En particulier, j'ai rédigé plusieurs études sur l'origine et les conséquences de la diminution du vent à l'approche du continent (le «drop-off» du vent) dans les Courants de Bord-Est. J'ai démontré son importance dans la détermination de la circulation moyenne et mésoéchelle mais aussi de la production primaire nette. Cependant, dans ce manuscrit, j'ai décidé de me concentrer sur un autre aspect de ma recherche qui a été très inspirant pour moi, et qui, comme discuté dans ce qui suit, pourrait (et je pense devrait) conduire à un changement de paradigme sur la façon de forcer un modèle océanique : l'influence des courants océaniques de surface sur le vent et la réponse océanique associée. Je présente aussi à la fin de ce manuscrit une réfléxion sur ma carrière ainsi qu'une présentation des principaux projets de recherche et des étudiants supervisés.

Table des matières

Résumé

Les interactions entre l'océan et l'atmosphère influencent largement le climat de la Terre ainsi que les écosystèmes à l'échelle des bassins océaniques. Les principaux modes de variabilité climatique (ex : Oscillation Madden-Julian, El Niño, Oscillation Nord-Atlantique) sont des modes couplés entre ces deux milieux. Les écosystèmes ont une forte réponse à ces variations à travers l'influence physique des vents, de la lumière et de la température, sur le réservoir de nutriments et donc sur la production primaire et la chaine trophique.

Les biais en température de surface de la mer dans les modèles globaux ont mis en lumière les limites d'une approche globale et ont ainsi fait surgir une nouvelle ligne de recherche basée sur une approche régionale des interactions entre l'océan et atmosphère permettant de mieux comprendre et prévoir la variabilité dans des régions clefs de l'océan. Il a donc récemment été montré qu'à l'échelle régionale, les interactions fines échelles entre l'océan et l'atmosphère peuvent aussi grandement moduler la variabilité et l'état moyen de l'océan et de l'écosystème associé. Le changement climatique a et aura une influence sur les interactions entre l'océan et l'atmosphère et donc sur l'écosystème aussi bien d'un point de vue global que régional. Comprendre quels sont les processus clés qui gouvernent l'état moyen et la variabilité physique et biogéochimique, et quel est et sera l'impact du changement climatique sur ces processus, s'avère donc primordial. C'est ce qui a motivé ma recherche dans ce domaine et a orienté mon parcours. Comme je vais le présenter dans ce manuscrit, ma ligne de recherche part du postulat suivant (que j'étaye ensuite par certains de mes travaux) : afin de comprendre l'évolution de l'océan, et ainsi l'impact du changement climatique, il est nécessaire d'avoir une approche intégrée basée sur la compréhension des phénomènes physiques. Je me suis donc toujours attaché à caractériser les fines échelles océaniques et atmosphériques à partir des observations, puis à les modéliser et analyser leurs interactions et impacts sur la variabilité et l'état moyen de l'océan et, quelques fois, de l'écosystème. Ma démarche s'est tout d'abord appliquée principalement aux Systèmes d'Upwelling de Bord-Est, mais, de par mes expériences professionnelles en Espagne et aux Etats-Unis, ainsi que les projets, étudiants, et postdocs que j'ai supervisés, j'ai pu l'étendre sur de diverses régions, allant de la Mer Méditérannée aux courants de Bord-Ouest.

Depuis ma thèse, je me suis toujours concentré sur les interactions air-mer.

Abstract

The Ocean-Atmosphere interactions have a large influence on the climate and on the ecosystems at the basin scale. The main climatic modes of variability (e.g., El Niño, NAO, ...) are coupled modes between the Ocean and the Atmosphere. The ecosystems have a strong response to those variations through the influence of the wind, the light, and the temperature on the nutrient stock and, thus, on the primary production and the oxygen concentration. Systematic biases in sea surface temperature in global models have highlighted the limitations of studies based on the global models and have, thus, spurred the investigation of the Ocean-Atmosphere interactions based on the regional modeling approach. In the past few years,it has been demonstrated that the regional Ocean-Atmosphere interactions can strongly modulate the variability and the mean physical and biogeochemical state of the ocean. My line of research starts from the following postulate: in order to understand the evolution of the ocean and ecosystems and thus the impact of climate change, it is necessary to have an integrated approach based on the understanding of physical phenomena and their interactions with the ecosystem at relevant spatial and temporal scales. I have always focused on characterizing fine oceanic and atmospheric scales from observations and then modeling them and analyzing their interactions and impacts on the ocean variability and mean state.

I applied my approach over different regions of the world, including Eastern and Western Boundary Current Systems, the Mediterranean Sea, and also more recently a large tropical channel (45 • S -45 • N).

Since my PhD, I have always focused on the air-sea interactions. In particular, I wrote several studies on the origin and the consequences of the slackening of the wind (the wind "drop-off") in Eastern Boundary Upwelling System. I demonstrated its importance in determining the mean and mesoscale circulation, and, overall, the net primary production However, in this HDR manuscript, I have decided to focus on another aspect of my research that has been very inspiring for me, which could lead to a change of paradigm on how to force an ocean model: the current feedback to the atmosphere. In this manuscript, I will try to synthesize my research on that topic. I also present at the end of this manuscript part of my on-going and future research line and my experience in projects management and supervision.

Introduction

While climate models (GCMs) generally agree globally and are relatively realistic, there is a large regional dispersion or common biases [START_REF] Cai | Assessing the regional variability of GCM simulations[END_REF]. Eastern Boundary Upwelling System (EBUS) and Western Boundary Currents (WBCs) are among the strongest bias areas (e.g., [START_REF] Wang | A global perspective on CMIP5 climate model biases[END_REF], Figure 1). Part of those biases arise because of a poor representation of the regional oceanic, atmospheric and biogeochemical dynamics. Those biases have thus created a new line of research based on a regional approach to the interactions between the ocean and the atmosphere and aiming to understand and predict variability in key areas of the ocean. Thus, it has recently been demonstrated (e.g., [START_REF] Chelton | Coupled ocean-atmosphere interaction at oceanic mesoscales[END_REF]; Renault et al. (2016aRenault et al. ( ,d,c, 2017b,a),a)) that at the regional scale, fine interactions between the ocean and the atmosphere can greatly modulate the variability and mean state of the ocean and its associated ecosystem.

My line of research starts from the following postulate: in order to understand the evolution of the ocean and ecosystems and thus the impact of climate change, it is necessary to have an integrated approach based on the understanding of physical phenomena and their interactions with the ecosystem at relevant spatial and temporal scales. I have always focused on characterizing fine oceanic and atmospheric scales from observations and then modeling them and analyzing their interactions and impacts on the ocean variability and mean state. I applied my approach over different regions of the world, including Eastern and Western Boundary Current Systems, the Mediterranean Sea, and also more recently a large tropical channel (45 • S -45 • N). I conducted my thesis (2005)(2006)(2007)(2008) at the Laboratory of Geophysical and Oceanographic Space Studies (LEGOS, Toulouse) in the ECOLA team (Echanges Cote-LArge), under the direction of B. Dewitte (IRD / LEGOS) and Y. duPenhoat (IRD / LEGOS). My research aimed at studying the impact of mesoscale atmospheric structures on the ocean variability. My approach combined the use of observed data (satellites and in situ) and oceanic and atmospheric modeling based on the Regional Ocean Modeling System (ROMS, [START_REF] Shchepetkin | The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model[END_REF]) and the Weather Research and Forecast model (WRF, Ska- this experience, I extended my knowledge and skills in coupled modeling (air-sea and physical-biogeochemical). I also got the opportunity to transpose my methodology to another region, i.e., the Mediterranean Sea, while maintaining collaborations with Chile (CEAZA). During that period, I maintained a sustained training activity by supervising master and PhD students and a post-doc (See Chapter 8). My expertise and the problems I have tackled have naturally led me to extend my network of international collaborations (Rutgers University, USGS, CEAZA), and to France (MIO and LEGI).

Finally, from June 2013, after 4 years in Spain, I moved to the United States to take a position of Researcher at the University of California, Los Angeles (UCLA) within J.C.

McWilliams' team. In 2014, I obtained a large NSF project (3 M$, PI) on the impact of the climate change on the ecosystem of the 4 main Eastern Boundary Upwelling System (i.e., California, Benguela, Canary Islands, Chile). I was also Co-PI of a project on the acidification and deoxygenation of the Upwelling of California (PI, J.C. McWilliams), which allowed me to deepen my knowledge and skills in biogeochemistry and to develop new collaborations with the University of Washington (C. Deutsch). These projects have been a great opportunity for me as I got to manage a small Research Team, by supervising one researcher and 3 post-doctorals, and collaborating with 2 students. It also developed my research line on air-sea interactions. I recently integrated the IRD as a "Chargé de Recherche". My research project naturally follows the research line I developed throughout my career and aims to better understand the Ocean-Land-Atmosphere interactions and their impact on the oceanic circulation and, thus, on the biogeochemical variability.

As stated above, since my PhD, I have always focused on the air-sea interactions. In particular, I wrote several studies on the origin and the consequences of the slackening of the wind (the wind "drop-off") in Eastern Boundary Upwelling System. I demonstrated its importance in determining the mean and mesoscale circulation, and, overall, the net primary production (see Renault et al. 2012Renault et al. , 2009Renault et al. , 2016b,a),a). However, as discussed in Chapter 7, in this manuscript, I have decided to focus on another aspect of my research that has been very inspiring for me, which, as discussed in the following, could lead to a change of paradigm on how to force an ocean model: the current feedback to the atmosphere. In this manuscript, I will try to synthesize my research on that topic.

