimates of the global mean thermosteric sea level rise (GMTSLR) presented in section 3.2.1 were used in **Slangen et al., 2017b**, in which we compared the total simulated global mean sea level rise (GMSLR) to tide gauge reconstructions and in **Meyssignac et al., 2017b**, in which we compared simulated regional sea level changes to tide gauges and altimetry data (see Chap. 4).

In **Slangen et al., 2017b**, simulated sea level changes over the 20th century (1901-2015) were assembled using the conventional method of estimating each contributors to GMSLR (thermal expansion, glacier mass loss, Greenland and Antarctic icesheets mass loss, land water storage -LWS-change) separately using outputs from CMIP5 models, and then summing them up. Updated contributions from AR5 (Church et al., 2013b) were used when available (LWS, glaciers) and the comparison period extended to 2015 (instead of 2005 in AR5) for a more comprehensive and robust comparison. In this analysis, we built on extensive previous work on comparisons between simulated and observed GMSL change and showed that the sum of the simulated three main contributors to GMSLR, i.e. thermal expansion, glaciers and Greenland ice-sheet surface mass balance (SMB), only accounts for 50% of the observed GMSLR from 1901-1920 to 1988-2007. For periods prior to 1970, this discrepancy between simulated and observed GMSLR is largely explained by the inability of climate models to reproduce some observed regional increase in air temperature around Greenland over the period 1900-1940, leading to smaller contributions from glacier and Greenland ice sheet SMB to GMSLR over that period. This increase in air temperature could be related to internal climate variability or biases in climate models. As a result, corrections for these two contributors were proposed in **Slangen et al., 2017b** based on regionally downscaled models using atmospheric forcing from observationally-constrained atmospheric reanalyses instead of simulated atmospheric forcing from coupled climate models. With these corrections, the simulated three main contributors to GMSLR explained 75% of the observed GMSLR from 1901-1920 to 1988-2007, reconciling the simulated model estimates with observed GMSL change.

The key messages from this study are:

* CMIP5 models tend to underestimate the observed GMSLR over the 20th century but compare more favorably with observations over the more recent period of 1970-2015 when observations are more reliable and the forced signal due to anthropogenic radiative forcing is dominant.
<figure><img src="image_18.png" /><figcaption>FIGURE 3.3: Comparison of observed and simulated (in 12 CMIP5 GCMs) global mean sea level change since 1901 (a) and since 1993 (b). The average estimate of 12 CMIP5 climate model simulations is shown in blue with the 5–95% uncertainty range shaded in blue. The average of the 12 model estimates corrected for the bias in glaciers mass loss and Greenland surface mass balance over 1900–1940, as proposed in Slangen et al., 2017b is shown in dashed blue. The estimates from tide gauge reconstructions is shown in other colours in panel a) (Church and White, 2011 in gray, Hay et al., 2015 in blue, Jevrejeva et al., 2014 in red, Ray and Douglas, 2011 in cyan), with the 5–95% uncertainty range shaded in grey. The satellite altimetry observations from Legeais et al., 2018 is shown in black in panel b). GMSL from altimetry corrected for the TOPEX- A drift (Watson et al., 2015) in orange as well as the tide gauge reconstruction. The 5-95% uncertainty range is shaded in orange Ablain et al., 2015. All curves in (a) represent anomalies in sea level with respect to the reference period 1986–2005. Vertical lines indicate the occurrence of major volcanic eruptions, which cause temporary drops in GMSL. Extracted from Oppenheimer et al., 2019, based on Slangen et al., 2017b.</figcaption></figure>

* We revised bias corrections in GMSLR estimated from process-based models regarding the contributions from Greenland and glaciers SMB, and the long-term adjustment of the deep ocean and ice sheets.

## 3.3 Understanding the spread of global mean steric sea level in climate models

This section discusses the contribution of Melet and Meyssignac, 2015.

As noted in section 3.2.1, although the CMIP5 ensemble mean GMTSL agrees with observations available since 1960, CMIP5 models exhibit a wide spread in their simulated GMTSL over the 20th century. The main processes responsible for this spread were analysed in Melet and Meyssignac, 2015.

Climate change is due to the Earth’s energy imbalance (N) at the top of the atmosphere (TOA) caused by anthropogenic greenhouse gases emissions (chap 2), as the latter absorb and re-emit part of the infrared longwave radiation emitted by the Earth surface (LWout in eq 3.1 below):

$$N = SW_{in} - (SW_{out} + LW_{out}). \qquad (3.1)$$
where $SW_{in}$ is the incident shortwave radiation received from the Sun and $SW_{out}$ is the shortwave radiation reflected back to space.

Most (~91%, chap. 2) of the heat accumulated in the climate system due to the Earth energy imbalance is uptaken and stored in the ocean, thanks to its large inertia and volume. Therefore, the total heat (in Joules) that enters the ocean (ocean heat uptake) between $t_0$ and $t$ under a radiative imbalance $N(t)$ is given by:

$$OHU_{t_0,t} = \beta S \int_{t_0}^{t} N(\tau) d\tau \qquad (3.2)$$

where $S$ is the surface area of Earth and $\beta$ is the fraction of Earth climate system heat energy excess that is stored in the ocean.

This linear relationship in CMIP5 models was tested by a linear regression of the ocean heat uptake, OHU (de-drifted from the pi-Control simulation), against the time-integrated time-series of $N$ (excluding the 5 years following major volcanic eruptions to capture the long-term response of OHU to the radiative forcing, see section 3.2.1). The correlation coefficient exceeds 0.9 for all models, validating the relationship 3.2 in CMIP5 models and allowing to estimate $\beta$. We showed that $\beta$ varies across models, which is due to the different spatial patterns of OHU in the models. However, $\beta$ does not vary substantially across emission scenarios (e.g. historical simulations or projections using RCP4.5 or RCP8.5 emission scenarios). In most CMIP5 models, $\beta$ is within 20% of 0.93, the observational estimate (Church et al., 2011). However, some CMIP5 models had values of $\beta$ outside this range. This suggested some energy conservation issues in these models, which were discarded from our analysis. Energy conservation in CMIP5 models is also discussed in Cuesta-Valero et al., 2021; Hobbs et al., 2016.

Ocean heat uptake causes sea level to rise through thermal expansion (decrease of ocean water density due to an increase of the temperature), with a scaling factor known as the expansion efficiency of heat and noted $\epsilon$ (Russell et al., 2000):

$$GMTSLR_{t_0,t} = \epsilon OHU = \epsilon \beta S \int_{t_0}^{t} N(\tau) d\tau \qquad (3.3)$$

The relationship 3.3 was found to be valid in CMIP5 models (also illustrated by comparing the first two groups of histograms in Fig. 3.4a). The least-square regression of $GMTSLR_{t_0,t}$ (de-drifted consistently with the drift correction applied to $N$ and OHU, see section 3.2.1 for details on the computation of GMTSL) also allowed us to infer the value of $\epsilon$ in CMIP5 models. We estimated it to be within the range $0.12 \pm 0.02 \text{ m YJ}^{-1}$, in agreement with observation-based estimates (Church et al., 2011; Levitus et al., 2005).

Based on 3.3, the across-model variance in GMTSLR can be expressed as a weighted sum of the across-model variance in the different parameters. We therefore attributed the fraction of across-model variance in GMTSLR to the across-model variance in $\epsilon$, $\beta$ and $\int N$ by allowing only one parameter to vary across models and assigning the model ensemble mean value to the other parameters. As shown in Fig. 3.4a, most of the spread (across model variance) in GMTSLR is explained by the model spread in the time-integrated TOA radiative imbalance $\int N$ (explaining 110% of the GMTSLR variance, against 2% for the variance in $\epsilon$, 5% for the variance in $\beta$ and -12% for a co-variance between $\epsilon$ and $\int N$).

To go a step further, we decomposed the TOA radiative imbalance $N$ as the sum of the radiative forcing of the climate system (due to greenhouse gases), $F$, and the radiative response of the climate system, which is proportional to the globally averaged surface temperature change $\Delta T$ due to $F$:

$$N = F - \alpha \Delta T = (\rho - \alpha) \Delta T \qquad (3.4)$$

where $\alpha$ is the climate feedback parameter (W m$^{-2}$ K$^{-1}$, Gregory et al., 2004). The radiative forcing
$F$ can also be expressed as $\rho\Delta T$ where $\rho$ is the climate resistance, corresponding to the radiative forcing needed to raise the Earth global mean surface temperature by 1K. As $\beta N$ can be identified as the energy flux entering the ocean, we set the ocean heat uptake efficiency as:

$$ \kappa = \beta(\rho - \alpha) \qquad (3.5) $$

By substituting $\Delta T$ in eq 3.4 by $F / \rho$ and $\rho$ by $(\kappa + \alpha\beta) / \beta$ as per eq 3.5, it comes:

$$ N = [\kappa / (\kappa + \beta\alpha)]F \qquad (3.6) $$

The heat uptake efficiency $\kappa$ was estimated for each model using values of $\alpha$ from Kuhlbrodt and Gregory, 2012.

Combining eqs (3.6) and (3.3) gives:

$$ GMTSLR_{t0,t} = \epsilon\beta S[\kappa/(\kappa + \beta\alpha)] \int_{t0}^{t} F(\tau)d\tau = S\mu \int_{t0,}^{t} F(\tau)d\tau \qquad (3.7) $$

We introduced $\mu$, a constant (m J⁻¹) expressed as:

$$ \mu = \frac{\epsilon\beta\kappa}{\kappa + \beta\alpha} \qquad (3.8) $$

and called it the transient thermosteric sea level response of the climate system. Indeed, as under transient climate change SLR linearly depends on the time-integrated TOA radiative imbalance (eq 3.3), it also linearly depends on radiative forcing (as per eq 3.6) when the latter is steadily increasing (Gregory and Forster, 2008). Linear regression of GMTSLR against the time-integrated radiative forcing $F$ confirmed the linear relationship (eq 3.7) (also illustrated by comparing the first two groups of histograms in Fig. 3.4b) and allowed to estimate the transient thermosteric sea level response of the climate system in the different climate models. We found values of $\mu$ of 0.055 ± 0.025 m YJ⁻¹, in agreement with observation-based estimates.

We used the linear climate coefficient relationship (eq 3.7) to understand the causes of the spread in GMTSLR across climate models. We attributed the across-model variance in GMTSLR to the across-model variance in the time-integrated radiative forcing $F$ and in the transient thermosteric sea level response of the climate system $\mu$. Fig. 3.4b shows that most of the spread (across-model variance) in GMTSLR over the 20th century is explained by the across-model variance in $\mu$ (explaining 73% of the variance) while the time-integrated forcing explains another 24%. The percentage of explained variance by $\mu$ is even larger for 21st century GMTSLR under the high-emission scenario RCP8.5. This can be explained by a larger spread in $F$ over the historical period because of a greater role for aerosol forcing during that period, and high uncertainties in aerosol forcing in CMIP5 models.

As the spread in transient thermosteric sea level response of the climate system $\mu$ explains most of the spread in GMTSLR during the 20th and 21st centuries under steadily increasing radiative forcing, we now use the climate coefficient relationship between $\mu$, $\epsilon$, $\beta$, $\alpha$ and $\kappa$ to explain the spread in $\mu$. Values of $\kappa$ and $\alpha$ were taken from Kuhlbrodt and Gregory, 2012. The relationship between the climate coefficients (eq 3.8) is used to explain the variance in $\mu$. We found that the variance in $\alpha$ dominates the variance in $\mu$, while the variance in $\kappa$ explains a substantial, but less important, fraction of the variance in $\mu$ (and thus in GMTSLR) (Fig. 3.4c). The across-model variance in the climate feedback parameter $\alpha$ essentially comes from differences in feedback processes to the radiative forcing perturbation across models (Andrews et al., 2012; Webb et al., 2006). The response of clouds to climate change and cloud-climate as well as cloud-aerosols-radiation
interactions are especially uncertain (Boucher et al., 2013). The spread in the ocean heat uptake efficiency $\kappa$ is essentially related to across-model differences in heat transport processes within the ocean (e.g. Hallberg et al., 2013; Kuhlbrodt and Gregory, 2012). Finally, the spread in radiative forcing $F$ comes from differences in prescribed natural and anthropogenic forcing (Collins et al., 2013), differences in the treatment of radiative transfer (Collins et al., 2006), and differences in the rapid tropospheric and land surface adjustment processes (Gregory and Forster, 2008).

The main conclusions from this study are:

* In CMIP5 climate models, GMTSLR depends linearly on the global mean, time-integrated radiative forcing under transient climate change with steadily increasing forcing. The scaling factor between the two is called the *transient thermosteric sea level response of the climate system* ($\mu$) and depends on the climate feedback parameter ($\alpha$), ocean heat uptake efficiency ($\kappa$) and the fraction of Earth energy excess that is stored in the ocean ($\beta$).