The Effect of the Current on the Atmosphere: The Current Feedback

Interactions between the ocean and the atmosphere largely influence the Earth's climate and ecosystems at the level of ocean basins. The main modes of climate variability (e.g., Madden-Julian Oscillation, El Niño, North-Atlantic Oscillation) are oceanatmosphere coupled modes. Ecosystems have a strong response to these variations through the physical influence of winds, light and temperature on the nutrient reservoir and therefore on the primary production and the trophic chain.

The ocean feedback to the atmosphere has been recently studied, mainly focusing on the thermal feedback (e.g., [START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF], Chelton et al. 2007[START_REF] Spall | Midlatitude wind stress-sea surface temperature coupling in the vicinity of oceanic fronts[END_REF][START_REF] Perlin | Numerical simulation of air-sea coupling during coastal upwelling[END_REF], Minobe et al. 2008[START_REF] Park | Drag reduction in flow over a two-dimensional bluff body with a blunt trailing edge using a new passive device[END_REF][START_REF] Cornillon | Warm core ring velocities inferred from NSCAT[END_REF]. [START_REF] Small | Air-sea interaction over ocean fronts and eddies[END_REF] provides a review of the different processes involved. Sea Surface Temperature (SST) gradients induce gradients in the lower-atmospheric stratification, hence, gradients in vertical momentum flux in the atmospheric boundary layer. Gradients in the surface wind and stress are induced beneath an otherwise more uniform mid-tropospheric wind. The thermal feedback has therefor a "top-down" effect: it modifies the Atmospheric Boundary Layer (ABL) turbulence and the wind, which in turn alter the surface stress. In that case, the surface stress induced anomalies are directly related and positively correlated to the wind induced anomalies [START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]. The thermal feedback has a linear effect on the stress and wind curl, divergence, and magnitude [START_REF] Small | Damping of tropical instability waves caused by the action of surface currents on stress[END_REF][START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF][START_REF] Chelton | Coupled ocean-atmosphere interaction at oceanic mesoscales[END_REF]. Recent studies over the Gulf Stream re-gion also highlighted how a mesoscale SST front may have an impact all the way up to the troposphere [START_REF] Minobe | Influence of the Gulf Stream on the troposphere[END_REF]. [START_REF] Hogg | The effects of mesoscale ocean-atmosphere coupling on the large-scale ocean circulation[END_REF], by using an ideal configuration of a high-resolution quasi-geostrophic ocean model coupled to a dynamic atmospheric mixed layer, suggest small-scale variation in wind stress induced by ocean-atmosphere interactions could modify the large-scale ocean circulation. [START_REF] Ma | Western boundary currents regulated by interaction between ocean eddies and the atmosphere[END_REF] and [START_REF] Seo | Distinct Influence of Air-Sea Interactions Mediated by Mesoscale Sea Surface Temperature and Surface Current in the Arabian Sea[END_REF] have recently suggested that the mesoscale thermal feedback to the atmosphere, by causing wind velocity and turbulent heat fluxes anomalies, could regulate Western Boundary Currents.

The current feedback to the atmosphere is another aspect of the interactions between atmosphere and ocean. Although generally much weaker than winds, the surface oceanic currents interactions with the surface stress and wind influences both the atmosphere and the ocean (e.g., [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF]; [START_REF] Rooth | Air-sea boundary layer dynamics in the presence of mesoscale surface currents[END_REF]; [START_REF] Dewar | Some effects of the wind on rings[END_REF]; [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF]; Renault et al. (2016d)). In a coupled model, when estimating the surface stress, the current feedback is taken into account by using the relative wind to the oceanic motions instead of the absolute wind. Under the assumption the oceanic motions are much weaker than the wind, the current feedback has been generally ignored although it has been shown in the past a possible consequent effect on the mesoscale and large scale oceanic circulation. My recent research contributes to have a better understanding of that interaction and highlights the necessity to take it into account to better understand and represent the ocean energy budget and the circulation (from submesoscale to large scale) of the ocean.

Contrarily to the thermal feedback, the current feedback modifies directly the surface stress [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF] and has a "bottom-up" effect on the wind: a negative stress anomaly causes a positive U a anomaly (Renault et al., 2016d;[START_REF] Takatama | The Role of Back Pressure in the Atmospheric Response to Surface Stress Induced by the Kuroshio[END_REF]. At the mesoscale, the ocean currents are mainly rotational and very nearly geostrophic (i.e., non-divergent), so that the mesoscale current feedback mainly affects the stress (wind) curl but not its magnitude nor divergence [START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]Renault et al., 2016d). Previous studies shows that the current effect on the surface stress can lead to a reduction of the Eddy Kinetic Energy (EKE) of the ocean via a "mechanical dampening" [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF][START_REF] Dewar | Some effects of the wind on rings[END_REF][START_REF] Dawe | Effect of ocean surface currents on wind stress, heat flux, and wind power input to the ocean[END_REF][START_REF] Hughes | Wind work on the geostrophic ocean circulation: An observational study of the effect of small scales in the wind stress[END_REF][START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF] and hence a reduction of the wind work. Yet, in those studies the atmospheric response to the current feedback is neglected.

In oceanic numerical modeling the surface stress is usually estimated as a function of the wind speed, ignoring the current feedback, i.e., the fact that the ocean surface current also has a drag force on the atmosphere. [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF] shows such a simplifica-tion can lead to an overestimation of the total energy input to the ocean by wind work and suggests the current should be included when estimating the surface stress. To my knowledge, the effects of surface currents on the surface wind speed were ignored in the literature. This will be one of my research topics.

In my recent research, using different sets of coupled and partially coupled simulations, the focus is therefore on this surface current feedback to the atmosphere. The main objectives are:

-To assess how the current feedback modifies the wind work -To address how it alters the oceanic circulation, from the submesoscale to the mesoscale and to the large scale circulation -To study the Western Boundary Currents response to a possible upscaling effect -To disentangle the thermal feedback from the current feedback -To address the atmospheric response and try to derive parameterizations to force an ocean model In this manuscript, I will synthesize my contribution to the understanding of the current feedback to the atmosphere and its various consequences on the ocean and atmosphere. I will also present part of my on-going and future research line. This HDR manuscript is organized as follow: Chapter 1 aims to present a brief sum-up of the coupled configurations and of the main methods I will use all along this manuscript. The objective of Chapter 2 is to characterize the direct effects of the current feedback on the oceanic circulation. In Chapter 3, I will demonstrate the current feedback, via an upscaling effect, has a strong control on the Western Boundary Currents dynamics. I choose to dedicate Chapter 4 to the atmospheric response to the current feedback. In this chapter, I will introduce the definition of two new coupling coefficients. These coupling coefficients raise the questions on (1) how to disentangle the thermal feedback from the current feedback and (2) how to parameterize the surface stress and wind responses to the current feedback. Chapter 5 aims to respond to the first question. Finally, I will sump up part of my on-going and future research in Chapter 6 and will conclude in Chapter 7. At the end of the manuscript (Chapter 8) , I will also present my experience in projects management and supervision. The very last chapter (Chapter 9) simply lists my publications. The surface stress and Equivalent Neutral Wind (ENW) are obtained from the QuikSCAT gridded product from Ifremer [START_REF] Bentamy | Compatibility of C-and Ku-band scatterometer winds: ERS-2 and QuikSCAT[END_REF] for the period 2000-2008. It has a spatial resolution of 0.25 • . I will also use the the Scatterometer Climatology of Ocean Winds (SCOW; [START_REF] Risien | A global climatology of surface wind and wind stress fields from eight years of QuikSCAT scatterometer data[END_REF] product based on the QuikSCAT satellite scatterometer.

It provides monthly data at a 0.25 • resolution.

AVISO Altimetry

The daily Absolute Dynamic Topography fields are obtained from the AVISO product [START_REF] Ducet | Global high-resolution mapping of ocean circulation from TOPEX/Poseidon and ERS-1 and-2[END_REF] for the period 2000-2008. The Sea Level Anomaly data is based on a square grid of 0.25 • . The daily Absolute Dynamic Topography maps are then produced by adding the Mean Dynamic Topographic data to the Sea Level Anomaly [START_REF] Rio | Beyond GOCE for the ocean circulation estimate: Synergetic use of altimetry, gravimetry, and in situ data provides new insight into geostrophic and Ekman currents[END_REF].

Sea Surface Temperature

The daily SST fields used here have a spatial resolution of 0.25 • and are obtained from the OI SST analysis version 2 over the time-period 2000-2008. A full description of the complete analysis procedure can be found in [START_REF] Reynolds | Daily high-resolution-blended analyses for sea surface temperature[END_REF].

Current Feedback in a Coupled Model

In a coupled model the current feedback to the atmosphere is simply represented by using a bulk formulae for stress with the surface wind relative to the oceanic current:

U r = U a -U o , (1.1)
where U a and U o are the surface wind and the surface current at the closest model grid levels to the surface (≈ 10 m in my simulations), respectively. When neglecting the current feedback, the wind U a is used instead of the relative wind U r . As described by [START_REF] Lemarié | Numerical modification of atmospheric models to include the feedback of oceanic currents on air-sea fluxes in ocean-atmosphere coupled models[END_REF], because of the implicit treatment of the bottom boundary condition in most atmospheric models, the use of relative winds involves a modification of both the surface-layer vertical mixing parameterization (MYNN2.5 or YSU, depending on the simulations used, see the next section on the experiments description) and the tridiagonal matrix for vertical turbulent diffusion.

Numerical Experiments

Table 1.1 summarizes the various experiments used in this manuscript to assess the impact of the oceanic currents on the surface stress, wind, and oceanic circulation. The experiments take into account various degrees of coupling.

The US West Coast configuration

The Ocean Model

The oceanic simulations were performed with the Regional Oceanic Modeling System (ROMS) [START_REF] Shchepetkin | The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model[END_REF] in its CROCO (Coastal and Regional Ocean COmmunity model) version [START_REF] Debreu | Two-way nesting in splitexplicit ocean models: Algorithms, implementation and validation[END_REF]. ROMS is a free-surface, terrain- for the barotropic mode [START_REF] Mason | Procedures for offline grid nesting in regional ocean models[END_REF] and Orlanski-type scheme for the baroclinic mode (including T and S; [START_REF] Marchesiello | Open boundary conditions for long-term integration of regional oceanic models[END_REF].

following
Bathymetry for all domains is constructed from the Shuttle Radar Topography Mission (SRTM30 plus) dataset based on the 1-min [START_REF] Sandwell | Marine gravity anomaly from Geosat and ERS 1 satellite altimetry[END_REF] global dataset and higher-resolution data where available. A Gaussian smoothing kernel with a width of 4 times the topographic grid spacing is used to avoid aliasing whenever the topographic data are available at higher resolution than the computational grid and to ensure the smoothness of the topography at the grid scale. Also, in order to avoid pressure gradient errors induced by terrain-following (sigma) coordinates in shallow regions with steep bathymetric slope [START_REF] Beckmann | Numerical simulation of flow around a tall isolated seamount. Part I: Problem formulation and model accuracy[END_REF], we apply local smoothing of the bottom topography, such as the maximum difference between adjacent grid cell depths divided by their mean depth (r = ∆h/h). Here local smoothing is applied where the steepness of the topography exceeds a factor r = 0.2.

Lateral oceanic forcing for the largest domain as well as surface forcing for all simulations are interannual. Temperature, salinity, surface elevation, and horizontal velocity initial and boundary information for the largest domain covering the whole North America West Coast are taken from the monthly averaged Simple Ocean Data Assimilation (SODA) ocean inter-annual outputs [START_REF] Carton | A reanalysis of ocean climate using Simple Ocean Data Assimilation (SODA)[END_REF]. A bulk formulae [START_REF] Large | Surface fluxes for practitioners of global ocean data assimilation[END_REF] is used to estimate the freshwater, turbulent, and momentum fluxes using the atmospheric fields derived from the uncoupled Weather Research and Forecast (WRF) simulation. In the coupled simulations, the fluxes are computed by WRF and then given to ROMS using the same bulk formulae.

The 12 km domain is first spun up from the SODA initial state,1st January 1994, for a few months, then run for an additional period until end of 1999. Kinetic energy in the domain is statistically equilibrated within the first few months of simulation. The second grid (4 km resolution) is then nested in the parent grid from 1st June 1994. Results obtained after a 6-month spin-up are then used in our analysis. All domains have 42 levels in the vertical with the same vertical grid system concentrating vertical levels near the surface [START_REF] Shchepetkin | Correction and commentary for "Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system[END_REF], with stretching surface and bottom parameters hcline = 250 m, θb = 1.5, and thetas = 6.5. Finally, vertical mixing of tracers and momentum is done with a K-profile parameterization (KPP; [START_REF] Large | Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization[END_REF]. In this study only the period 1995-1999 is analyzed.

The Atmospheric Model

The A full set of parameterization schemes is included in WRF. The model configuration was setup with the following parameterizations: the WRF Single-Moment 6-class microphysics scheme (Hong and Lim, 2006a) modified to take into account the droplet concentration [START_REF] Jousse | Climatic Importance of Aerosol Indirect Effects in the Northeast Pacific[END_REF]; the Tiedtke cumulus parameterization [START_REF] Zhang | Improved representation of boundary layer clouds over the Southeast Pacific in ARW-WRF using a modified Tiedtke cumulus parameterization scheme[END_REF]; the new Goddard scheme for shortwave and longwave radiation (Chou and Suarez, 1999b);

the Noah land surface model [START_REF] Skamarock | A description of the Advanced Research WRF version 3[END_REF]; and the MYNN2.5 planetary boundary layer (PBL) scheme [START_REF] Nakanishi | An improved Mellor-Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog[END_REF]). 1

A High Resolution Configuration of the US West Coast

The Ocean Model

The oceanic simulations were performed with ROMS [START_REF] Shchepetkin | The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model[END_REF][START_REF] Shchepetkin | An adaptive, Courant-number-dependent implicit scheme for vertical advection in oceanic modeling[END_REF] in its CROCO (Coastal and Regional Ocean Community) version [START_REF] Debreu | Two-way nesting in splitexplicit ocean models: Algorithms, implementation and validation[END_REF]. CROCO is a free-surface, terrain-following coordinate model with Other WRF PBL schemes were tried (e.g., Yonsei University, (Hong et al., 2006a), University of Washington, [START_REF] Park | The University of Washington shallow convection and moist turbulence schemes and their impact on climate simulations with the Community Atmosphere Model[END_REF]). The MYNN2.5 gave, in general, more realistic features, especially in terms of cloud cover.

(http://www.myocean.eu). The 12 km and the 4 km domains are run for 5.5 years from June 1995 to June 2000, using interannual lateral oceanic and surface forcing. The 500 m domains is run from June to September 2000. Only the summer period (July-September) is analyzed. Vertical mixing of tracers and momentum is done with a K-Profile Parameterization (KPP; [START_REF] Large | Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization[END_REF]. The diffusive part of the advection scheme is rotated along the isopycnal surfaces to avoid spurious diapycnal mixing [START_REF] Lemarié | Are there inescapable issues prohibiting the use of terrain-following coordinates in climate models[END_REF].

The atmospheric fields are simulated using the Weather Research and Forecast (WRF)

model. The [START_REF] Fairall | Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm[END_REF] bulk formulae is used to estimate the freshwater, turbulent, and momentum fluxes provided to the ocean model. Two sets of simulations are done.

In the first set (NOCRT500), WRF gives the ocean model hourly averages of freshwater, heat, and momentum fluxes; whereas, the ocean model sends WRF the hourly SST. In the second set (CRT500), the ocean model sends WRF both SST and surface currents, and the surface stress is estimated using the relative wind to the ocean motions:

U r = U a -U o .

WRF

The North Atlantic Configuration

The Ocean Model

The oceanic simulations were performed with ROMS [START_REF] Shchepetkin | The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model[END_REF][START_REF] Shchepetkin | An adaptive, Courant-number-dependent implicit scheme for vertical advection in oceanic modeling[END_REF] in its CROCO (Coastal and Regional Ocean Community) version [START_REF] Debreu | Two-way nesting in splitexplicit ocean models: Algorithms, implementation and validation[END_REF]. ROMS is a free-surface, terrain-following coordinate model with split-explicit time stepping and with Boussinesq and hydrostatic approximations. The main grid covers the full North Atlantic Gyre and Subpolar Gyre, extending from 133. (1997) global dataset and higher-resolution data where available. A Gaussian smoothing kernel with a width 4 times the topographic grid spacing is used to avoid aliasing whenever the topographic data are available at higher resolution than the computational grid and to ensure the smoothness of the topography at the grid scale. Also, to avoid pressure gradient errors induced by terrain-following coordinates in shallow regions with steep bathymetric slope [START_REF] Beckmann | Numerical simulation of flow around a tall isolated seamount. Part I: Problem formulation and model accuracy[END_REF], we apply local smoothing of the bottom topography where the steepness of the topography exceeds a factor r = 0.2.

The domain is initialized using the SODA climatological state of Jan. 1st and spun up for 14 years using climatological monthly surface fluxes and lateral oceanic boundary conditions. It is then run for an additional period, from year 2000 to 2004, using interannual lateral oceanic forcing for the largest domain as well as interannual surface forcing for all simulations. Temperature, salinity, surface elevation, and horizontal velocity initial and boundary information for the domain are taken from the monthly averaged Simple Ocean Data Assimilation (SODA) ocean interannual outputs [START_REF] Carton | A reanalysis of ocean climate using Simple Ocean Data Assimilation (SODA)[END_REF].

In the coupled simulations the atmospheric fields are simulated using the Weather

Research and Forecast (WRF) model. The [START_REF] Fairall | Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm[END_REF] bulk formulae is used to estimate the freshwater, turbulent, and momentum fluxes provided to ROMS. The very same atmosphere and bulk formulae are used in the uncoupled simulations.

The boundary condition algorithm consists of a modified Flather-type scheme for the barotropic mode and Orlanski-type scheme for the baroclinic mode (including T and S; [START_REF] Marchesiello | Open boundary conditions for long-term integration of regional oceanic models[END_REF]. The domain has 50 levels in the vertical with a vertical grid system concentrating vertical levels near the surface [START_REF] Shchepetkin | Correction and commentary for "Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system[END_REF].

The stretching surface and bottom parameters are h cline = 300 m, θ b = 2, and θ s = (Hong and Lim, 2006a), modified to take into account the droplet concentration [START_REF] Jousse | Climatic Importance of Aerosol Indirect Effects in the Northeast Pacific[END_REF]; the new Arakawa-Shubert cumulus parameterization [START_REF] Han | Revision of convection and vertical diffusion schemes in the NCEP global forecast system[END_REF]; the new Goddard scheme for shortwave and longwave radiation (Chou and Suarez, 1999b); the Noah land surface model [START_REF] Skamarock | A description of the Advanced Research WRF version 3[END_REF]; and the MYNN2.5 planetary boundary layer scheme [START_REF] Nakanishi | An improved Mellor-Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog[END_REF].