* The spread in CMIP5 GMTSLR is due to across model spread of the climate feedback parameter ($\alpha$), ocean heat uptake efficiency ($\kappa$) and radiative forcing ($F$) during the 20th century but mostly on $\alpha$ over 21st century

* The importance of the spread in radiative forcing ($F$) in explaining the GMTSLR spread decreases under climate warming due to a reduced spread in aerosol forcing, an enhanced forcing from GHG.

The across CMIP5 model variance in the ocean heat uptake efficiency $\kappa$ relates to key uncertainties in models impacting ocean heat transport (mean state and circulation, thermocline depth and width, diapycnal mixing, eddies in the Southern Ocean...) In the next section, we investigate the sensitivity of the ocean global mean thermal expansion to the magnitude of ocean mixing.

## 3.4 Ocean mixing and global mean steric sea level

Ocean thermal expansion due to ocean heat uptake explains ~1/3 of the GMSLR observed over the 20th century and 50% over 1971-2018 (Slangen et al., 2017b, Fox-Kemper et al., 2021). Due to their inertia and long equilibrium timescales, the deep ocean responses on centennial to millennial time scales are relevant to the transient and equilibrium climate response (e.g. Bouttes et al., 2013; Ehlert et al., 2017; Zickfeld et al., 2017). The efficiency of ocean heat uptake depends on how fast heat gained at the ocean surface can be transported at depth, away from any contact with the atmosphere, through advection and diffusion. OHU is therefore a significant source of uncertainty in both the transient and equilibrium responses to increased greenhouse gases emissions. In climate models, the spread in OHU relates to the ocean heat uptake efficiency ($\kappa$, section 3.3) and the representation of vertical and lateral mixing (Griffies et al., 2015; Krasting et al., 2018; Kuhlbrodt and Gregory, 2012).

Based on the thermosteric sea level change calculation in CMIP5 models presented in section 3.2.1, we showed that the contribution of the deep ocean (below 700 m depth) to GMTSLR exhibits a large spread (Fig. 3.5). This spread can be caused by inter-model differences in heat uptake and redistribution in the ocean by advection and diffusion as the thermal expansion coefficient depends on the temperature. The Southern Ocean dominates the global OHU, with a major role in deep ocean heat uptake (below 2000m depth) (Kuhlbrodt and Gregory, 2012) as watermasses formed there then fill the abyssal ocean basins around the world.

Ocean mixing influences the ocean heat uptake efficiency $\kappa$ notably through its influence on stratification and the distribution of heat within the ocean interior and in the surface mixed layer, thereby affecting air-sea fluxes of heat. Although the prescribed and effective diapycnal mixing can substantially differ in ocean models, the spread in CMIP5 modeled GMTSLR is only partly
<figure><img src="image_19.png" /></figure>

FIGURE 3.4: (a) Climate model GMTSL rise in 2005 relative to 1900 (mm) computed from the 3D temperature and salinity fields (first group), from the climate coefficient relationship $\epsilon\beta \int N(t)dtS$ (second group), from the climate coefficient relationship when only $\epsilon$ varies across models (using the ensemble mean values for $\beta$ and $\int N(t)dt$) (third group), when only $\beta$ varies across models (fourth group), and when only $\int N(t)dt$ varies across models (fifth group). (b) Climate model GMTSL rise in 2005 relative to 1900 (in mm) computed from the 3D temperature and salinity fields (first group, as in a), from the climate coefficient relationship $\mu \int F(t)dtS$ (second group), from the climate coefficient relationship $\mu \int F(t)dtS$ using the model ensemble mean values for $\int F(t)dt$ (third group), and for $\mu$ (fourth group). (c) $20^{th}$ century values ($10^{-25} \text{ m J}^{-1}$) of the transient thermosteric sea level response of the climate system $\mu$ (first group), of $\epsilon\beta\kappa / (\kappa + \beta\alpha)$ (second group), of $\epsilon\beta\kappa / (\kappa + \beta\alpha)$ when only $\epsilon$ varies across models (third group), when only $\beta$ varies across models (fourth group), when only $\kappa$ varies across models (fifth group), and when only $\alpha$ varies across models (sixth group). In (a-c), the overbar denotes an averaging across the model ensemble. Only models conserving energy ($\beta$ within 20% of 0.93) are included. Adapted from Melet and Meyssignac, 2015.
<figure><img src="image_20.png" /><figcaption>FIGURE 3.5: Contribution in percentage of the 0-700m layer (dark green) and of the deep ocean (below 700m depth, light green) to the global mean steric sea level rise during 1961-2005 in 33 CMIP5 climate models.</figcaption></figure>

explained by inter-model differences in the ocean heat uptake efficiency $\kappa$ (section 3.3, **Melet and Meyssignac, 2015**). However, ocean vertical mixing (aka diapycnal mixing as isopycnal surfaces are almost horizontal in the ocean interior) remained poorly parameterized in CMIP5 models at this time (substantial progresses have been made since, e.g. Lavergne et al., 2020, **MacKinnon et al., 2017**). Analyzing the sensitivity of the ocean state in climate models to parameterizations of the various processes leading to ocean interior diapycnal mixing and further developing parameterizations of key processes leading to diapycnal mixing has been a major research topic for me (Lefauve et al., 2015; MacKinnon et al., 2017; Melet et al., 2015, 2014, 2013a, 2016a, 2013b; Melet et al., 2022; Timko et al., 2017; Vic et al., 2019). Some of these parameterizations are now implemented in MOM6 (Adcroft et al., 2019), used as the ocean component of some CMIP6 models. Yet, this research line won't be discussed in this manuscript unless related to sea level changes.

Different studies analyzed the sensitivity of climate models projected GMTSLR in response to increased GHG emissions to the intensity of diapycnal diffusivity ($K_d$) in the model (e.g. Dalan et al., 2005; Hallberg et al., 2013; Hieronymus et al., 2019). For instance, Dalan et al., 2005 showed that increasing $K_d$ from $10^{-5}$ to $10^{-4}$ m$^2$ s$^{-1}$ in a 1% yr$^{-1}$ CO$_2$ concentration increase idealized scenario leads to an increase in GMTSLR of about 4 cm after 70 years (i.e. time of doubling of atmospheric CO$_2$ pre-industrial levels).

In a study led by R. Hallberg and together with B. Samuels at GFDL, we further analyzed the sensitivity of GMTSLR to the magnitude of diapycnal diffusivities during the model spinup and climate change experiment (1% yr$^{-1}$ CO$_2$ increase until quadrupling pre-industrial levels) using a wide range of diapycnal diffusivity levels in the GFDL-CM2G CMIP5 model. In this idealized study, we performed a series of simulations in which diapycnal diffusivity was uniformly increased by a constant value of 0, 0.1, 0.2, 0.4, 0.6 and $0.8 \ 10^{-4}$ m$^2$ s$^{-1}$. After a spin-up phase of the 6 simulations with pre-industrial forcing, we applied a forcing of +1% CO$_2$ per year up until a quadrupling of pre-industrial CO$_2$ levels. For each of the 6 equilibrium states, we then performed simulations with different levels of increase in vertical diffusivity (Fig. 3.6a).
In this model ensemble with perturbed diapycnal mixing magnitude, for each 6-member ensemble using the same span-up state, GMTSLR in response to increasing CO$_2$ was larger by ~ 0.2 m/Munk (1 Munk $\equiv 10^{-4}$ m$^2$ s$^{-1}$, here added during the climate change experiment). This rise is substantial compared with GMTSLR with the model's background diffusivities (zero added diffusivity) of 0.43 m during the same period. Enhanced diapycnal mixing in the ocean interior
<figure><img src="image_21.png" /></figure>

FIGURE 3.6: (a) Time-series of GMTSL during the spinup (2000 yrs, using 1860 radiative forcing throughout) and climate change simulations (1% yr⁻¹ CO₂ concentration increase until quadrupling pre-industrial levels - at year 146, then held at 4x the preindustrial values until year 200) in GFDL's coupled model CM2G. The color indicates the amount of additional diapycnal diffusivity prescribed in the simulations. At the end of each of the 6 spinup integrations, 6 new climate change experiments are initialized and ran using the 6 levels of additional diapycnal mixing under the idealized increasing CO₂ scenarios, resulting in 36 climate change simulations. (b) GMTSLR averaged over years 181-200 of the climate change simulations (relative to control runs with the corresponding history of additional diffusivity but using 1860 radiative forcing all way long, not shown here). The horizontal axis indicates the amounts of added diapycnal diffusivities during the spinup. The colored lines connect the GMTSLR in simulations using the same level of diapycnal diffusivity during idealized climate change scenario but initialized with different span-up state (using different K_d as indicated on the x-axis). Work performed with R. Hallberg and B. Samuels (GFDL).

erodes the stratification in the upper ocean, leading to a weaker and more diffuse thermocline, increases the stratification at depth (depending on the vertical profile of the vertical diffusivity), enables more downward heat transport by mixing warm upper waters with cooler deep water, and expands the range of the wind-driven ventilated thermocline enabling a larger ocean heat uptake (Ehlert et al., 2017; Hieronymus et al., 2019; Schmittner et al., 2009, Melet et al., 2016a). GMTSLR is more sensitive to K_d than OHU since GMTSLR combines effects of an overall warmer ocean with increasing K_d and of induced larger thermal expansion coefficients, as the latter increase with temperature and depth (for a given warming, a warm ocean parcel expands more than a cooler water parcel).

Although the upper range of diffusivities used here is much larger than those in the main thermocline of the real ocean (which largely contributes to GMTSLR), the sensitivities reported here should scale with magnitude of the explicit or numerically induced diffusivities, permitting estimates of the likely effects of much smaller diffusivities.

These results strongly suggest that a coupled climate model’s ability to reproduce the ocean’s historically observed thermal structure with minimal drift during its spun-up state and during historical runs are valuable metrics of its utility in projecting steric sea level rise.
# 4 Sea Level Variations at Regional Scale

## 4.1 Introduction

As reliable information on SLR is needed to guide adaptation in coastal zones, information on global-mean sea level rise only is not satisfactory (see Chapter 7). Observations from tide gauges and altimetry have indeed shown that sea level is not rising uniformly across the world at decadal-to-multidecadal timescales, with substantial deviations from the global mean (Chapter 2, Fig. 2.5). Projections of regional sea level changes are constructed based on climate models outputs (section 2.2), and are therefore limited to the climate model resolution. Regional sea level changes addressed in this section are thus of scales of O(100-1000)km.

Although climate-model based regional SLR projections have a coarse resolution and lack the representation of important processes for the coastal zone (Chapters 2, 5, 7), their outputs are also used to provide boundary conditions for dynamical downscaling experiments that can provide sea-level projections at local coastal scales of less than 10 km, as presented in Chapter 7.

In this chapter, I discuss different research activities I've conducted on regional sea level changes based on climate models. As for the research activities I've performed regarding global mean sea level rise (Chapter 3), these activities have provided me with a good understanding of climate models and of their limitations wrt the representation of regional SL changes. In particular, a better knowledge on the climate model biases and their ability to represent observed changes is of importance for the development of regionally downscaled projections of sea level, which corresponds to my current and future activities (see Chapter 7).

## 4.2 Ability of climate models to reproduce regional sea level changes

### 4.2.1 Over the world ocean in CMIP5 models

In this section based on **Meyssignac et al., 2017b**, we evaluate the ability of CMIP5 climate models to reproduce observed SLR over the 20th century. This work has been performed as part of an international team supported by the International Space Science Institute (ISSI) and focused on *Contemporary Regional and Global Sea Level Rise: Assessment of Satellite, in-situ Observations and Climate Models*.

Regional relative SLR based on climate models can deviate from the global mean by ± 30% (Church et al., 2013b; Palmer et al., 2020; Slangen et al., 2014). In **Meyssignac et al., 2017b**, we (i) evaluated the ability of climate models to simulate regional sea level changes and (ii) determined the causes of the temporal and regional variations in the 20th sea level rise.