The Greater Agulhas Region

The Ocean Model

The oceanic simulations were performed with ROMS [START_REF] Shchepetkin | The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model[END_REF][START_REF] Shchepetkin | An adaptive, Courant-number-dependent implicit scheme for vertical advection in oceanic modeling[END_REF] in its CROCO version. ROMS is a free-surface, terrain-following coordinate model with split-explicit time stepping and with Boussinesq and hydrostatic approximations. The grid covers the south African region, including the Mozambique Channel, Madagascar, the AC retroflection, and the Benguela, extending from 11.5 Jan. 1st and spun up for 5.5 years using climatological monthly surface fluxes and lateral oceanic boundary conditions, reaching an equilibrium state. It is then run for an addi-tional period, from June 1999 to 2004, using interannual lateral oceanic forcing as well as interannual surface forcing for all simulations. Temperature, salinity, surface elevation, and horizontal velocity initial and boundary information for the domain are taken from the monthly averaged SODA ocean interannual outputs [START_REF] Carton | A reanalysis of ocean climate using Simple Ocean Data Assimilation (SODA)[END_REF]. Vertical mixing of tracers and momentum is done with a K-profile parameterization (KPP; [START_REF] Large | Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization[END_REF]. The diffusive part of the advection scheme is rotated along the isopycnal surfaces to avoid spurious diapycnal mixing [START_REF] Lemarié | Are there inescapable issues prohibiting the use of terrain-following coordinates in climate models[END_REF]. As in [START_REF] Penven | Madagascar: A pacemaker for the Agulhas Current system[END_REF] and [START_REF] Loveday | Decoupling of the Agulhas leakage from the Agulhas Current[END_REF], excess western boundary current variability is selectively damped via a horizontal viscosity parameterization A h [START_REF] Smagorinsky | General circulation experiments with the primitive equations: I. the basic experiment*[END_REF]:

A h = 0.025 × ∆ x ∆ y 2 × |deformation tensor| , (1.2)
where ∆ x , and ∆ y are the zonal and meridional scales. Only the period 2000-2004 is analyzed.

The Atmospheric Model

WRF (version 3. The parameterizations used here are similar to the one described above for the North Atlantic Basin. A bulk formulae is used [START_REF] Fairall | Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm[END_REF] to estimate the freshwater, turbulent, and momentum fluxes provided to ROMS.

The Tropical Chanel Configuration

The numerical models and configurations are the same to the ones employed in [START_REF] Samson | Roles of land surface albedo and horizontal resolution on the Indian summer monsoon biases in a coupled ocean-atmosphere tropical-channel model[END_REF], and the following models descriptions are derived from there. The oceanic simulations were performed with the Nucleus for European Modelling of the Ocean (NEMO) v3.4. A complete description of this model can be found in [START_REF] Madec | NEMO ocean engine[END_REF]. The atmospheric component is the WRF version 3.3.1, which solves compressible, non-hydrostatic Euler equations with the Advanced Research WRF (ARW) dynamical solver [START_REF] Skamarock | A description of the Advanced Research WRF version 3[END_REF]. NEMO and WRF are coupled through the OASIS3-MCT coupler [START_REF] Craig | Development and performance of a new version of the OASIS coupler, OASIS3-MCT_3. 0[END_REF].

The oceanic (atmospheric) component uses an Arakawa-C grid, based on a Mercator projection at 1/12 N, with the oceanic grid being a prefect subdivision by 3 of the atmospheric grid. The ocean vertical grid has 75 levels, with 25 levels above 100 m and a resolution ranging from 1 m at the surface to 200 m at the bottom. The atmospheric grid has 60 eta-levels with a top of the atmosphere located at 50 hPa. The WRF default vertical resolution has been multiplied by three below 800 hPa.

Thus, the first 33 levels are located below 500 hPa with the first theta base-level located at 10m over the ocean.

As in [START_REF] Samson | Roles of land surface albedo and horizontal resolution on the Indian summer monsoon biases in a coupled ocean-atmosphere tropical-channel model[END_REF]; the physical package we use in WRF is the longwave Rapid

Radiative Transfer Model (RRTM; [START_REF] Mlawer | Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave[END_REF], the "Goddard" Short Wave (SW) radiation scheme (Chou and Suarez, 1999a), the "WSM6" microphysics scheme (Hong and Lim, 2006b), the Betts-Miller-Janjic (BMJ) convection scheme [START_REF] Betts | A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets[END_REF]; [START_REF] Janjić | The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes[END_REF]), the Yonsei University (YSU) planetary boundary layer scheme (Hong et al., 2006b), the unified NOAH Land Surface Model (LSM) with the surface layer scheme from MM5 [START_REF] Chen | Coupling an advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system. Part I: Model implementation and sensitivity[END_REF]. WRF lateral boundary conditions are prescribed from the European Centre for Medium-Range Weather Forecasts ERA-Interim 0.75 • resolution reanalysis [START_REF] Dee | The ERA-Interim reanalysis: Configuration and performance of the data assimilation system[END_REF] at 6 hourly intervals.

The ocean physics used in NEMO corresponds to the Upstream-Biased Scheme (UBS, [START_REF] Shchepetkin | Correction and commentary for "Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system[END_REF]) advection for the tracers and the dynamics with no explicit diffusivity and viscosity. The vertical eddy viscosity and diffusivity coefficients are computed from a TKE turbulent closure model [START_REF] Blanke | Variability of the tropical Atlantic Ocean simulated by a general circulation model with two different mixed-layer physics[END_REF]. The oceanic open boundary conditions are prescribed with an interannual global 1

4

• DRAKKAR simulation [START_REF] Brodeau | An ERA40-based atmospheric forcing for global ocean circulation models[END_REF]. In order to benefit, at a limited coast, from a fully spunup meso-scale circulation in the initial conditions of the • ocean, we first run a 5-year long ocean forced simulation initialized from • DRAKKAR simulations and using the exact same NEMO • configuration than in our coupled simulations.

As described in Table 1.1, three main 5 years coupled simulations are performed with this setup over the 1989-1993 period, only differing by the degree of coupling they consider. In the control run (PULS_CTRL), WRF gives NEMO hourly averages of freshwater, heat, and momentum fluxes; whereas, the ocean model sends WRF the hourly Sea Surface Temperature (SST) and surface currents. In PULS_CTRL, the surface stress is estimated using the relative wind to the ocean motions: U r = U a -U o . In PULS_NOCRT, the ocean model sends WRF only the SST. In the third simulation, called hereafter PULS_SMTH, NEMO sends to WRF the surface currents and a smoothed SST. The smoothed SST fields are obtained using the filter described hereafter.

Finally, to confirm the results obtained with PULS_SMTH_NOCRT and to test the ro-bustness of the spatial filter, an additional coupled simulation called PULS_SMTH_NOCRT has been carried out. In such a simulation, the ocean model sends WRF only the smoothed SST (the CFB is ignored). The comparison between PULS_SMTH and PULS_SMTH_NOCRT

shows that some of the mesoscale stress (and wind) signal in SMTH is still due to the TFB as it can not be attributed to the CFB (See Chapter 5). To remove all the mesoscale signal, a much larger filter should be used. However, such a filter would suffer from the drawback that it could also modify the large scale signal, which would complicate the comparison of the simulations.

A Simplified Kinetic Energy Budget

In this manuscript, all quantities are decomposed into the mean indicated with an overbar (-) and estimated over the whole period as a long-term mean, or a seasonal mean (and sometimes a spatial mean). Their deviations from this mean are referred to using primes (').

As in e.g., [START_REF] Stern | Ocean circulation physics[END_REF] and following closely the description in Renault et al. (2016d), the total wind work is defined as

FK = 1 ρ 0 (τ x u o + τ y v o ) , (1.3)
where u o and v o are the zonal and meridional surface currents, τ x and τ y are the zonal and meridional surface stresses, and ρ 0 is mean seawater density.

The two main pathways of mechanical energy from the surface to the deeper ocean are wind forcing of near inertial oscillations and wind forcing of surface geostrophic flows.

Previous estimates of the wind power input to the oceanic general circulation (e.g., [START_REF] Wunsch | The work done by the wind on the oceanic general circulation[END_REF][START_REF] Von Storch | Wind-generated power input to the deep ocean: An estimate using a 1/10 general circulation model[END_REF][START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF] use Eq. (1.3) and support the assumption that wind power to ageostrophic motions does not feed into the general circulation.

In this study the oceanic simulations are forced by a high frequency wind forcing (hourly) that produces large inertial oscillations and thus a large ageostrophic wind work that is not significantly impacted by the current feedback (Renault et al., 2016d). The current feedback causes a deflection of energy on eddy-time-scale from the ocean geostrophic currents to the atmosphere. The current feedback effect on the geostrophic wind work and its consequences on the oceanic circulation is the focus of this study.

The oceanic geostrophic surface currents are estimated using the geostrophic approximation and the daily average sea surface height from the simulations:

u og = - g f ∂h ∂y , (1.4)
and .5) where u og and v og are the zonal and meridional geostrophic currents, respectively; g is the gravitational acceleration, f the Coriolis parameter, and h the daily average sea surface height from the simulation.

v og = g f ∂h ∂x , ( 1
The oceanic surface currents can then be split into their geostrophic and ageostrophic parts:

u o = u og + u oa , (1.6)
and

v o = v og + v oa , (1.7)
with u og , v og , u oa , and v oa the zonal and meridional geostrophic and ageostrophic currents, respectively.

Substituting the decomposition of Eq.(1.6) into Eq. (1.3), the total wind work on the geostrophic flow is

FK g = 1 ρ 0 (τ x u og + τ y v og ). (1.8)
FK g can be split into its mean (F m K mg ) and eddy parts (F e K eg ) using a simple Reynolds decomposition that leads to:

-The mean geostrophic wind work:

F m K mg = 1 ρ 0 (τ x u og + τ y v og ) . (1.9)
-The mean geostrophic eddy wind work:

F e K eg = 1 ρ 0 (τ x u og + τ y v og ) (1.10)
and As in [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF], I will also focus on the following relevant energy source and eddy-mean conversion terms:

-Barotropic (Reynolds stress) conversion K m K e : .11) where w is the vertical velocity and x, y, and z are the zonal, meridional, and vertical coordinates, respectively.

K m K e = z -(u o u o ∂u o ∂x + u o v o ∂u o ∂y + u o w ∂u o ∂z + v o u o ∂v o ∂x + v o v o ∂v o ∂y + v o w ∂v o ∂z ) , ( 1
-Baroclinic conversion P e K e : .12) where g is the gravitational acceleration.

P e K e = z - g ρ 0 ρ w , ( 1
F m K mg represents the transfer of energy from mean surface wind-forcing to mean Kinetic Energy. It is the main source of energy of the ocean at basin scale (Fig. 2.1 and e.g., [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF]). F e K eg represents the transfer of energy between the surface stress anomalies and the geostrophic currents. K m K e represents the barotropic conversion from mean kinetic energy to EKE, and PeKe represents the baroclinic conversion from eddy available potential energy to EKE. We computed those conversion terms at each model grid point. The wind work is estimated at the free surface, whereas the barotropic and baroclinic conversion terms are integrated over the whole water column.

Cross-shore sections are evaluated using d as the cross-shore distance.

A Full KE budget

Following Capet et al. (2008e) and [START_REF] Marchesiello | Submesoscale dynamics in tropical instability waves[END_REF], a spectral decomposition of the KE balance for the Primitive Equations has been computed. To that end, the co-spectrum between velocity and the term that enters the momentum equations is computed on each 6-hours snapshots and, then, averaged over the 3 months-period considered here and over 100m depth (note similar results are found when considering only e.g., 70m depth). It is expressed as:

T(k) = C(k) + P(k) + V(k) + A(k) + R(k) (1.13) C(k) = R w * b (1.14) P(k) = R [- 1 ρ 0 u * • ∇p (1.15) V(k) = R u * h • ∂K v ∂u h ∂z ∂z (1.16) A(k) = R -u * h • (u h • ∇)u h -u * h • w ∂u h ∂z (1.17)
where b is buoyancy (b = -g ρ ρ 0 ) and K v is the vertical viscosity. The caret stands for an horizontal Fourier transform after removing the area mean and applying a 2D

Hanning window [START_REF] Jenkins | Spectral analysis[END_REF], which has the effect to symmetrize the signal and suppressing the advective horizontal fluxes through the boundary. * denotes the complex conjugate operator; R represents the real part operator; indicates an average over the 3-months considered here and over 100m depth, (at 100m depth the vertical flux is small, choosing 70m depth does not qualitatively change the results). C represents an injection of energy by baroclinic conversion; P is the 3D pressure work; V corresponds to the wind and vertical mixing work; A represents the horizontal and vertical advection contribution; and the horizontal mixing (H).

Spectral Flux of Surface Ocean Geostrophic Kinetic Energy

As in [START_REF] Marchesiello | Submesoscale dynamics in tropical instability waves[END_REF]Arbic et al. (2013), the spectral fluxes π of surface ocean geostrophic kinetic energy in the isotropic wavenumber k domain is computed as the energy transfer rate in k space, which is the integral in k of the surface geostrophic advective term of the KE balance A(k), assuming the flux vanishes at the highest wavenumber k max .

A(k) is first estimated as:

A(k) = A H (k) + A V (k) = -u * h • (u h • )u h -u * h • w ∂u h ∂z (1.18)
where the caret denotes a horizontal Fourier transform after removing the areal mean and performing the symmetrization which has the effect of suppressing the advective horizontal fluxes through the lateral boundaries. The asterisk notation * indicates the complex conjugate operator; the symbol represents the real part operator; the overbar represents an average in time over whole period of the simulation (5 years).

Then π(k) computed as:

Π(k) = k max k A dk (1.19)
The π(k) associated error is assessed using a bootstrap method; π(k) is computed 10 000 times using random samples from the distribution. The error bars are defined as plus or minus the standard deviation of the obtained π(k).

Coupling Coefficients

The different coupling coefficients used in this manuscript are presented in Table 1.2.

Current Feedback Coupling Coefficients

As in Renault et al. (2016dRenault et al. ( , 2017b)), s τ is defined as the slope of the robust regression [START_REF] Li | Robust regression[END_REF] between surface stress curl and oceanic current vorticity. It is evaluated at each grid point for both the simulations and the observations. The fields are first temporally averaged using a 29day running mean to suppress the weather-related variability [START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF], and the large-scale signal is removed using a high-pass Gaussian spatial filter with a 250 km cutoff (roughly corresponding to the eddy scale, as in e.g., [START_REF] Seo | Distinct Influence of Air-Sea Interactions Mediated by Mesoscale Sea Surface Temperature and Surface Current in the Arabian Sea[END_REF], see filter description bellow). Note a e.g., 15day running mean does not efficiently suppress the the weather-related variability.

s w is defined as the slope of the robust regression between 10-m (or ENW) wind curl and oceanic current vorticity. It is evaluated at each grid point for both the simulations and the observations. As for s τ , the fields are first temporally averaged using a 29day running mean and spatially filtered. wind stress divergence and down-stress SST gradient (s Dstr ). The method used here is similar to the one applied by [START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF] and [START_REF] Wang | Variability in the coupling between sea surface temperature and wind stress in the global coastal ocean[END_REF]. Daily

SST is used (a 3-day average does not change the result). The cross-wind (cross-stress) and down-wind (down-stress) components of the SST gradient is computed within each daily QuikSCAT wind U ENWr (surface stress) and the daily SST. To remove the atmospheric synoptic variability, a 29-day running window is then applied on the cross-wind and down-wind (cross-stress and down-stress) SST gradients, wind and surface stress curl and divergence. Anomalies of each variable are finally computed using a the spatial Gaussian high-pass filter (250km cutoff, see above). Following such a method allows to reproduce, e.g., the Figure 1 from [START_REF] Wang | Variability in the coupling between sea surface temperature and wind stress in the global coastal ocean[END_REF]. The same method is applied on the model fields. SST feedback). It removes less than 10 % of the points. The mesoscale anomalies are then estimated using the spatial filter described below.

Miscellaneous

10-m wind and Equivalent Neutral Wind

As described in the main text, we define 3 different sorts of wind:

-The relative wind U r = U a -U o , with U o being the oceanic surface current. Because the first vertical level is often not defined around 10m, the 10-m wind is often diagnosed from the friction velocity and some atmospheric parameters. However, such a definition does not allow to estimate the absolute 10-m wind but rather the relative U r .

-the 10-m wind U a is defined as the first vertical level of the atmospheric model, which has been defined at ≈ 10m.

-Satellite scatterometers (such as QuikSCAT) provide a 10m-wind, however it does not correspond to U a : it is estimated from the pseudo-stress and is reported as the so-called Equivalent Neutral stability Winds (ENW, [START_REF] Bentamy | Compatibility of C-and Ku-band scatterometer winds: ERS-2 and QuikSCAT[END_REF]), i.e., the wind that would exist if the conditions were neutrally stable [START_REF] Ross | Oceanic surface winds[END_REF]). As confirmed in the manuscript, it actually represents the relative ENW to the surface current rather than the absolute ENW (U ENWr ). As in, e.g., [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF], the U ENWr is computed as:

U ENWr = u * k (ln 10 z 0 ) (1.20)
where the friction velocity u * and roughness length z 0 (in meters) are taken at each output interval, and k = 0.4 is the von Karman constant.

Submesoscale characterization

As in Capet et al. (2008c), the submesoscale is isolated from the signal using a highpass spatial filter that consists of a five-point operator with a 12-km smoothing length and 2-days smoothing. Note, the use or not of the 2-days smoothing does not change qualitatively the results.

Spectrum

To compute the spectrum the area mean is first removed and a symmetrization is performed using an Hanning window [START_REF] Jenkins | Spectral analysis[END_REF].

Available Potential Energy

The mesoscale APE is estimated as [START_REF] Fox-Kemper | Parameterization of mixed layer eddies. Part I: Theory and diagnosis[END_REF]; Srinivasan et al. (2017):

APE = 1 2 H 2 b |∇ h b ME | z , (1.21)
where b ME represents the mesoscale component estimated using a spatial low-pass filter of 250 km, and the depth average is computed over the mixed layer depth H b . H b is estimated using the classic approach of the depth at which the density is 0.03 • C below that at 10 m depth (de Boyer Montégut et al. ( 2004)).

Surface Stress Induced Ekman Pumping

The Ekman pumping induced by the surface stress is computed as: .22) where f is the Coriolis frequency.

w τ = k • ∇ × τ ρ 0 f , ( 1

Spatial Filter

As described in Renault et al. (2017b), the mesoscale anomalies are isolated from the large scale signal by using a spatial filter. A field φ is smoothed using a Gaussian spatial filter with a standard deviation of 4 grid points. Gaussian weight of points located at a distance larger than 3σ are considered zero. The Gaussian filter is thus applied on a (6σ + 1) x (6σ + 1) window which makes 25x25 points (≈ 6

= C d ρ a (U a -U o ) 2 < C d ρ a (U a ) 2
, where C d is the drag coefficient).