We used the same 12 climate models as in **Slangen et al., 2017b**, but added the contribution of atmospheric loading (which has a zero global mean) and accounted for the sea level change patterns associated with the contemporary transfer of terrestrial water and grounded ice to the ocean with a sea level equation solver (chap 2). GIA was also accounted for.
<figure><img src="image_22.png" /></figure>

FIGURE 4.1: 20th century simulated regional sea level changes by coupled climate models and comparison with a selection of local tide gauge time series. In the upper left corner: map of changes in simulated relative sea level (RSL) for the period 1901-1920 to 1996-2015 estimated from CMIP5 climate model outputs. Insets: Observed RSL changes (black lines) from selected tide gauge stations for the period 1900-2015. For comparison, the estimate of the simulated RSL change at the tide gauge station is also shown (blue plain line for the model estimates and blue dashed line for the model estimates corrected for the bias in glaciers mass loss and Greenland surface mass balance (SMB) over 1900-1940, see Section 3.2.2). The relatively large, short-term oscillations in observed local sea level (black lines) are due to the natural internal climate variability. For Mediterranean tide gauges (Venice and Alexandria), the local simulated sea level has been computed with the simulated sea level in the Atlantic ocean at the entrance of the strait of Gibraltar following (Adloff et al., 2018). Tide gauge records have been corrected for vertical land motion (VLM) not associated with GIA where available (New York, Balboa and Lusi). Extracted from SROCC (Oppenheimer et al., 2019), adapted from Meyssignac et al., 2017b.
The comparison of low-frequency CMIP5 modeled sea level changes with tide gauge records over 1900-2015 indicates that the modeled interannual-to-multidecadal variability, which is primarily due to dynamic sea level variability, is well reproduced (Fig. 4.1), but that climate models tended to systematically underestimate the observed sea level trends, particularly in the first half of the twentieth century. The analysis of climate model based sea level changes showed that the spatial variability in sea level trends observed by tide gauge records is dominated by the GIA contribution and by the dynamic sea level contribution over the 20^th^ century, although other contributors can substantially explain local deviations from the global mean SLR. This work allowed for more robust and comprehensive comparisons between observed past sea level changes and modeled ones (Oppenheimer et al., 2019).

### 4.2.2 A regional focus with one CMIP6 model

*This section discusses a study carried out by Alisée Chaigneau during her Master 2 (MSc.) internship (SeaTech Engineering School), that I supervised with G. Reffray (Mercator Ocean) and A. Voldoire (Meteo France/CNRM).*

Global scale climate projections over the 21^st^ century are based on global coupled ocean-atmosphere climate models, such as these discussed in the section above. Climate models are subject to climate drift (e.g. Sen Gupta et al., 2013) and to various biases due to numerics, missing physics etc (Knutti and Sedláček, 2013). One source of uncertainty in climate models is related to their resolution. The typical resolution of these models (1° for CMIP5 models analyzed in the 5^th^ Assessment Report of the IPCC, and up to 0.25° for CMIP6 models) is coarse and do not allow to capture some dynamical processes.

During this internship, we first evaluated the climate simulation produced by CNRM-CERFACS for CMIP6 over the northeastern Atlantic ocean (western Europe) for the last decades of the 20^th^ century. This work prepared the development of high-resolution regional ocean projections on the northeast Atlantic through a dynamical downscaling of the high-resolution version of the CNRM-CERFACS climate model (available at the start of the PhD, but not during the internship) as part of Alisée Chaigeau’s PhD thesis, that I am supervising (see section 7.3). Outputs from the CNRM-CM6-1 climate simulation (1° nominal resolution for the ocean component) were analysed. The climate drift was characterized and dedrifted outputs compared to satellite and in-situ observations and to reanalyses, particularly to the regional ocean reanalysis produced by Mercator Ocean (IBIRYS). We focused on variables that are particularly relevant for a dynamical downscaling of climate models for regional climate projections, e.g. ocean temperature, salinity, currents, sea level; and surface atmospheric variables such as wind, pressure, temperature and humidity fields that are used in bulk formulae to force an ocean model (e.g. Brodeau et al., 2017). An exemple is provided in Fig. 4.2 for the sea water potential temperature at the western boundary of the IBI domain (Iberia Biscay Ireland regional seas, northeastern Atlantic), which largely controls the dynamics of this region.

Overall, the climate model satisfactorily represents ocean temperature, currents and surface winds over the global ocean and IBI region. This allows for a good agreement of the climate model steric sea level changes with these based on observations and reanalyses. However, two main biases were identified in the climate model and will need to be corrected for in subsequent dynamical downscaling of the model over the IBI region. The first one relates to large biases in salinity in the Mediterranean Sea, related to river runoff, leading to inaccurate representation of the Mediterranean outflow water mass. The second relates to the low contribution of land ice to global mean sea level rise diagnosed from the climate model. To limit the GCM bias propagation
a) Mean temperature in CNRM-CM6.1

<figure><img src="image_23.png" /></figure>

c) Temperature trend in CNRM-CM6.1

<figure><img src="image_24.png" /></figure>

b) Temperature bias (CNRM-CM6.1-GREP)

<figure><img src="image_25.png" /></figure>

d) Temperature trend in GREP

<figure><img src="image_26.png" /></figure>

FIGURE 4.2: Temperature mean state and trends at the western boundary of the IBI domain. (a) CNRM-CM6-1 mean potential temperature over 1993-2014 (in degree Celsius) and (b) bias compared to the GREP reanalysis ensemble (Storto et al., 2019). (c) Trend in potential temperature over 1993-2014 (in degree Celsius / year) and (d) bias compared to the GREP reanalysis ensemble. From the Master 2 internship of A. Chaigneau (MOi).
<figure><img src="image_27.png" /></figure>

FIGURE 4.3: (Steric sea level changes over the IBI area, in meters, detrended from the pi-control. (Left) Steric sea level changes averaged over the IBI area, for the historical simulations (1850-2014, black), and different climate change scenarios (2015-2100). The bold lines indicate the 10-member ensemble mean while the shading indicates the ensemble standard deviation. (Right) Ensemble mean steric sea level rise from 1986-2005 to 2081-2100 for scenarios SSP1-2.6 (low emissions, high mitigation, left) and SSP5-8.5 (high emissions, low mitigation, right). From the Master 2 internship of A. Chaigneau (MOi).

into a regional model, the need for bias correction of the seasonal cycle of ocean temperature, salinity and sea surface height at the boundaries was also suggested.

In a second step, an analysis of the changes projected by the climate model during the 21st century on ocean variables, including sea level, and on surface atmospheric variables was conducted over the study area for several climate change scenarios. This is exemplified in Fig. 4.3 for sea level changes over the IBI area over 1850-2100 and provided a reference for comparison of subsequent regionally downscaled sea level projections in this region performed in the follow-up PhD of Alisée Chaigneau (chap 7).

## 4.3 Detection of a forced signal in SLR over 1993-2015

While the GMSLR has been attributed to anthropogenic forcing (e.g. Slangen et al., 2016), detecting a forced trend in sea level becomes more challenging on smaller space- and shorter time-scales as the signature of internal variability on sea level (especially on dynamic sea level) is much more pronounced at regional scale. Internal variability thus masks out the forced signal until this one becomes large enough to emerge from the internal variability (which corresponds to the time of emergence). Estimates of the time of emergence were provided based entirely on climate models analysis (Carson et al., 2019; Fasullo and Nerem, 2018; Lyu et al., 2014; Richter and Marzeion, 2014). In Lyu et al., 2014, the time of emergence of regional sea level changes was found to be earlier than 2020 over half of the ocean (relative to the period 1986-2005), with a large contribution of global-mean sea level rise to reduce the time of emergence.

The same ensemble of 12 climate models described in section 4.2.1 was used in **Richter et al., 2020** to compare the spatial patterns of simulated geocentric sea-level change to observations from satellite altimetry over the period 1993-2015 to assess whether a forced signal in regional sea level rise was detectable over this period, or if regional sea level variability was still dominated by internal climate variability. In **Richter et al., 2020**, zonal averages were performed to reduce the signature of internal variability. We concluded that over 1993-2015, model-simulated and observed trends in zonally-averaged total sea level are well above what would be expected from internal variability alone (Fig. 4.4). This holds for zonal averages over the global ocean and over
<figure><img src="image_28.png" /></figure>

FIGURE 4.4: Linear trends of observed and simulated total sea level and their residual (observed minus simulated). The red shading represents the standard deviation around the ensemble mean. The grey shading represents the ensemble mean size of internal variability in the sterodynamic contribution as derived from control simulations. After Richter et al., 2020.

the individual ocean basins. A forced signal can thus be detected at all latitudes in each major ocean basin, but this mostly stems from the global-mean sea-level rise (at 3 mm yr⁻¹). If GMSLR is first removed, then zonally averaged sea level trends do not emerge from the range expected from internal variability alone.

Open questions still remain on this topic, such as what is the part of observed regional sea level changes that is due to internal climate variability and to anthropogenic forcings, can we already detect the fingerprints of anthropogenic forcings, including for the different contributors to regional sea level changes (e.g. glaciers, icesheets, dynamic sea level...)?

## 4.4 Ocean mixing and regional steric sea level

*This section discusses the contribution of Melet et al., 2016a.*

We saw in section 3.4 that ocean mixing influences ocean heat uptake in response to climate change, with consequences on the global mean thermosteric sea level change. Ocean mixing also contributes to the heat and salt spatial redistribution within the ocean. As such, it influences the heat patterns and hence steric sea level changes induced by changes in seawater density. In the ocean interior, away from any boundaries, diapycnal mixing is largely due to breaking internal waves. Internal tides, generated by the interaction of the barotropic tide with the seafloor, are a major contributor to the internal wave field. Once generated, some internal tides can propagate thousands of kilometers away from their generation site, while part of the internal tide energy flux is dissipated more locally, close to the generation site (Vic et al., 2019). A wealth of processes lead to internal tide breaking, feeding 3D turbulence. The patterns of ocean mixing in the ocean
interior are therefore largely shaped by the patterns of internal tide generation, propagation and dissipation. As a result, ocean mixing is very patchy (MacKinnon et al., 2017) and not only the overall magnitude of diapycnal mixing matters for the ocean state, but also its 3D spatial pattern. The vertical distribution of mixing is of particular importance, as it is the convergence of the buoyancy flux that can change a given watermass temperature or salinity (Melet et al., 2013a). This is illustrated in Fig. 4.5 with three climate model experiments (using the CMIP5 GFDL ESM2G climate model) that have the same total magnitude of internal-tide dissipation but different spatial distribution (Melet et al., 2016a). When remote internal-tide dissipation is located on topographic slopes and its vertical profile is proportional to the buoyancy frequency (experiment S80N), so that diffusion is inversely proportional to buoyancy frequency, the thermocline is sharper, oceanic heat uptake is reduced, and thermosteric sea level is lower than when the commonly used constant background diffusivity (experiment KdLMcst) is used. In contrast, using a remote internal-tide dissipation located on topographic slopes but with a vertical profile that is proportional to the squared buoyancy frequency (experiment S80N2) leads to increased diffusivities in the upper ocean and reduced diffusivities at depth relative to the constant diffusivity control run (experiment KdLMcst) and consequently to relatively more ocean heat uptake, a broader thermocline, warmer ocean, and higher steric sea level (Fig. 4.5, Melet et al., 2016a). Although these simulations were run using a pre-industrial radiative forcing, they inform on the importance of the spatial distribution of ocean diapycnal mixing for simulating regional steric sea level changes.

In Melet et al., 2022, I provide a more complete discussion of feedbacks between time-evolving mixing and sea level in different climate states.
<figure><img src="image_29.png" /></figure>

FIGURE 4.5: Diapycnal diffusivities and regional sea level in three climate model simulations using the same total magnitude of internal-tide dissipation but different spatial distribution. In all 3 simulations, 80% of internal-tide energy is dissipated remotely from their generation sites, but with a constant and spatially uniform diapycnal diffusivity of 1.4 10⁻⁵ m² s⁻¹ in KdLMcst, on slopes with remote internal-tide dissipation scaling with the buoyancy frequency for S80N and with the squared buoyancy frequency for S80N2. (Top) Global zonal mean of diapycnal diffusivities due to internal-tide mixing parameterizations (log₁₀ m² s⁻¹ so that a value of -6 means 10⁻⁶ m² s⁻¹) averaged over the last century of the 1000-yr simulations. In KdLMcst, the reference simulation, the constant and spatially uniform diapycnal diffusivity of 1.4 10⁻⁵ m² s⁻¹ representative of unresolved remote internal-tide mixing has not been added (panel a). (Bottom) Thermosteric sea level referenced at the ocean bottom (m). Panels e) and f) show differences in thermosteric sea level from the KdLMcst simulation (panel d). Note the resulting different colorbars for panel (d) and panels (e, f). Adapted from Melet et al., 2016a.
# 5 Sea Level Variations in the Coastal Zone

## 5.1 Introduction

As introduced in section 2.1.3 and reviewed in Woodworth et al., 2019, sea level at the coast can differ from that in the adjacent open, deep ocean due to the signature of a number of processes that take place near the coast and are sensitive to the water depth and to the presence of the coastal boundary (e.g. tides, surges, wind-wave setup, coastal currents, coastally trapped waves, seiches, effects of river discharges etc.). In this chapter, I present activities I've developed wrt coastal sea level changes.

One important scientific question which still remains quite open is whether sea level interannual-to-multidecadal variations and trends differ between the coastal zone and the adjacent offshore deep ocean, and what processes would be responsible for differences in sea level variations and trends from the offshore to coastal ocean. This question remains open partly because available tools (altimetry, models including all processes driving SL changes at the coast and in the deep ocean) have limitations in coastal zones (Fig. 5.1).

Variations of sea level at the coast have traditionally been studied through the analysis of tide gauge data. Tide gauge records capture high-frequency changes in sea level (e.g. Woodworth et al., 2017) and measure relative sea level changes at the coast (thus including vertical land motion due to natural processes or human activities). But the temporal and spatial coverage of tide gauges is very heterogeneous. Although a few tide gauges date back to the 18th century (e.g. at Brest, France), less than a hundred tide gauge records span more than 100 years over the world coastline and they tend to be concentrated in Europe and North America (e.g. Marcos et al., 2019b). In addition, disentangling signals from sea level changes from signals from vertical ground motion requires having a high-precision GNSS station close to the tide gauge, which is not yet the case for the majority of them.

Since 1993, (high-precision) spatial altimetry has enabled to monitor sea level changes with a quasi-global coverage and rather high revisit time. Satellite altimetry has largely improved our understanding of sea level variability and sea level rise from global to regional scales. But despite the recognized invaluable contribution of satellite altimetry to better monitor sea level and ocean dynamics over most of the world's ocean, conventional satellite altimetry methods remain limited for the monitoring of sea level changes in the coastal zone (Fig. 5.1), notably due to land contamination of the radar footprint and less accurate geophysical corrections.

In this chapter, I first address the question of how sea level variations are evolving from the offshore regional scale to the coastal zone (section 5.2). To do so, I started by characterizing coastward changes in sea level interannual variability and trends in observations, with a specific preprocessing of altimetric data for coastal zones (section 5.2.1). This contributed to the overall effort in developing coastal altimetry, which has substantially progressed over the past years. Then, with a PhD student from Fiji we tackled the translation of regional climate information into coastal sea level information for small islands in the Pacific by implementing a statistical downscaling and simple ocean models (section 5.2.2).
The second main question I've addressed on coastal sea level changes relates to the contribu-
tion of wind-waves to coastal sea level changes (section 2.1.3, Dodet et al., 2019), over a broad
range of timescales. Our results indicated that despite waves are transients by nature, wave setup
and swash exhibit substantial interannual-to-multidecadal variations and long-term trends due to
the low-frequency modulation of their characteristics related to wind changes, thereby modulat-
ing coastal sea levels at these timescales as well.

<figure><img src="image_30.png" /></figure>

FIGURE 5.1: Schematic section of the ocean, from the coast to the open and deep ocean to illustrate scales resolved in climate models and the limitation of conventional altimetry to provide valid data in the coastal zone (in a coastal strip of ~ 10 km). The grey dashed box illustrates one grid cell of the ocean component of a climate model (typical horizontal scale of 100 km).

**5.2 From regional, offshore sea level to coastal sea level**

**5.2.1 Spatial altimetry**

My main collaborators for this work have been F. Birol (CTOH, LEGOS, Toulouse), P. Cipollini (NOC, UK), B. Meyssignac (LEGOS, Toulouse). This section describes work performed with students I've supervised: Marcellin Nonti (internship for a Master of oceanography, Benin) and Baptiste Chide (internship for Su- paero, Toulouse); and with Sara Padilla Polo, CNES engineer who I supervised together with B. Meyssignac.

**Reprocessing of altimetric data for coastal zones: X-TRACK**

The need for coastal sea level products from dedicated satellite altimetry processing of sea level data in coastal zones over the world has yet again been recently identified as a remaining gap in sea level cities (Cazenave et al., 2018). To partly overcome issues of classical altimetric data for coastal zones mentioned in section 5.1, three specific processing actions can improve the retrieval (number of valid data) and accuracy of sea level altimetric data in the coastal zone (Fig. 5.2): (1) applying a more specific retracking of altimetric data in coastal zones (Passaro et al., 2014), (2) applying improved corrections for the atmospheric, surface or geophysical effects and (3) a refinement of the statistical techniques used for screening and filtering the altimetric data.

In collaboration with the Center of Topography of the Ocean and Hydrosphere (CTOH) in Toulouse, I've reprocessed along-track satellite data specifically to analyse sea level variations in coastal regions, using the **X-TRACK** processing algorithms developed by the CTOH (Birol et al.,
<figure><img src="image_31.png" /><figcaption>FIGURE 5.2: Schematic of the spatial altimetry principles and issues encountered in coastal zones with more complex waveforms.</figcaption></figure>

2017). X-TRACK allows to retrieve more meaningful altimetric data closer to the coast through a refined editing of data and the use of more accurate geophysical corrections, but with no specific retracking of waveforms. The X-TRACK reprocessing includes the definition of a more accurate land-sea mask, a refined editing of geophysical corrections (which are a source of significant errors and discard numerous data in coastal zones), a refined estimate of the mean sea surface, and a refined editing of the sea level anomaly (SLA) data themselves (SLA corresponds to sea surface height -SSH- anomalies from a time-mean reference - Mean SSH-, Fig. 5.2). In particular, a specific editing of the ionospheric, wet tropospheric and sea state bias corrections is performed in X-TRACK to better detect outliers and provide meaningful replacement values through interpolation/extrapolation and filtering methods (for other corrections derived from models, such as tides and the dynamic atmospheric correction, editing is less substantial).

## Variability of coastal western boundary currents

I first worked on the analysis of spatial altimetry data for coastal zones or areas of complex topography during my PhD to examine the variability of coastal currents in the Solomon Sea. Due to the intricate bathymetry of this semi-enclosed sea and the presence of many islands, specifically reprocessed along-track altimetry data were needed to retrieve more information on the narrow coastal western boundary currents. After adapting the X-TRACK processing to my region of study, I've analyzed the reprocessed altimetric data to document the fine structure of the complex western boundary coastal currents system in the Solomon Sea, their seasonal cycle and interannual variability (Melet et al., 2010b).

## Coastward evolution of sea level variations

For the studies described below, I've used two versions of X-TRACK: X-TRACK2011 and X-TRACK2016. The editing and extrapolation of geophysical corrections has been improved in X-TRACK2016 compared to X-TRACK2011, especially for the radiometer-derived wet tropospheric, the ionospheric and the sea state bias corrections (see Birol et al., 2017).

This editing of geophysical corrections and of SLA ensures more realistic evolutions of the data along the track coastward, and maximizes the number of valid SLA data, especially in the coastward end side of the track (Birol et al., 2017). This is illustrated in Fig. 5.3 for one satellite track.
<figure><img src="image_32.png" /></figure>

FIGURE 5.3: (Upper left) Number of valid cycles (out of 737 cycles over the 1993-2012 period) for Topex/Poseidon (T/P), Jason-1 (J-1) and Jason-2 (J-2) track 177 in the western equatorial Pacific as a function of latitude for the standard AVISO product (blue circles) and the X-TRACK reprocessed product (red crosses). (Lower left) Bathymetry along the track as a function of latitude. (Right) Location of valid 1-Hz points along a portion of the track (delimited by the black rectangle on the upper left panel), for the standard AVISO (blue circles) and X-TRACK (red crosses) products. This figure highlights the gain of valid SLA data along the track, especially closer to the coast. From the internship of B. Chide (LEGOS).

Thanks to the reprocessing, valid data can be accessed up to a few kilometers to the coast for a substantial number of cycles for specific tracks compared to more traditional altimetric products (e.g. AVISO in Fig. 5.3).

To examine the coastward evolution of sea level variations and provide insights on the open question "is sea level rising at the same rate in the coastal ocean than in the adjacent open ocean", I reprocessed and examined, together with students I was supervising, along-track altimetric data with the X-TRACK software. We started by examining the western coast of Africa, as this region is particularly vulnerable to sea level rise (Cazenave and Le Cozannet, 2014) and because it has a relatively simple coastline, open to the ocean. We used along-track nadir altimetry data from the TOPEX/Poseidon, Jason-1 and Jason-2 satellites, which share the same ground tracks and provided the longest sea level anomaly time series, at that time over the 1993 - 2012 period.

The number of valid independent measurements for which the sea level trend was computed in the coastal sections is larger in the X-TRACKv2016 than in the X-TRACKv2011, especially in the last few kilometers towards the coast, due to a better editing of the data and to a more refined processing of geophysical corrections applied to altimetric data. The number of measurements is much lower in the conventional altimetry AVISO dataset (Fig. 5.4, right panels, in red) and decreases significantly in the last 30 km off the coast due to both the spatial sub-sampling of AVISO data, less adapted geophysical corrections in the coastal zone, and a more conservative editing of the data in AVISO than in X-TRACK datasets.

As the coastal shelf is narrow off western Africa (a few tens of km), we selected the sections of
<figure><img src="image_33.png" /></figure>

FIGURE 5.4: (Left): Relative changes in SLA trend (mm/year) over 1993-2012 in percentages along coastal sections of altimetry tracks offshore Western Africa for the (top) X-TRACKv2016, (middle) X-TRACKv2011 and (bottom) AVISO along-track datasets. Only the sections of altimetry tracks located less than 200 km off the African coast are studied. Changes are relative to the open-ocean trend defined here as the trend of sea level anomalies averaged over the sections of altimetry tracks located from 160 to 200 km offshore the African coast. (Right): Relative changes in SLA trend (in %) were averaged as a function of the distance to the coast, using 5 km wide bins (blue line, left axis) for the (top) X-TRACKv2016, (middle) X-TRACKv2011 and (bottom) AVISO along-track datasets. The grey envelope shows plus and minus one standard deviation from the average. The number of valid points used to compute the mean and standard deviation of SLA trend changes for each bin is shown in red (right axis). As in the left panels, changes are relative to the trend over the 160-200 km off the coast band (this reference part is shown in light grey shading). Results are only shown for bins in which at least 15 coastal sections had valid points for this bin for the calculation of the mean and standard deviation of the trend. Results are based on the TOPEX/ Poseidon, Jason-1 and Jason-2 missions over 1993-2012. From Cipollini et al., 2017 based on my work with contributions from the Master 2 internship of M. Nonti.
the altimetry tracks that are located less than 200 km off the coast (referred to as coastal sections hereafter) to characterize the evolution of sea level trends from the open to the coastal ocean (Fig. 5.4). Due to the lack of correction for the slightly varying orbit of the satellite and for long-wave errors in the X-TRACK data, the trends in sea level anomalies along the different tracks are not inter-calibrated at cross-points. Yet, the spatial variations of sea level along the tracks are almost not affected by these missing corrections, so that we can analyse sea level variations *relative* to a referenced section of the track. Therefore, for each coastal section, the changes in sea level trend were calculated relative to the ‘open ocean trend’ for that section (defined as the mean trend for the part of the section located in the open ocean from 160 to 200 km off the coast; this choice was made to exclude the continental shelf).

<figure><img src="image_34.png" /></figure>

FIGURE 5.5: Illustration of the coastward evolution of the bathymetry (top), sea level trend (upper middle), root mean square (RMS) variability (of the detrended time series) (lower middle) and interannual variability (bottom) for T/P, J-1 and J-2 track 083 (see inset on the upper right for location) as a function of the distance from the shelf break along this track (positive distance toward the deep ocean, negative distance toward the coast). Data from X-TRACK2016 (CTOH) data over 1993-2015 were used. The location of the coast along this track is indicated with a vertical green line, the shelf break with a red line, the deep ocean (defined by the location were the isobath 1000-m is crossed) by a dashed blue line, and the reference deep ocean (from 100 to 150 km offshore of the 1000-m isobath) by a grey shading. After work performed with Sara Padilla Polo.

The changes in sea level trend from the open to the coastal ocean are shown in terms of percentage in Fig. 5.4 (left panels), using the deep ocean as the reference. Sea level trend coastward changes were also bin-averaged across the coastal sections of all altimetric tracks as a function of the distance to the coast (Fig. 5.4, right panels) to provide a more synthetic regional view. As shown in Fig. 5.4, the coastward changes in sea level trends off the western coast of Africa vary depending on the dataset used, with no robust evolution of the sea level trend from the open to the coastal ocean in the AVISO dataset, a substantial increase in the sea level trend for most coastal
sections when using X-TRACK2011 (reaching an increase of 25% 25–30 km off the coast; Fig. 5.4, middle right panel), and in-between results when using the X-TRACK2016 dataset (Cipollini et al., 2017).

A similar analysis was performed during the internship of Baptise Chide over the southwest Pacific (30°S 10°N, 120°E 180°E). Corresponding results confirmed the substantial retrieval of meaningful data closer to the coast, and different regional behavior for the coastward evolution of sea level trends with changes ranging from -5% to +25% compared to the adjacent deep ocean.