The weakening of the surface stress is realistic and reduces the biases with respect to the SCOW product (Fig. 2.1c).

The presence of the GS has a very clear effect on the surface stress curl. By weakening the surface stress, in GS_CRT, the current feedback reduces both the large scale negative and positive stress curl with respect to GS_NOCRT, improving the realism of the simulation (Fig. 2.2). In GS_NOCRT, consistent with the literature, the SST feedback produces a band of positive surface stress curl that is situated westward of the GS path (Fig. 2

.2b).

There is an eastward positive SST gradient from the coast to the GS path (not shown). It induces a decrease of the surface stress [START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF], and thus a positive stress curl, which is clearly overestimated with respect to SCOW (Fig. 2.2a). In GS_CRT, the SST feedback is still active, however, the current feedback produces an increase of the surface stress: the current vorticity is positive (Fig. 2.2a,b) and creates a negative surface stress curl (Renault et al., 2016d). It thus counteracts and dampens the SST feedback effect, reducing the intensity of the positive band of surface stress curl along the U.S. East

Coast. In the observations and in GS_CRT along the GS path, there is a band of positive stress curl that is not present in GS_NOCRT. Here, again, due to the current feedback, the surface stress is decreased along the GS path (Fig. 2.2ab), inducing a positive surface GS_NOCRT reproduce the main spatial pattern of F m K mg . By weakening the large scale surface stress, the current feedback induces a reduction of F m K mg (Fig. 2.1), in average by 30%. The main reduction occurs where the current is largest, i.e., the southwestern part of the gyre (including the Gulf of Mexico Loop Current), and the GS. GS_CRT still overestimates F m K mg with respect to the observation estimates; this could be due partly to models biases but also to the spatial resolution and smoothing used in AVISO. The F m K mg reduction in GS_CRT is consistent with the [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF] findings. Using the observations, they suggest that ignoring the current feedback in the estimation of the surface stress leads to a systematic overestimation of F m K mg of 10% to 30%. The overestimation of F m K mg in GS_NOCRT compared to GS_CRT is about 50%, which is larger than the estimate by [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF]. However, although [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF] uses the observations that by definition include all the feedback [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF] could not estimate the F m K mg for a non-active atmosphere that results in stronger oceanic currents. Figure 2.3 shows the depth integrated Kinetic Energy (KE) for GS_CRT and GS_NOCRT. The reduction of F m K mg slows down the entire gyre circulation and hence reduces the total Kinetic Energy (KE) by 27%. This is in agreement with [START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF][START_REF] Pacanowski | Effect of equatorial currents on surface stress[END_REF][START_REF] Luo | Reducing climatology bias in an ocean-atmosphere CGCM with improved coupling physics[END_REF], who all found a significant reduction of the Equatorial Current (SEC) and Equatorial Under Current induced by the current feedback to the surface stress. The slowing down of the gyre -and hence the weakening of the geostrophic surface current (up to 0.3 m s -1 , not shown) -explains the large reduction of F m K mg from GS_NOCRT to GS_CRT.

A F m K mg reduction equivalent to the [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF] estimate can be computed using the surface geostrophic surface currents from GS_CRT and the surface stress from GS_CRT or GS_NOCRT (i.e., with or without current feedback). In that case ignoring the influence of the surface current on the surface stress (as GS_NOCRT does) leads to an overestimation of F m K mg by 10%, in good agreement with [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF]. Finally, the net transport estimated over the North Atlantic Basin (Colin de Verdière and Ollitrault, 2016) from the ARGO and World Ocean Atlas data [START_REF] Levitus | The world ocean database[END_REF], and from

GS_CRT and GS_NOCRT, is estimated (not shown). Consistent with the KE reduction, the net transport is reduced with the current feedback, thus reducing the biases of the simulation with respect to the Colin de Verdière and Ollitrault ( 2016) estimates. In particular, the transport is reduced along the GS path, especially after the GS separation at Cape Hatteras.

Similar results are found for the Agulhas Current. To illustrate it, Fig. 2.4 depicts the mean surface geostrophic currents from AVISO and from the AGH_CRT and AGH_NOCRT simulations. The mean surface geostrophic currents are better represented in AGH_CRT:

the AC path is narrower and the AC retroflection is more realistic (see Chapter 3). In the observations and in AGH_CRT, at the surface, the AC reaches on average a maximum velocity of 1.1 ms -1 , whereas in AGH_NOCRT, due to a too persistent eastern retroflection (Chapter 3), it reaches only 0.8 ms -1 . Consequently, the Good Hope Jet reaches values of 0.4 ms -1 in AGH_CRT and in AVISO, vs. 0.3 ms -1 in AGH_NOCRT. This may alter the interactions between the AC and the Benguela Current. As pointed out by e.g., [START_REF] Penven | A numerical study of the southern Benguela circulation with an application to fish recruitment[END_REF], in both simulations and AVISO, the currents are weak on the Agulhas Bank.

From AGH_NOCRT to AGH_CRT some other biases are reduced, as for example the too

At the Mesoscale:

An "Eddy Killer"

A Dampening of the Mesoscale Activity

Here, I will mainly focus on the case of the U.S. West coast (Renault et al., 2016d), although I will also illustrate the eddy killing mechanism for the the North Atlantic Basin and the Greater Agulhas where similar results are found (Renault et al., 2016c(Renault et al., , 2017b)).

The surface Eddy Kinetic Energy (EKE) from the U.S. West Coast experiments is estimated using the daily surface current perturbations. The mean surface EKE and the temporal evolution of US West coast domain-average are depicted in Fig. 2.5. With good From US_NOCRT to US_CRTF, the EKE is reduced by 55%, whereas from US_NOCRT to US_CRT, the EKE is reduced by 40%. Figure from Renault et al. (2016d) agreement to the literature [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF]Renault et al., 2016a), in all the experiments the EKE has larger values nearer to shore and exhibits a broad decay further offshore. US_NOCRT shows a relatively weak decay with high values of EKE offshore.

From US_NOCRT to US_CRTF (i.e., a forced simulation with current feedback), the EKE is reduced by 55%, and, in particular, is strongly reduced the offshore, improving the realism of the simulation (e.g., see Fig. 2 from Capet et al. 2008a). US_CRT, where the wind response is simulated by the atmospheric model, also reduces the surface EKE relative to

US_NOCRT, but only by 40%, which is in good agreement with [START_REF] Seo | Eddy-wind interaction in the California Current System: dynamics and impacts[END_REF]. The atmospheric response to the reduced wind work with current feedback leads to an increase in surface wind strength (See Chapter 4), hence the EKE reduction observed in US_CRTF is diminished. To my knowledge, this was the first time this phenomenon was documented.

Similar conclusions can be drawn using the depth-integrated EKE: from US_NOCRT to US_CRTF, it is reduced by 35%; whereas, from US_NOCRT to US_NOCRTF, it is reduced by only 27%. The exclusion of an atmospheric response in US_NOCRTF leads to an overestimation of the oceanic EKE reduction, both near-shore and offshore. The EKE reduction can be split into two processes: on one hand there is a surface stress adjustment that tends to reduce the EKE. On the other hand, there is also a wind adjustment that partly counteracts the surface stress reduction, thus partly re-energizing the EKE.

Energy Conversion and Large Scale Sink of Energy

A simplified EKE budget (See Chapter 1) is computed to diagnose which processes lead to the EKE reduction by the current feedback. For the U.S. West Coast, because of the weak mean dynamic of this system, the time-mean quantities and then F m K m are barely affected by the current feedback (about 1% change, not shown). (2003), the baroclinic instability and the eddy wind work are the main sources of EKE, and they have higher values in the near-shore region. Note here, that K m K e is a secondary term. The wind work is also stronger in those simulations than in [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF], which can be attributed to the poor quality of the wind used in [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF] (i.e., Comprehensive Ocean-Atmosphere Data Set, COADS): it is monthly, and in particular it does not resolve the high frequency wind forcing (hourly here, which excites inertial currents), nor resolve the slackening of the winds near the coast ("drop-off", e.g., Renault et al. 2016a). The COADS wind stress forcing induces levels of EKE that are too low. As in [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF], in the nearshore region, a coastal band of about 80 km width is marked by a large values of F e K e . In all the experiment the wind perturbations induce an offshore Ekman surface current and an oceanic coastal jet (e.g., Renault et al. 2009) that flows partially in the same direction as the wind, inducing a positive F e K e . Also offshore, the Ekman surface current is partly in the direction of the wind with a generally positive F e K e .

The main effect of the current feedback is a reduction of F e K e in both the near-shore and offshore regions (Figs. 2.6 and2.7). The oceanic surface currents can be split into their geostrophic and ageostrophic parts (see Chapter 1) and F e K e can in turn be split into its geostrophic (F e K eg ) and ageostrophic (F e K ea ). Figure 2.8 shows F e K eg from US_NOCRT and US_CRT, and Fig. 2.7c shows the cross-shore profile of F e K eg from US_NOCRT, US_CRTF, US_CRT. In all the experiments, the offshore positive F e K e is essentially due

to F e K ea (more than 95%); whereas, nearshore F e K ea accounts for only 37% of F e K e .

The induced current feedback reduction of F e K e mainly acts through the geostrophic currents. Offshore, the current-induced reduction of F e K e is due to two different mechanisms: 1) a slight reduction of its ageostrophic part F e K ea (3%; Fig. 2.7), which is explained by changes in Ekman induced surface current, and 2) a sink of energy through its geostrophic part F e K eg (actual negative values of F e K eg ). In that sense the current feedback acts as an "eddy killer".