<figure><img src="image_35.png" /></figure>

**FIGURE 5.6:** (Left) Relative changes in % of coastward SLA (a) variability (RMS) and (c) interannual variability over 1993-2015 in percentages along coastal sections of altimetry tracks offshore Western Africa using T/P, J-1 and J-2 missions reprocessed with X-TRACK2016. The reference is taken as the average of SLA over a deep ocean part of the track, defined as the part of the track located from 100 to 150km offshore the location where the track crosses the 1000-m isobath. (Right) Relative changes in SLA (b) variability and (d) interannual variability, (in %), were averaged as a function of the distance to the shelf break for each track, using 5 km wide bins (blue line, left axis). The grey envelope shows plus and minus one standard deviation from the average. The number of valid points used to compute the mean and standard deviation of SLA RMS changes for each bin is shown in red (right axis). Results are only shown for bins in which at least 10 coastal sections had valid points for this bin for the calculation of the mean and standard deviation of the trend.

We extended the case study off the west coast of Africa with Sara Padilla Polo, to reference the sections to the shelf break (defined by the location where the track crosses the 200-m isobath) and to the deep ocean (defined by the 1000-m isobath). An illustration for one track is given in Fig. 5.5.

Fig. 5.6 shows a robust coastward increase of the sea level variability off the tropical coasts of western Africa, including at interannual timescales. This increase is regular from the deep ocean
<figure><img src="image_36.png" /></figure>

FIGURE 5.7: Coastward evolution of the sea level variability (RMS, in mm) along different T/P, J-1, J-2 tracks off the western coast of Africa as a function of the distance from a reference point along the track. For each track, the reference point is the distance to the coast corresponding to the first baroclinic Rossby radius of deformation, a representative scaling for the offshore extension from the coast of sea level anomalies due to coastal Kelvin waves.

to the coast when all timescales are considered (Fig. 5.6b), resulting in 25% larger sea level variability at the coast compared to the deep ocean. When only interannual timescales are considered, the coastward sea level variability increase starts closer to the coast, e.g. when reaching the continental slope (1000-m isobath) (Fig. 5.6d).

Kelvin waves propagating poleward along the western coast of Africa are causing sea level anomalies with an amplitude following an exponential profile from an offshore distance which can be approximated by the first baroclinic Rossby radius of deformation to the coast. An intercomparison of the coastward evolution of sea level variability across the tracks with respect to the local Rossby radius of deformation was also conducted (Fig. 5.7). As most sections show that the increase in sea level variability tend to start from the Rossby radius of deformation to the coast, this diagnostic indicates that coastal Kelvin waves could explain a large part of the coastward increase in sea level variability in this region.

These different results showed that efforts made to improve satellite nadir altimetry products in the coastal ocean allowed to recover more data and to obtain more coherent long-term signals in the coastal zone. Yet, these analyses also revealed that efforts were still needed at that time on the processing of altimetric data and on the geophysical corrections applied to satellite data for studying the sea level trend in the coastal zone over the altimetric era more robustly. In particular, a specific retracking of the waveforms in coastal zones (Passaro et al., 2014) combined with better geophysical corrections could improve the accuracy and reliability of altimetry data in the coastal zone. An effort in this direction has been funded in a dedicated ESA-CCI+ project, posterior to the work presented here. Recent advances from this ESA-CCI+ project are presented in Gouzenes
et al., 2020; Marti et al., 2019; The Climate Change Initiative Coastal Sea Level Team et al., 2020. Sea level altimetric data are recovered closer to the coast, with the first valid point along the track being as close as 5km and up to less than a kilometer from the coast. Analyses of the time-series indicate that for a large part of the world ocean, sea level is actually rising at a similar rate in the deep and coastal oceans, at least when getting as close as a few kilometers to the coast (The Climate Change Initiative Coastal Sea Level Team et al., 2020).

### 5.2.2 Statistical downscaling

This section describes work performed during the PhD thesis of Vandhna Kumar, from Fiji, that I co-directed with B. Meyssignac and A. Ganachaud (LEGOS). Results were published in Kumar et al., 2018.

Rising sea levels are already representing a threat for numerous Pacific islands (Wong et al., 2014, Oppenheimer et al., 2019). Most Pacific islands have a high population density and infrastructure concentrated along the coastal zones. Together with geographical isolation, limited financial resources and technical expertise, these features combine to make islands among the most vulnerable in the world to the growing threats of sea level rise (Barnett and Campbell, 2010; Garschagen et al., 2016), with some of them already facing relocation (McNamara and Jacot Des Combes, 2015). Due to committed sea level rise, coastal impacts could be exacerbated. Information on regional sea level variability and its key drivers is thus increasingly needed to help plan proper adaptation measures and to build capacity for climate resilience.

In this study, we aimed at reconstructing sea level changes at interannual-to-interdecadal timescales and sea level trends at selected sites in the southwest Pacific (Noumea, Suva and Lau-toka, Fig. 5.8), based on a statistical downscaling. This approach was selected given its practical advantages; regression methods are relatively easy to implement and require low computational resources, making them more easily transferable to local communities. An underlying objective was to provide insights as to whether the statistical model could be used for future projections of sea levels for these islands.

We expressed sea level as a multiple linear regression (MLR) of statistically determined ocean and atmospheric variables acting as regressors. These variables were preselected based on their representation of remote and local drivers of sea level changes. The statistically modeled sea level is expressed as:

$$sla\text{(site, t)} = \sum_{i} \alpha_{i} P_{i}(\bar{x}_{i}, \bar{y}_{i}, t - \tau_{i}) + \epsilon\text{(site, t)} = sla_{\text{MLR}}\text{(site, t)} + \epsilon\text{(site, t)} \quad (5.1)$$

In this equation, the reference sea level anomaly timeseries (the predictand, coming here either from the ORAS4 reanalysis or tide gauge records) is modeled ($sla_{MLR}$) through a sum of predictors $P_i$, each averaged over a specific region ($\bar{x}_i, \bar{y}_i$), and including a potential temporal lag $\tau_i$. The site specific residual $\epsilon$ is not part of the MLR model but represents the difference between the predictand and modeled sea-level timeseries.

Sea level changes, $\eta$, are due to volume (steric, $\eta_{st}$) and mass changes ($\eta_{mass}$) of the ocean (Chapter 2).

$$\eta = \eta_{st} + \eta_{mass} = \eta_{st}^{a} + \eta_{st}^{d} + \eta_{st}^{bf} + \eta_{mass}^{largescale} + \eta_{mass}^{coastal} \quad (5.2)$$

Steric sea level changes are due to changes in seawater density, and include both thermosteric (due to changes in temperature) and halosteric (due to changes in salinity) effects. Steric changes can arise from changes in heat and salt advection by the ocean circulations, mostly driven by wind stress changes ($\eta_{st}^a$); from heat or salt diffusion ($\eta_{st}^d$); and from buoyancy forcing at the ocean
<figure><img src="image_37.png" /><figcaption>FIGURE 5.8: Sea level trends in the Pacific region from altimetry observations over the 1993-2014 period. The lower inset shows the study sites: Suva, Lautoka, and Noumea. From Kumar et al., 2018.</figcaption></figure>

boundaries ($\eta_{st}^{bf}$; air-sea fluxes of heat, precipitation and evaporation, salinity exchanges with sea ice, geothermal heat flux at the sea floor). The mass term ($\eta_{mass}$) comprises both a "large-scale" term, with changes in ocean bottom pressure caused by the redistribution of water masses by ocean circulations in response to the atmospheric forcing and by the transfer of terrestrial water to the ocean, and a "coastal" term, with effects such as wind setup.

In the tropical Pacific Ocean, sea level changes at interannual-to-interdecadal timescales are mostly thermosteric in nature, and related to wind stress changes ($\eta_{st}^a$) (e.g. Forget and Ponte, 2015; Timmermann et al., 2010). Wind stress curl anomalies modulate Ekman pumping, which in turn induce pressure gradients in the ocean interior and drive geostrophic circulations. Wind stress curl anomalies also generate local sea level and pycnocline depth anomalies which propagate westward as planetary Rossby waves. Given this critical role of wind stress curl in determining and/or reproducing regional sea level trends in the southwest Pacific, wind stress curl is considered as the dominant predictor of thermosteric sea level, and hence of sea level in the region. The dominant regressor in the MLR is taken as the sea level anomaly given by a linear, reduced-gravity model of long quasi-geostrophic Rossby waves (from Kessler and Cravatte, 2013), which gives the first-order off-equatorial and low-frequency wind-driven sea level response at each site. Once the regression coefficient of $\eta$ on the wind-stress curl is computed (eq. 5.1), the residual sea level is step-wised regressed on to other predictors. Among them, we selected the local halosteric sea level (for salinity changes and surface freshwater fluxes), the local sea surface temperature as a proxy for local air-sea heat fluxes (to approximate $\eta_{st}^{bf}$) and the local wind stress components to approximate wind setup (for $\eta_{mass}^{coastal}$, eq. 5.1). A step-wise regression is used to minimize cross-correlations between the potential regressors and to only add in the MLR new terms ($\alpha_i P_i$, eq. 5.1) that lead to a statistically significant increase in predictand variance explained by the MLR. More details on the methodology can be found in Kumar et al., 2018.

The MLR-reconstructed time-series of interannual-to-interdecadal sea level at the three study sites when the wind stress curl is used as the dominant predictor are skillful (Fig. 5.9). Overall,
<figure><img src="image_38.png" /></figure>

FIGURE 5.9: Undetrended ORAS4 (ocean reanalysis, blue) and wind stress curl dominated multi-linear regression modeled (statistical dowscaling, red) interannual sea level time series over the 1988-2014 period for (top) Suva, (middle) Lautoka, and (bottom) Noumea. From (Kumar et al., 2018).

more than 80% of the predictand variance is explained by the MLR-reconstructed sea level. In addition, the dominant, wind-stress curl proxy term (from the Rossby wave model) captures from 60 to 75% of the interannual-to-interdecadal variance, indicating that local regressors only explain a small fraction of island sea level variability at these timescales. The fact that the sea level at the three coastal sites selected here is largely explained by large scale ocean dynamics forced by wind stress curl across the Pacific Ocean and that local processes are secondary can be instrumental
<figure><img src="image_39.png" /><figcaption>FIGURE 5.10: Stationarity test for wind stress curl dominated MLR model for Suva over 1988-2014. The predictand sea level (from the ORAS4 reanalysis) is shown in blue. The sea level timeseries from the MLR calibrated over the whole period is shown in red. The solid magenta (resp. green) line shows the MLR model calibrated over the first half (resp. second half) of the ORAS4 sea level time series, and the dashed magenta (resp. green) line shows the model applied to second (resp. first) half of the time series. From **Kumar et al., 2018**.</figcaption></figure>

for statistical downscaling of low-resolution climate simulations (possibly with a bias correction of surface winds provided by climate models) to reconstruct local-scale information on sea level changes at our three selected island sites for periods over which we do not have observed sea levels, such as for climate projections. We explored the potential skill of the model for application to future projection of sea levels by performing stationarity tests to assess whether a MLR model calibrated over a given period can be successfully applied to another period (assuming a stationarity in the regression coefficients). For these stationarity tests, we calibrated the MLR model over one half of the study period (1988-2014) and applied the corresponding MLR to the remaining half (Fig. 5.10). We found that the MLR models retain sufficient skill to replicate the larger majority of the predictand interannual-to-interdecadal variability as it captures the amplitude and phasing of the variability to a large extent. The stationarity test performance is however comparatively lower for sea level trends, which could be expected given the short duration of the timeseries.

Our reconstructions provided insights on key drivers of sea level variability at the selected sites, showing that while local dynamics and the global signal modulate sea level to a given extent, most of the variance is driven by large-scale regional forcing (wind-stress curl anomalies) in this region whose interannual variability is dominated by the El Niño Southern Oscillation. The Rossby wave model provided an efficient proxy for the thermosteric sea level changes, showing the importance of the wind stress curl-driven sea level changes at interannual-to-interdecadal time scales at Suva, Lautoka, and to a lesser extent at Noumea.
**5.3 Contribution of wind-waves to coastal sea level changes**

When I’ve started working on the contribution of wind-waves to coastal sea level changes with my colleagues Benoit Meyssignac and Rafael Almar, it was unclear up to which time-scales wave setup and runup (see Chap 2) could substantially contribute to total water level (TWL) changes at the coast (TWL include contributions from the mean regional sea level, tides, storm surges and waves, Fig. 2.7). The focus on wind-waves wrt coastal sea level changes was mostly (i) on the con- tribution of wind-waves to coastal SL during extreme events, at local scales, and (ii) on past and projected changes in offshore wave climate (including interannual variability and trends). I’ve therefore addressed the question of the contribution of waves to TWL changes at different time- scales with my co-authors to bridge these two areas of research with first a local study focused on Cotonou, Benin (sec 5.3.1) and then with global scale estimates of the contribution of wind-waves to interannual TWL changes over the past decades and to long-term projected coastal SL changes (sections 5.3.2 and 5.3.3).

As the different processes contributing to TWL changes impact the coast differently, evaluat-
ing their relative importance is essential for assessing the local coastline vulnerability. In addition,
a better understanding of TWL changes at all timescales is needed, not only for extreme events.
Indeed, although extreme water levels represent an important hazard for low elevation coastal
zones as they are the major cause for temporary flooding, mean sea level changes are nonetheless
important as they are causing different risks related to sea level rise, such as permanent flooding,
salinization of surface and ground waters, degradation of coastal ecosystems (salt marshes, man-
groves, beaches...). Furthermore, mean sea level changes are directly relevant for extreme water
levels and their return periods, as even a small increase (or decrease) in mean sea level can signif-
icantly increase (or reduce) the frequency of occurrence of extreme water levels and the intensity
of flooding, as reviewed in Oppenheimer et al., 2019.

I mostly focused on wave setup changes on sandy beach environments as sandy beaches are
ubiquitous along the world's coastlines (Luijendijk et al., 2018), can represent the first line of de-
fense for flooding, and are among the most vulnerable coastal environment to SL rise (Wong et al.,
2014). I also focused on wave setup changes, as they contribute to time-mean sea level changes
and are more directly comparable to other contributors in current sea level change projections.
Yet, wave runup changes are also important for coastal impacts and were also discussed in these
studies.

**5.3.1 Local scale study, from extreme events to interannual timescales**

My first study on the contribution of wind waves to TWL changes developed a case study at Cotonou, in the Gulf of Guinea. Cotonou is one of the largest West African city, is located on a low-lying sand barrier and has a low adaptation ability, making it at risk from sea level changes. The coast corresponds to an open, wave-dominated sandy environment receiving energetic swells generated in the Atlantic sector of the Southern Ocean and by the easterlies off southwest Africa (Fig. 5.11).

Wave setup and runup were estimated over 1993-2012 using empirical formulations (Stockdon et al., 2006) based on a beach slope estimate (0.15, Almar et al., 2015) and deep water wave height and period from the ERA-interim reanalysis (Dee et al., 2011). By summing up wave contributions with tides (from a tidal model), wind setup (estimated with an empirical formulation), the inverse barometer (from altimetric geophysical corrections) and closest altimetric sea level from a gridded product, we constructed the TWL anomaly time-series for Cotonou. An analysis of the
<figure><img src="image_40.png" /></figure>

FIGURE 5.11: (a) A picture of a sandy beach off Cotonou. (b) Bathymetry (in m) and main regions generating swells and wind-waves impinging on the Gulf of Guinea (white ovals) and their major direction of propagation (white arrows). (c) Zoom on the Gulf of Guinea region off Cotonou, showing the site of the study (green pin), the closest tide gauge (red pin) and the tracks of the satellite missions merged in the gridded product used for the altimetric sea level. Adapted from (Melet et al., 2016b).

explained variance of the time-series focusing on different time-scales was conducted to highlight the processes that dominated the TWL changes at different time-scales. We found that the leading contributors to TWL variability off Cotonou differ depending on the time-scales considered. The trend is largely dominated by processes captured in altimetric data (see Chap 2). Wave contributions, in particular runup induced by swells, were found substantial at all timescales, including for interannual variability and trends (Fig. 5.12).

Extreme events were found to be dominated by the conjunction of high tides and large swell run-up, exhibiting a clear seasonal cycle with more events in boreal summer. The most devastating storm surge of the 1985-1995 period in Lagos was documented to occur on the 17th of August, 1995 (see picture in Fig. 5.13). This event resulted in a 5- to 8-m erosion of the beach and occurred at neap tide. It was not captured in the tide gauge record (not designed to capture wave runup and often missing wave setup as tide gauge are located in wave sheltered areas), but was captured in TWL time-series only when wave contributions were accounted for (Fig. 5.13). This case study showed for the first time to our knowledge that wave contributions to TWL changes can be substantial even at long time-scales (interannual variability and 20-yr trends).

## 5.3.2 Global scale study, interannual timescales

### Relative contributions of coastal sea level components to its interannual variability

The main results of the Cotonou case study motivated us to extend the analysis of the contribution of wave setup and runup to interannual TWL changes at global scale. Indeed, most broad-scale studies of sea-level impacts have essentially focused until then on modeling tides and storm surges and on the analysis of tide gauge extreme water levels (Muis et al., 2016; Woodworth et al., 2017). Coastal processes, in particular waves, have been shown to be dominant contributors to
<figure><img src="image_41.png" /></figure>

FIGURE 5.12: (a) Time-series of TWL anomalies at Cotonou over 1993-2012, its trend (green), interannual variability (red) and sub-annual variability (cyan). (b) The percentage of TWL variance explained by each of the contributors to TWL considered in this study for different time-scales, with the color legend on the right side. Adapted from (Melet et al., 2016b).

<figure><img src="image_42.png" /></figure>

FIGURE 5.13: (Upper panel) TWL anomalies at Cotonou over 1993-2012, with extreme events (above the 98th percentile) in red dots. A zoom on one particular event in August 1995 that leaded to flooding (see picture) but was not recorded by the closest tide gauge (red time-series) is provided in the middle and bottom panels, together with a comparison to the closest tide gauge data (in red). Time-series of tidal levels are shown in green, of TWL without wave contributions in black, and with wave contributions in blue. Adapted from (Melet et al., 2016b).

extreme sea levels (Rueda et al., 2017; Serafin et al., 2017; Vitousek et al., 2017) but few studies have analyzed impacts of long-term (interannual and longer periods) sea-level changes on the
coast, although at regional scales they have highlighted the importance of the wave contribution (Ruggiero, 2013). When performed at global scale, such long-term studies mostly overlook wave contributions.

Wave setup and runup can be predicted using different methodologies, such as direct numerical modeling with process-based local coastal models, meta-models, and empirical formulations (see Dodet et al., 2019, Power et al., 2019). As this study aimed at providing a first-order global estimate of the contribution of wave setup and runup changes to coastal TWL changes over a long time-scale, wave setup and runup were computed using widely-used empirical formulae (eqs 5.3 and 5.4) (see Melet et al., 2020a for a discussion on the choice of empirical formulae). Empirical formulae relate wave setup (S) and runup (R$_{2%}$) to a set of environmental parameters, such as the beach face slope β, the deep-water wave height H$_{0}$ and wavelength L$_{0}$. We used the Stockdon et al., 2006 parameterizations :

$$S = 0.35\beta\sqrt{H_0L_0} \qquad (5.3)$$

$$R_{2\%} = 1.1 \left( 0.35\beta\sqrt{H_0L_0} + 0.5 \left[ H_0L_0(0.5625\beta^2 + 0.004) \right]^{1/2} \right) \qquad (5.4)$$

The foreshore beach slope β is an essential parameter in the estimation of wave setup and swash. Beach slopes generally range between 0.01 and 0.20. They can substantially evolve over different timescales (events, seasonal, interannual, and in response to SLR) and spatial scales, from alongshore at a given local beach to regional scales. At the time of this study, no observations of beach slopes applicable in parametric formulae (corresponding to the section of the beach where waves wash up) was available worldwide. Since this study, important progresses have been made in estimates of beach slopes at regional scales (Vos et al., 2020). To extend calculations at global scale, we therefore mainly relied on a time and space constant beach slope value along the world's coastline, an approach commonly used for regional to global scale analysis.

Our results indicated that in spite of the fact that waves are transients by nature, wave setup and swash exhibit substantial interannual-to-multidecadal variations due to the low-frequency modulation of waves characteristics related to wind changes. This result is regionally dependent, but for some regions, the wave contribution can strongly dampen or enhance the effects of other contributors (e.g. dynamic SL, atmospheric surges) on coastal water-level changes over unexpectedly long periods of several decades (Fig. 5.14). We therefore advocated that past, present and future coastal sea-level rise need to consider low-frequency wave contributions. In particular, regarding projections of sea level extremes, our results indicate that assuming a stationary wave contribution to extremes based on the historical data record is not valid. Finally, this study called for future research efforts to refine estimates of wave set-up and swash, and of beach slopes.

Following that study, I contributed to review papers on the contribution of wind-waves to coastal sea level changes (Dodet et al., 2019) and on forcing factors affecting sea level changes at the coast (Woodworth et al., 2019).

## Influence of climate modes on coastal sea level components interannual variability

This section describes work performed during the Master 2 internship of Marjorie David (ENSTA Bretagne), that I co-supervised with J. Boucharel and R. Almar (LEGOS). Results are submitted in Boucharel et al., 2022.

I pursued the topic of interannual variations of TWL at the coast in 2021 through the Master 2 internship of Marjorie David (ENSTA Bretagne) in collaboration with R. Almar and J. Boucharel
<figure><img src="image_43.png" /></figure>

FIGURE 5.14: Contribution to interannual-to-multidecadal total water-level variations over 1993-2015. (a) Pie charts of the relative contribution of wave setup (green), altimetry-derived sea level (violet) and atmospheric surges (yellow) to total water-level detrended interannual-to-multidecadal variations. (b) Pie charts of the relative contribution of swell set-up (dark green), wind wave set-up (light green), swell swash (dark orange) and wind wave swash (light orange) to the wave-induced detrended interannual-to-multidecadal water-level variations. The size of the pie charts indicates the standard deviation of detrended interannual-to-multidecadal sea-level variations. Scalings are indicated on the lower left corner of the panels. Adapted from (Melet et al., 2018).

(LEGOS). During this internship, we analyzed the influence of the main climate modes of variability on the different components of TWL at the coast. Interannual variability of regional sea level is mainly caused by climate modes. It induces large variations around the long-term mean (Han et al., 2019) and can also modulate extreme coastal sea levels at interannual timescales through a modulation of atmospheric synoptic variability (including extratropical storms and tropical cyclones) and ocean forcings (regional sea levels, waves, e.g. Barnard et al., 2017; Boucharel et al., 2021).

Three dominant climate modes were selected: the Pacific Mode (combinaison of ENSO and PDO), the North Atlantic Oscillation (NAO) and the Southern Annular Mode (SAM), as they are respectively dominant in the Pacific, Atlantic, Indian and Southern Oceans. Using notably Mercator Ocean's GLORYS12 ocean reanalysis (Lellouche et al., 2021) and the Copernicus Marine Service WAVERYS wave reanalysis, we highlighted the contrasted influence of the three climate modes on the interannual variations of coastal total water level components (Fig. 5.15, 5.16). Waves and atmospheric surges have substantial contributions at high latitudes and are related to the NAO in the northern hemisphere and to the SAM in the southern hemisphere through their strong influence on extra-tropical storm activity. Yet, the influence of these two extra-tropical climate modes can propagate to tropical coastlines and affect TWL at the coast via swell induced wave setup (although some limitations of this simple method emerge at high-latitudes with unexpected correlations between SAM or NAO and water level components).

After the establishment of statistical connections between dominant modes of climate variability in major oceanic basins and the different contributors to the TWL interannual variability along
<figure><img src="image_44.png" /></figure>

FIGURE 5.15: (a) Percentage of variance of TWL interannual anomalies explained by the multi-linear regression of TWL onto the three climate modes (i.e. the Pacific mode, NAO and SAM indices) over the total 1993-2019 period. (b) Zonally averaged variance of the TWL interannual anomalies explained by the 3 modes (thick black line) and their individual contribution to the multi-linear regression (NAO in orange, SAM in yellow and Pacific mode in purple). (c) Same as (b) but restricted to the Atlantic basin (i.e. between 70°W and 30°E). (d) Same as (b) but for the meridionally averaged explained variance. From the Master internship of M. David (MOi/LEGOS), Boucharel et al., 2022.

<figure><img src="image_45.png" /></figure>

FIGURE 5.16: Maps of the dominant climate driver (i.e., Pacific mode, NAO or SAM) to the interannual variability of TWL (a), regional mean sea level/SLA (b), atmospheric surges/DAC (c) and wave setup (d). A dominant driver is identified if the variance explained by one of the climate modes is above 60% of the total variability of the multilinear regression of the TWL or a component onto the three climate modes. From the Master internship of M. David (MOi/LEGOS), Boucharel et al., 2022.

the global coastlines, we tested the forecasting skills of a simple climate-mode-based regional predictions of total water level at the coast though a multi-linear regression model (as in Kumar et al.,
2018). This builds on the predictability skills of ENSO (L'Heureux et al., 2020). Assuming perfect predictions of the three climate model indices, we showed that a multilinear regression model of TWL on the three climate modes produces skillful interannual forecasts of TWL over most of the global shorelines. This is particularly the case over regions where the climate variability is essentially accounted for by these indices (Fig. 5.15) and especially in the Pacific basin due to the strong control of ENSO on all contributors to the TWL (Fig. 5.17). In these regions, given the high predictability of ENSO event duration which suggests the potential for extending by up to one additional year already skillful 12-month operational forecasts of El Niño and La Niña events (Wu et al., 2021), our results indicate that the skill scores from the simple statistical regression model could be close to the ones shown in Fig. 5.17 in real forecast mode setting (i.e., run with actual ENSO forecasts instead of its observed values). Furthermore, the forecasting skills of the simple climate-mode-based model are similar to those provided by operational centers using state-of-the-art numerical approaches (e.g. Roberts et al., 2016), but they are considerably more efficient in terms of computational power.