Figure 2.9 illustrates the geostrophic sink through F e K eg for an anticyclonic eddy with a southward uniform wind blowing up over such an eddy. In US_NOCRT, over such an eddy, F e K eg is equal to zero. Indeed, there is a positive F e K eg on the eastern branch and a negative F e K eg on the western branch, with a uniform wind; the net F e K eg is zero.

In US_CRTF the wind is still uniform in that it does not react to the current feedback.

However, the eastern branch has currents moving in the same direction as the wind, and hence has a reduced surface stress,

τ = C d ρ a (U a -U o ) 2 < C d ρ a (U a ) 2 (C d is the drag coefficient).
The western branch has currents moving against the wind, and hence has

an increased surface stress, τ = C d ρ a (U a -U o ) 2 > C d ρ a U 2 a .
As a result, the positive (negative) part of F e K eg is reduced (increased), and the net F e K eg becomes negative, deflecting energy from the ocean to the atmosphere. In US_CRT the current feedback not only acts on the surface stress but also on the atmosphere and, in particular, on the wind.

Due to local changes in the surface stress, the wind can locally accelerate or decelerate.

The wind response dampens the efficiency of the F e K eg sink, explaining the dampening of the offshore EKE reduction from US_CRTF to US_CRT shown in Fig. 2.5. Indeed, on the eastern branch of the eddy, there is less friction, the wind can accelerate, increasing the relative wind and hence increasing F e K eg . On the western branch there is more friction, which leads to a decrease in the wind and hence to a less negative F e K eg . The net F e K eg in US_CRT is still negative but less than US_CRTF; the atmospheric response tends to re-energize the ocean.

In the coastal band 80 km in width, there is a reduction of energy input through F e K eg .

As for the offshore region, the presence of eddies weakens the wind work. However, the wind perturbations induce an oceanic geostrophic coastal jet that blows partially the same direction as the wind. Hence, the relative wind U = U a -U o taken into account to estimate the surface stress in US_CRTF and US_CRT is weaker than the absolute wind U a used in US_NOCRT to estimate the stress. As a result, the stress perturbations are reduced in US_CRTF and US_CRT in respect to US_NOCRT, thus reducing F e K eg (Fig. 2.10). In US_CRT, as for the offshore region, the atmospheric response dampens the current-induced surface stress reduction by changing the wind (Fig. 2.9 and . 2.10).

More generally, at the mesoscale, the current feedback induces large scale sinks of energy everywhere over the whole Ocean (e.g., Renault et al. (2016cRenault et al. ( , 2017b,a),a). The larger the EKE, the larger the sink of energy. The efficiency of the eddy killing process will be discussed in Chapter 4). In the past decades, supercomputers and improved numerical techniques have seen the emergence of regional coupled models, and a growing interest in fine-scale air-sea interaction. However, in the recent eddy-rich simulations, the eddy energy is excessive, to the point that spurious dissipation is needed to improve US C RTF). And (c) a fully coupled simulation, ı, that has the current feedback in the surface stress estimate and the atmospheric response (e.g., US C RT). In US N OCRT (i.e., simulations without current feedback), the net F e K e is equal to zero. In US C RTF (i.e., simulations with current feedback to the surface stress), over an eddy, the amount of positive wind work (F e K e ) is reduced, and the amount of negative F e K e becomes more negative. As a result, the net F e K e becomes negative, deflecting energy out of the eddy into the atmosphere. In a fully coupled model (US C RT), the atmospheric response dampens the sink of F e K e by increasing the positive F e K e and decreasing the negative F e K e ; the net F e K e remains negative. The current feedback induces a positive (negative) stress curl (wind curl) in the eddy's center. Figure from Renault et al. (2016d). A simulation that takes into account the current feedback in the estimation of the surface stress but neglects the atmospheric response (e.g., US C RTF). And (c) A fully coupled simulation, i.e., that has the current feedback into the stress estimate and the atmospheric response (e.g., US C RT).

The green, black, and blue arrows represent the wind, surface stress, and oceanic surface current, respectively. The red shade represents the induced F e K e (positive in all cases). The wind induces an oceanic coastal geostrophic jet that is partially in the same as direction the wind, inducing a positive F e K e . From US N OCRT to US C RTF, the reduction of the stress induces, in turn, a weakening of F e K e . From US C RTF to US C RT, the wind accelerates, increasing the surface stress and hence F e K e and the oceanic coastal geostrophic jet. Figure from Renault et al. (2016d). WBC representation. A simple numerical trick was to apply diffusive numerical scheme to dissipate the excessive energy. In my recent papers and in the present manuscript, I demonstrate those simulations were missing a physical process: the eddy killing and the associated sink of energy from the mesoscale currents to the atmosphere. Those sinks of energy are crucial to represent in the ocean energy budget as they cause a dampening of the mesoscale activity by: 27% for the North Atlantic Basin, 25% for the Agulhas Current, and ≈ 35% over the whole ocean (Jullien et al., 2018). CFB 2.11 and 2.12 illustrates the sink of energy for the Greater Agulhas Current System and globally from the observations. The larger the EKE, the larger the sink of energy. An eddy-rich simulation without current does not reproduce the negative F e K eg (see Figure 2.11), and, thus, overestimates the mesoscale activity.

At the Submesoscale: A Catalizer but Still a Killer, the case of the California Current System

Here, I will focus on the submesoscale effect of the current feedback using the California Current System (CCS), where I carried out, as detailed hereafter, submesoscale permitting coupled simulations. At first, I was expecting to observe a very large dampening of the submesoscale activity under two main assumptions: 1) The reduction of the mesoscale activity should reduce the Mesoscale Available Potential Energy (APE) and, thus, the submesoscale generation by baroclinic instability. 2) As for the mesoscale, the surface stress anomalies induced by the submesoscale currents should create a sink of energy from the submesoscale currents to the atmosphere, and, thus, a dampening of the submesoscale currents. However, as detailed hereafter and in a paper published in Nature Scientific Report (Renault et al., 2018b), the story is a bit more complicated, and, thus, interesting.

The CCS is also under a strong influence of the submesoscale activity (Capet et al., 2008c,d,e). Oceanic submesoscale currents (SMCs) occur on an intermediate scale on the order of 0.1 -10 km horizontally, i.e., smaller than the mesoscale currents that are well known as the primary reservoir of kinetic energy in the ocean. SMCs typically occur at the oceanic surface and bottom, and emerge from various mechanisms such as frontal instabilities, frontogenesis, or topographic wakes [START_REF] Mahadevan | An analysis of mechanisms for submesoscale vertical motion at ocean fronts[END_REF]Capet et al., 2008c,d,e;[START_REF] Thomas | Submesoscale processes and dynamics[END_REF][START_REF] Mcwilliams | Submesoscale currents in the ocean[END_REF]Srinivasan et al., tted). SMCs can provide a major route of energy dissipation [START_REF] Mcwilliams | From stirring to mixing of momentum: cascades from balanced flows to dissipation in the oceanic interior[END_REF][START_REF] Gula | Topographic generation of submesoscale centrifugal instability and energy dissipation[END_REF].

By inducing large vertical velocities, they also lead to significant vertical eddy fluxes of materials with an important influence on ecosystems (Capet et al., 2008b;[START_REF] Lévy | New production stimulated by highfrequency winds in a turbulent mesoscale eddy field[END_REF][START_REF] Lévy | Bringing physics to life at the submesoscale[END_REF].

As presented in this Chapter, air-sea interactions have a strong influence on the mesoscale activity and on the primary production of the CCS in particular during the upwelling season [START_REF] Perlin | Coastal atmospheric circulation around an idealized cape during wind-driven upwelling studied from a coupled oceanatmosphere model[END_REF][START_REF] Boé | What shapes mesoscale wind anomalies in coastal upwelling zones?[END_REF]Renault et al., 2016a;[START_REF] Seo | Eddy-wind interaction in the California Current System: dynamics and impacts[END_REF]Renault et al., 2016d). As a brief reminder, the mesoscale Thermal FeedBack (TFB) can influence the wind drop-off and, thus, the generation of eddies by baroclinic instability [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF]Renault et al., 2016b). By generating fine scale wind curl anomalies, the TFB also affects eddy propagation [START_REF] Seo | Eddy-wind interaction in the California Current System: dynamics and impacts[END_REF] but does directly dampens the eddies (Renault et al., 2017b). The surface current effect on the atmosphere (the Current FeedBack, CFB) systematically induces fine-scale structures in the surface stress. [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF]; [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF] In contrast with the TFB, these stress anomalies drastically dampens the mesoscale activity [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF][START_REF] Dewar | Some effects of the wind on rings[END_REF]; Dawe and Thomp- son, 2006;[START_REF] Hughes | Wind work on the geostrophic ocean circulation: An observational study of the effect of small scales in the wind stress[END_REF][START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF][START_REF] Small | Damping of tropical instability waves caused by the action of surface currents on stress[END_REF]Renault et al., 2016d), by 40% for the CCS [START_REF] Seo | Eddy-wind interaction in the California Current System: dynamics and impacts[END_REF]Renault et al., 2016d). For the CCS, the eddy dampening is mainly driven by an "eddy killing" effect, i.e., a sink of energy from the oceanic geostrophic currents to the atmosphere [START_REF] Xu | Subtleties in forcing eddy resolving ocean models with satellite wind data[END_REF][START_REF] Hughes | Wind work on the geostrophic ocean circulation: An observational study of the effect of small scales in the wind stress[END_REF]Renault et al., 2016dRenault et al., , 2017a)). The resulting coupling coefficient between current vorticity and surface stress curl (s τ [N s m -3 ]) expresses that sink of eddy energy that represents a source of atmospheric energy. From a mechanistic point of view, the sink of energy is associated with Ekman pumping vertical velocities in the ocean induced by the surface stress gradients. This additional Ekman pumping, which does not significantly affect the mesoscale baroclinic instability, can be interpreted as the mechanism for weakening an eddy [START_REF] Dewar | Some effects of the wind on rings[END_REF][START_REF] Small | Damping of tropical instability waves caused by the action of surface currents on stress[END_REF][START_REF] Gaube | Satellite observations of mesoscale eddy-induced Ekman pumping[END_REF]. So far, relatively little is known about air-sea coupling at the submesoscale because of computational costs and measurement limitations. In particular, it is not yet known to what extent the CFB might dampen the SMCs. In Renault et al. (2018b), the Regional Oceanic Modeling System (ROMS [START_REF] Shchepetkin | The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model[END_REF] in its Coastal and Regional Ocean COmmunity (CROCO) version [START_REF] Debreu | Two-way nesting in splitexplicit ocean models: Algorithms, implementation and validation[END_REF] is an accommodation with its greater computational cost. We run two simulations, a control one where both TFB and CFB are taken into account (CTRL500 simulation) and one where only the TFB is considered (NOCRT500 simulation). The focus of this study is on the characterization of the CFB effect on the SMCs variability during the upwelling season in the CCS. Specifically, we aim to answer to the following two main questions: (i) What is the effect of the CFB on the SMCs during the Upwelling season ? (ii) What are the main related processes ? Only a summer period corresponding to the upwelling season is considered, which is enough to obtain robust SMCs statistics, at least for the considered season [START_REF] Gula | Topographic generation of submesoscale centrifugal instability and energy dissipation[END_REF][START_REF] Barkan | Submesoscale Dynamics in the Northern Gulf of Mexico. Part I: Regional and Seasonal Characterization, and the Role of River Outflow[END_REF].