<figure><img src="image_46.png" /></figure>

FIGURE 5.17: Correlation coefficients (i.e., forecast scores) between observed coastal TWL interannual anomalies and predictions from the multi-linear regression model using the three climate modes (i.e. the Pacific mode, NAO and SAM indices) as predictors, averaged over different randomized periods of predictions and range of lead-times along the 1993-2019 total period. For forecast lead times ranging from (a) 1-2 years, (b) 2-4 years. From the Master internship of M. David (MOi/LEGOS), Boucharel et al., 2022.

This study highlighted that the dominant climate modes exert a contrasted influence on the different contributors of coastal TWL interannual-to-decadal variability. Extratropical climate modes of variability such as the NAO and SAM impact TWL in remote regions, including the tropics, through wave setup induced by swells generated in the extra-tropical regions under the direct influence of NAO or SAM. Depending on the different phases of the various climate modes, compensation effects or accumulation effects can occur for the different components of TWL at the coast.

### 5.3.3 Global scale study, projected trends

The previous studies and reviews described in the sub-sections above acknowledged that wave-driven contributions to TWL at the coast could exhibit low-frequency changes and trends including in response to both climate change and internal climate variability over parts of the global ocean due to changes in ocean wave climate.

Although there remains uncertainties regarding the robustness of externally-forced trends in wave height and their extremes over the last decades (e.g. Mori et al., 2019; Reguero et al., 2019; Semedo et al., 2011; Young and Ribal, 2019, Dodet et al., 2019), robust changes in wave height, period and direction are projected for the 21st century over several oceanic regions (e.g. Hemer et al.,
2013; Morim et al., 2018, 2019). In particular, wave height are projected to increase in the South-
ern Ocean, and such changes would impact remote coastlines of other ocean basins through the
northward propagation of swells. Low frequency changes in wave climate are transmitted to TWL
changes at the coast through wave setup and swash changes. Yet, how wave setup will change
in response to climate change and how such changes will compare to other contributors typi-
cally accounted for in SL projections remained an open question. The need for comprehensive
broad-scale projections of TWL at the coast accounting for changes in the wave climate was also
acknowledged in **Oppenheimer et al., 2019**.

To contribute to that overall goal, we evaluated for the first time the 20-yr mean changes in
wave setup and runup during the 21st century induced by changes in deep-water wave char-
acteristics in response to changes in surface winds at global scale. Our study was the first one
that translated large scale projected changes in the offshore wave climate into information more
directly relevant for mean sea level at the coast and that compared these to other contributors to
the time-mean changes in sea level at the coast, therefore extending the study of Carson et al., 2016.

Our global scale analysis relies on empirical formulae for wave setup and runup, on an en-
semble of global wave models to get projected offshore wave characteristics and on different es-
timates of beach slopes (locally reported values, globally constant, static or time-evolving). We
notably used 308 local estimated reported in the literature (based on Barboza and Defeo, 2015 and
complemented by a literature search). To extend the study at global scale, we also used a globally
uniform beach slope of 0.04, corresponding to the median value of the 308 local sites.

<figure><img src="image_47.png" /></figure>

FIGURE 5.18: Contributions to projected coastal mean sea level changes at local sites. Projected coastal SL changes (ΔSL) (sum of sterodynamic SL, glaciers, Antarctic ice sheet, Greenland ice sheet, terrestrial water, GIA, wave setup estimated with local beach slopes) from 1986-2005 to 2026-2045 under RCP8.5, in meters. Insets show the contribution of the different processes (legend at the bottom) to coastal SL changes at different coastal grid points (indicated by black circles). Units are in meters. Sp. stands for Spain, AUS for Australia, NZ for New Zealand, and Baja CA for Baja California. Adapted from (Melet et al., 2020a).

We found that projected wave setup 20-yr mean changes over the middle and end of the 21st century are overall small compared to dominant contributors to coastal SL changes (the ocean component and glacier mass-loss), and even more so at the end of the century than at mid-century (Fig. 5.18). When averaged over the world coastlines, wave setup changes unsurprisingly mostly average out as wave setup changes considered here solely arise from changes in surface winds. Regional wave setup changes are therefore much more limited than SLR due to land ice mass loss or the thermal expansion of the ocean. The latter is expected to continue for centuries as it is only
limited by the amount of heat excess in the climate system that can be stored in the ocean.
Regional patterns of projected wave setup changes are however largely heterogeneous (Fig. 5.19).
The use of a globally uniform beach slope and impossibility to account for very local features (e.g.
beach orientation) in this study contributes to a consistency in wave setup changes over regional
portions of the coastlines, and most probably leads to an underestimate of the spatial heterogene-
ity of wave setup projected 20-yr changes. The spatial variability and amplitude of wave setup
changes make wave setup a small yet substantial contributor to spatial departures of coastal SL
changes from global-mean SLR (Fig. 5.19).

Locally, 20-yr mean wave setup changes can be substantial compared to projected changes in other
contributors of coastal SL change (the different land ice components, land water) over the 21st
century. The wave setup contribution could be larger locally, especially for beaches with slopes
greater than the global constant of 0.04 used here.

Thus, wave setup changes can substantially either enhance or reduce local coastal SL changes departure from GMSLR due to other contributors such as sterodynamic effects and should be included in regional patterns of coastal SL changes. When considering wave runup 20-yr mean changes, incorporating changes in swash amplitude in addition to wave setup changes, wave contributions to local departure from GMSLR are larger with a median contribution along the coastlines of order 10%.

Our results highlight that projected changes in wave setup and swash, mostly in response to climate change (through the analysis of 20-yr mean changes, a model ensemble mean and two climate change scenarios in our study), can be substantial and attenuate or add-up to mean sea levels induced by other drivers. It should be noted wave setup and runup can exhibit low frequency changes through their dependence on various factors that can change over long timescales, including changes in geomorphology (e.g. beach orientation, nearshore bathymetry), changes in ocean currents or water depth (including sea level rise) and their interaction with waves. We only accounted for changes induced by the atmospheric circulation changes here.

Time-mean changes in wave setup are also relevant for extreme events. Indeed, studies focusing on projections of extreme sea level events are often assuming a stationarity of the wave climate and therefore of the wave setup and swash contributions to TWL (Vitousek et al., 2017). Yet, accounting for wave contributions has implications for extremes and for adaptation time to flood hazard (Lambert et al., 2020).

The results presented in **Melet et al., 2020a; Melet et al., 2018** are first order estimates of wave
contributions to TWL changes. We acknowledge that given the state of the art in terms of wave
modeling, estimates of wave setup and runup, nearshore and foreshore slopes, global scale anal-
yses are necessarily coming with limitations (discussed in **Melet et al., 2020a**). One of the main
limitation of our estimates arises from the use of a constant beach slope, chosen to be 0.04 in **Melet
et al., 2020a**. Progresses have been made recently in estimating beach slopes over broad regions.
Considering two different regions (eastern Australia and California), Vos et al., 2020 estimated
beach slopes to have values of 0.062 ± 0.019 and 0.068 ± 0.024 respectively. Our choice of 0.04 was
therefore in the lower range of such estimates, leading to underestimates of wave setup changes.
Our results showing a non-negligible contribution of wind-waves to TWL changes are original,
with very few studies focusing on the non-stationarity contribution of waves to coastal sea levels.
They thus call for future research efforts to refine estimates of wave set-up and swash as all pro-
cesses contributing to TWL changes and shoreline changes should be considered to provide more
accurate assessments of the hazards at the coast (Bouwer, 2018; Oppenheimer et al., 2019). The
conclusions of **Melet et al., 2020a; Melet et al., 2018** were taken up in the SROCC and AR6 IPCC
reports (**Oppenheimer et al., 2019**, Fox-Kemper et al., 2021).
<figure><img src="image_48.png" /></figure>

FIGURE 5.19: Spatial heterogeneity of the different contributions to projected coastal sea level changes from 1986-2005 to 2081-2100 under RCP8.5. (a) Projected coastal SL changes (sum of sterodynamic SL, glaciers, Antarctic ice sheet, Greenland ice sheet, terrestrial water, GIA, wave setup computed with a slope of 0.04), shown as anomalies from the coastal global mean. The colorbar is centered on the global coastal mean SL. The lower left inset shows the global coastal mean of each contributor to coastal SL changes. Other insets show regional anomalies of each contributor to the coastal SL changes from their own global coastal mean (see legend at the bottom), at different coastal grid points (indicated by black circles). Units are in meters. (b) Histograms showing the relative importance, in percentage, of each contributor (Ci) to the regional departure of coastal SL changes from the global-mean coastal SL change. This is computed as, for contributor i: |Ci'| / Σ |Cj'|.100, where the prime denotes the local departure of the contributor i or j from its global coastal mean, and the sum is over j where j denotes the different contributions accounted for in this study. The colored dots along the coast show the contribution of the absolute value of regional anomalies of wave setup changes to the sum of absolute regional departure from GMSLR from each component, in percentage. The size of the colored dots indicates the amplitude of the absolute value of the departure from GMSLR (also given by the blue/red colormap in panel (a), with a scaling on the lower-left side of the panel.

Adapted from (Melet et al., 2020a).
# 6 From Science to Society: The Copernicus Marine Service

## 6.1 Introduction

Since November 2015, I've worked at Mercator Ocean International (MOi), mostly in the framework of the European Copernicus program (section 6.2) for the management and coordination of its Marine service (section 6.3). In parallel to my research activities, I've thus coordinated scientific evolutions of the Copernicus Marine Service and since July 2021, I've been head of the Copernicus Marine Service scientific evolution and managing its R&D program (section 6.4). This includes the development of the long-term scientific strategy of the service. The Copernicus Marine Service covers a wide range of thematics, related to the ocean physics, wind-waves, sea-ice and ocean biogeochemistry from observations and models (section 6.3). By managing its R&D program, I've strongly widened and rounded my knowledge of ocean sciences, enabling me to develop research activities on different thematics. In addition, the service is user and policy driven. As such, it provides scientific data and information for the ultimate benefit of society, and thus creates a pathway for authoritative and actionable science for society.

Although I've historically developed sea level change research (Chapters 3 to 5) on the one hand, and managed the Copernicus Marine Service R&D program on the other hand (this chapter), these two streams of activities have fed one another and have recently began to converge (Chapter 7). My activities for the Copernicus Marine Service have also enabled me to (i) develop a broad scale and long-term scientific strategy, with the identification and prioritization of scientific evolutions and organization of the corresponding program (ii) develop a good understanding of climate services (in their broad sense, section 7.1.3) and put me in a strong position for developing research activities on sea-level changes from global to coastal scales that are actionable for the society through climate services (Chapter 7). Before moving to the description of my on-going and future research activities that combine sea level change research and the development of climate services, including through the long-term evolution of Copernicus, I present in this chapter the Copernicus Marine Service (section 6.3), my role and related activities (section 6.4), and planned Copernicus Marine evolutions wrt sea level changes and coastal zones (section 6.5).

## 6.2 The Copernicus Programme

Copernicus is the European Union's Earth Observation (EO) Programme. It is implemented by the European Commission (EC) and expert entrusted entities, under the control of the EU Parliament and Council. The program monitors our planet and its environment, and is driven by requirements from users and to support policies for the ultimate benefit of society.

The space component of Copernicus, with the Sentinel satellite family, is currently the largest world producer of freely and openly available EO data (Benveniste et al., 2020). In particular, Sentinel-1, 2, 3 and 6 deliver information on the ocean state (including sea level, see also section 6.5.1). Copernicus Services then transform the wealth of satellite data and combine them with
in-situ and integrated numerical models to produce added-value, qualified datasets and information. On top of this integrated-systems, added-value products layer, additional layers have been developed in Copernicus Services to analyse and process the data into information useable by the scientific community, managers and policy makers, the downstream sector and to provide services associated to the information delivery.

Copernicus value-adding activities and products are streamlined through six services. Of particular importance for SLR change and adaptation are:

* the Copernicus Marine Environment Monitoring Service (CMEMS), or Copernicus Marine Service, implemented by Mercator Ocean International. CMEMS provides regular and systematic reference information on the physical and biogeochemical state, variability and dynamics of the ocean, including sea level, for the global ocean and the European regional seas.

* the Copernicus Land Monitoring Service (CLMS), implemented by the European Environmental Agency and the European Commission Directorate General Joint Research Centre (JRC). CLMS provides geospatial information on land cover, land use, vegetation state, water cycle, cryosphere to a broad range of users in Europe and across the world in the field of environmental applications.

* the Copernicus Climate Change Service (C3S), implemented by the European Centre for Medium-Range Weather Forecasts (ECMWF). C3S supports the adaptation and mitigation policies of the European Union by providing consistent and authoritative information about the past, present and future climate change in Europe and the rest of the world.

* the Copernicus Emergency Management Service (CEMS), implemented by the JRC. CEMS provides maps to first responders, showing the impact on the ground in the first hours following a large natural disaster or a humanitarian crisis. These maps assist the organisation of the safe evacuation and sheltering of people affected by disasters such as floods.

## 6.3 The Copernicus Marine Service

The Copernicus Marine Service is the European Union service for a sustainable use of the Ocean. It provides the European Union with a world-leading capacity for monitoring the Ocean worldwide. The Copernicus Marine Service is recognized internationally as one of the most advanced service capacity in ocean monitoring and forecasting, while the Ocean is higher and higher on political agendas.

Over the last decade, Mercator Ocean International has developed for the European Union a marine service firmly grounded in European leadership, and has extended its influence beyond Europe. MOi was entrusted at the end of 2014 by the European Union to implement the operational phase of the service from 2015 to 2021, and in July 2021 to implement the operational phase of the service from 2021 to 2027. The Marine Service is now a structuring component of the Copernicus program, using the EO capacity offered by the Sentinels - Sentinel 1, 2, 3 and 6 - and other contributing missions (e.g. through EUMETSAT), cooperating with the other Copernicus Services and providing them with marine information, to feed a growing demand of users and policy makers for reliable ocean information.

The Copernicus Marine Service monitors the world ocean by providing regular and systematic reference information on the physical and biogeochemical ocean states and on sea-ice for the global ocean and the European regional seas. This capacity encompasses the description of
the current situation (analysis), the prediction of the situation 10 days ahead (forecast), and the provision of consistent retrospective data records (reprocessed in situ and satellite datasets and ocean reanalyses). The development of the Copernicus Marine Service has required collaboration and innovation across research and technology, in observations, modeling, assimilation, reporting and product and service delivery. The Copernicus Marine Service has set global standards for 'research-to-operations' and 'operations-to-research' processes. This European Union service is unique in the world by its coverage and comprehensiveness, its balance between state-of-the-art science and operational commitments, and the consistency of its portfolio where satellite observations, in situ observations, and 3D model simulations are coherently proposed to describe the ocean.

Copernicus-Marine is a user-driven and policy-driven service, and as such, it provides scien-
tific data and information for the ultimate benefit of society. The service responds to public and
private user needs and supports policies related to all marine and maritime sectors: maritime
safety, coastal environment monitoring, trade and marine navigation, fishery, aquaculture, ma-
rine renewable energy, marine conservation and biodiversity, ocean health, climate and climate
adaptation, recreation, education, science and innovation. The Copernicus Marine Service is a
powerful instrument to support the European Union in the Green Deal, Digital Strategy and the
environmental policies implementation. Among the different policies related to SLR risks and
adaptation, the EU Flood Directive is of particular importance. Copernicus-Marine maintains a
digital depiction of the ocean which can be derived into invaluable datasets for environmental
assessment performed by Member States and expert organizations, but also into synthetic indi-
cators and reports to build a unique ocean monitoring dashboard for policy makers and decision
makers as well as for the general public to support actions and assess progresses in policy im-
plementation. The Copernicus Marine Service publishes an annual Ocean State Report (see Von
Schuckmann et al., 2021b for its 5th issue) and produces Ocean Monitoring Indicators for policy
and decision makers as well as for the general public. These reports and indicators are used to as-
sess and report on past and present marine environmental conditions and to analyze and interpret
changes and trends in the marine environment. At the end of 2021, close to 40,000 users registered
to the Copernicus Marine Service, 65% of which are in academia.

In practice, the Copernicus Marine Service relies on a distributed architecture of production
centers both for observations (Thematic Assembly Centers - TACs) and modeling/assimilation
(Monitoring and Forecasting Centers - MFCs):

* TACs generate data sets directly useable for assimilation and validation in models (MFCs) and high-level products (i.e. gridded multi-sensor products, near real time and long-time series) directly useable for downstream applications. The Copernicus Marine Service comprises eight TACs. Six of them are satellite-based and organized by ocean variables: sea level, wind-waves, ocean color, sea-surface temperature, sea ice, surface winds; one TAC deals with in situ observations and one TAC with multi-observations (merging in situ and satellite data to elaborate high-level products). These production centers gather observation data from in situ networks (e.g. the Global Ocean Observing System (GOOS) and the European Global Ocean Observing System (EuroGOOS)) and from the Copernicus satellite component, through the European Space Agency (ESA) and the European organization for the exploitation of Meteorological Satellite (EUMETSAT).

* MFCs generate model-based products on the ocean physical, sea-ice and biogeochemical states, including forecasts, analyses and reanalyses. MFCs also generate initial and/or boundary conditions for nested coastal and ocean/atmosphere coupled modeling systems. Seven
MFCs are contracted and distributed over the global ocean and the different European regional seas (Arctic Ocean, Baltic Sea, North Atlantic West Shelf, North Atlantic Iberia-Biscay-Ireland area, Mediterranean Sea and Black Sea).

The Copernicus Marine Service distributed architecture of production centers (TACs and MFCs) responds to the double objective of engaging the best experts from where they are while also creating service value as close to the field as possible. Different European consortium have been contracted for the different production centers.

The Copernicus Marine Service is interfaced with and / or includes external dependencies with ESA and EUMETSAT for the Copernicus Space component data services, other Copernicus Services (C3S, CEMS, CLMS and CAMS), in situ observations international, European and national networks, national marine centres worldwide and with the Copernicus WEkEO DIAS platform and services.

The first operational phase 2015-2021 of the Copernicus Marine Service has successfully implemented a unique European Union ocean monitoring and forecasting service (see Le Le Traon, 2021 for a synthesis of its achievements). Thanks to a well-established approach to organize evolutions of the Copernicus Marine Service system of systems, the capabilities to operate a marine service responsive to user needs and scientific/technological advances have fully been demonstrated. The product and service portfolios have thus evolved from 2015 to 2021 with, in particular, the integration of new parameters (e.g., waves, carbon, turbidity, sea ice thickness and icebergs), the improvement of resolution and quality, longer time series, the full uptake of Sentinel missions (S1, S3 and recently S2) and the development of new means to access and visualize the data.

More information on the Copernicus Marine Service can be found in Le Traon et al., 2019 and on its website.

## 6.4 My Role in the Copernicus Marine Service

Since July 2021, I've been head of the Copernicus Marine Service scientific evolution and managing its R&D programme (Melet and Le Traon, 2021). As such, I participate to the Copernicus Marine Service core steering committee.

### 6.4.1 Scientific evolutions of the Copernicus Marine Service: strategy

As part of its role to implement the Copernicus Marine Service, MOi develops and maintains a Service Evolution Strategy in order to respond to new needs and take advantage of improved methodologies. The Service Evolution Strategy is maintained on the basis of direct feedbacks from users, scientific and technical gaps analysis of emerging and existing user requirements, support to policies and the potential to improve the elements composing the Copernicus Marine Service. I contribute to the definition of the Copernicus Marine Service strategy for its scientific evolution component, which is detailed in a regularly updated Service evolution strategy- R&D roadmap document. This Copernicus Marine Service R&D roadmap is prepared by a core team of the Scientific Directorate at MOi (the team in which I work) with support from the Copernicus Marine Scientific and Technical Advisory Committee (STAC). The STAC is composed of independent and internationally recognized scientific and technical experts on the various thematics of interest for the Copernicus Marine Service.
Together with PY Le Traon, MOi's scientific director, we have organized interfaces with the STAC and managed the Copernicus Marine Service Evolution R&D programme (Melet and Le Traon, 2021) presented in the following section. I also largely contributed to defining the scientific content and evolutions of the Copernicus Marine Service over 2021-2017 by:

* defining the proposed Marine Service portfolio of products and services during 2021-2017 in the Technical Annex of the Contribution Agreement between the European Union (represented by the EC) and MOi.

* defining the scientific and technical evolution requirements in the Statement of Work for the call for tenders for TACs and MFCs over the 2022-2024 period. The Statement of Work describes the work to be performed by Copernicus Marine Service producers.

### 6.4.2 The Copernicus Marine Service Evolution R&D programme

A leading-edge research and innovation capacity is critical for maintaining a state-of-the-art Marine Service which is both responsive to user and policy needs and that provides high-quality, continuously improving products. This is required across all parts of the Copernicus Marine Service: observations, data processing, quality control, modeling, data assimilation and service layers. The R&D strategy and programme are based on a 3-tier approach, corresponding to short, mid and long-term development objectives (Fig. 6.1). These three streams of R&D activities are conducted by different players and with different funding mechanisms, but with the overall objective of integrating the developments into the Copernicus Marine operational systems (see section 6.4.3 for the research-to-operations implementation cycle). This strategy allows anticipating the necessary research to prepare for evolutions of the Marine Service so that the Marine Service complies with EU policies and political priorities (e.g. the Green Deal and SDGs) and remains at the state-of-the-art.

<figure><img src="image_49.png" /><figcaption>FIGURE 6.1: The Copernicus Marine Service Evolution R&D programme and its three tiers of activities, with corresponding timescales, funding frameworks and players.</figcaption></figure>

#### Long-term R&D activities

Long-term evolution needs are identified in the Copernicus Marine service evolution R&D strategy based on an analysis provided by MOi and by the STAC. They are included in the **R&D roadmap**. Long-term R&D activities are as crucial as short and mid-term activities for the sustainable evolution of the Copernicus Marine Service, especially to develop new service lines.
Long-term Service Evolution R&D activities are promoted in the framework of external projects, such as Horizon 2020, Horizon Europe and other European and national R&D programmes (Fig. 6.1). Of particular importance for the long-term evolution of Copernicus Marine Service are the EU H2020/Horizon Europe Space Programme with Copernicus Evolution calls. MOi, as entrusted entity by the EC for the implementation of the Copernicus Marine Service, provides guidance to the EC regarding the content of these calls for them to address priority Copernicus-Marine long-term R&D needs. This is essentially managed by MOi's scientific director and I.

In addition, to maximise the project developments uptake in Copernicus Marine, MOi moni-
tors several projects funded through H2020 and Horizon Europe, some funded through the H2020
Copernicus Evolution programme (e.g. H2020 CEASELESS, IMMERSE, SEAMLESS, FORCOAST),
other funded from different H2020 programmes (e.g. H2020 KEPLER, EUROSEA, CoCliCo, etc.).
In particular, interfaces are organized by MOi between these projects and the Copernicus Marine
Service coordination teams, to assess the impact of the projects on operational production centers.

Mid-term R&D activities

Mid-term R&D objectives (2-year cycle) are mainly addressed through Copernicus Marine Service
calls for tenders funding R&D projects, and to a lesser extent by the Copernicus Marine Service
production centers themselves. The goal of these calls is to ensure the scientific evolution of the
Service and to improve the operational service within 3-4 years from the start of the projects (Fig.
6.1). I prepared, with support from the STAC and MOi teams, the two service evolution calls for
tenders issued during the 2015-2021 period and the corresponding evaluation by external review-
ers, and selection process. Following the first open call for tenders, a batch of 12 R&D projects
were funded for 2 years. The second call for tenders led to the funding of 18 2-year R&D projects.
The total budget for these two calls was 5 M€.

I managed these two calls and acted as project officer for the corresponding 30 2-yr R&D
projects. As such, I closely monitored these projects together with the STAC and analyzed the
potential research-to-operation transition. I organized coordination activities gathering the pro-
duction centers and R&D project teams twice during the lifetime of a project: at mid-term and
at the end. After completion of the projects, I also monitored the uptake of the corresponding
developments by CMEMS production centers especially during the formal development process
for the evolution of production centers' systems and products (section 6.4.3).

Short-term R&D activities

Short-term R&D objectives (timescale of several months to 1 year) are carried out by the Coper-
nicus Marine Service production centers, i.e. TACs and MFCs (Fig. 6.1). Tier 1 activities address
issues requiring fast responses for rapid implementation within the Copernicus Marine Service.
They can integrate developments from Tier 2 or Tier 3 activities that have reached maturity and
have proven benefits for uptake into operational systems, thereby transferring research to opera-
tions.

**6.4.3 Research-to-operations management**

Evolutions proposed by production centers (TACs, MFCs) following MOi's requirements (section 6.4.1) are coordinated and validated by MOi through a formal development process. Their implementation follows a formal development process with three technical milestones (Fig. 6.2):