Dampening of the Submesoscale Activity

The surface Submesoscale Kinetic Energy (SKE) is a measure of the intensity of SMC activity. The SMCs are computed by applying a five-point operator with a 12-km smoothing length and a 2-day smoothing interval to the currents in the simulations (Capet et al., 2008b). The CFB induces a dampening of the SKE by ≈ 17% ± 2% from CTRL500 to NOCRT500 (the errorbar is obtained using a bootstrap method: the SKE reduction is computed 10,000 times using random samples from the distribution). This dampening is furthermore confirmed by analyzing the surface Kinetic Energy (KE) spectrum (Fig. m 2 s -2 to 2.04 × 10 -9 m 2 s -2 (i.e., by 13%).

The dampening induced by the CFB is weaker at the submesoscale than at the mesoscale (NB, the mesoscale KE dampening is ≈ 40% (Renault et al., 2016d)). To explain it, following citecapet2008c and [START_REF] Marchesiello | Submesoscale dynamics in tropical instability waves[END_REF], a spectral decomposition of the KE balance for the Primitive Equation with respect to horizontal wavenumber is computed for both simulations over the first 100 m (see Chapter 1 and Fig. 2.15). At the submesoscale, the KE budget is dominated by an injection of energy by baroclinic conversion (C,i.e., a conversion of potential to kinetic energy due to baroclinic instability and frontogenesis) that is compensated by dissipation (V, which corresponds to the effect of the wind-work (FK = ø • u) and vertical mixing work). These two dominant terms are the most impacted by the CFB. V is enhanced by ≈ 10%, while surprisingly there is more injection of energy by baroclinic conversion (C, ≈ 6% larger in CTRL500 than in NOCRT500). The nonzero tendency rate (T) is related to seasonal variability (only 3 months of simulations are used) and is reduced by ≈ 19% from CTRL500 to NOCRT500.

A Submesoscale Sink of Energy

To express the sink of ocean energy at the SMCs induced by the CFB, the coupling coefficient s τ is estimated at the submesoscale over the whole period (3 months) using daily means. Surprisingly, when ignoring the CFB, we get s τ = 0.2 × 10 -2 N s m 2 , which implies an energization of the SMCs. Such an energization is not present at the mesoscale and is likely the indirect effect of the TFB on the wind at the submesoscale because the thermal signature arises through correlations with the SMCs even when the CFB is not included in the model. When the CFB is included, it overwhelms the TFB In CTRL500, a negative linear relationship is found: s τ = -0.4 × 10 -2 N s m 2 (Fig. 2.16a). For the CCS, at the submesoscale s τ is weaker than at the mesoscale for two principal reasons: (1) s τ at the submesoscale does not allow to disentangle the CFB effect on the surface stress from that due to the TFB although we can do so at the mesoscale (s τ ≈ 0), so, the TFB effect in s τ partially counteracts the CFB; and (2) the estimation of s τ at the submesoscale is complicated by the obscuring effect of other processes, e.g., the presence of atmospheric inertia gravity waves that have similar spatial frequencies than the SMCS. To illustrate it, s τ is also estimated using 6-hours snapshots; in this case s τ = -0.2 × 10 -2 N s m 2 is smaller because inertial gravity waves are not filtered out. The TFB is present in both NOCRT500 and CTRL500, but s τ is not a good metric to characterize it. ONeill et al. An energy route induced by the CFB should be present at the submesoscale due to the negative s τ in CTRL500. The submesoscale wind-work (F s K s [m 3 s -3 ]) can be defined as:

F s K s = 1 ρ 0 (τ x u o + τ y v o ) , (2.1)
where prime denotes the submesoscale part of the signal (see Chapter 1), the overbar is the mean over the summer period, ρ 0 is the oceanic surface density, τ x and τ y are the zonal and meridional surface stresses, and u o and v o are the zonal and meridional surface currents. F s K s expresses the exchange of energy between the SMCs and the atmosphere. CTRL500 explains the difference of V (averaged over 100 m depth) in Fig. 2.15, confirming its primary role in dampening the SMCs.

A Catalizer of Submesoscale Baroclinic Instability

The increase of C that partly counteracts the SMCs dampening by submesoscale windwork is less straightforward to explain. Indeed, consistent with a reduction of the SMCs, both vertical velocities and b are reduced in CTRL500 with respect to NOCRT500, consistent with a reduction of the SMCs. The increase of C could have been explained by a larger mesoscale Available Potential Energy (APE) reservoir available to energize SMCs.

However, from CTRL500 to NOCRT500, the APE is reduced by roughly 8% with the CFB (not shown), which is consistent with a reduction of the mesoscale activity. The reduction of the APE is mechanically explained by the dampening of the mesoscale activity, which in turn causes a weakening of the mesoscale buoyancy horizontal gradients. Hence, the energization of SMCs due to submesoscale baroclinic instability should be weaker when including the CFB. However, the baroclinic conversion can also include effects related to Ekman pumping velocities.

In CTRL500, w τ induced by the CFB is responsible of the enhanced V and the resulting sink of energy [START_REF] Gaube | Satellite observations of mesoscale eddy-induced Ekman pumping[END_REF]Renault et al., 2016d) but has also positive correlations with the SMCs and the buoyancy fronts. w τ may therefore cause an additional injection of energy by baroclinic conversion, which is not significantly the case at the mesoscale. The wave-number spectrum of baroclinic conversion induced by w τ (i.e., C τ , co-spectrum of w τ and b) is computed for NOCRT500 and CTRL500. Without CFB, at the submesoscale, C τ is slightly negative. With CFB, C τ becomes much larger and even larger than the wind-work spectrum when taking its total contribution over 100 m. depth (Fig. 2.16d,e).

For the CCS, the potential reduction of C due to weaker mesoscale APE is overwhelmed by the effect of w τ , explaining the larger injection of energy in CTRL500 with respect to NOCRT500. It also explains why the SMCs are reduced by 17% only, which is much weaker than the reduction of the mesoscale activity (≈ 40%): Over the CCS, the CFB induces a sink of energy from the SMCs to the atmosphere that is partly counteracted by an enhancement of the baroclinic conversion.

Discussion

In this study, we assess the impact of the Current FeedBack (CFB) on Submesoscale Currents (SMCs) using high-resolution ocean-atmosphere coupled models carried out over the California Current System (CCS) during the summer. We show that the main effect of the CFB is to cause a dampening of the Submesoscale Kinetic Energy (SKE) by roughly 17%. As at the mesoscale, the CFB induces a sink of energy from SMCs to the atmosphere that also involves additional Ekman pumping in the ocean (w τ ). The reduction of the mesoscale activity causes a weakening of the APE; however, the injection of energy by baroclinic conversion is not reduced, as might be expected, but rather enhanced. At the submesoscale, over the California Upwelling System, the coupling coefficient between SMC vorticity and surface stress (s τ ) is positive in a simulation that considers only TFB, which is not expected at the mesoscale: a simulation that neglects the CFB has a s τ ≈ 0. It further induces a positive submesoscale wind-work, and, thus, a slight energization of the SMCs by the atmosphere. The positiveness of s τ can be explained by the TFB that induces submesoscale surface stress anomalies that are to some extent coherent with the SMCs. However, the positiveness of s τ and the resulting energization of the SMCs is overwhelmed by the CFB effect, resulting in a negative s τ and a sink of energy from SMCs to the atmosphere. Future studies should aim at better understanding the atmospheric response to the TFB and CFB. We also show that the effect of the TFB effect on the wind is the same with or without CFB. The TFB at the submesoscale is expected to have an impact on the turbulent heat fluxes. At the mesoscale this impact is important and modulates western boundary currents [START_REF] Ma | Western boundary currents regulated by interaction between ocean eddies and the atmosphere[END_REF][START_REF] Seo | Distinct Influence of Air-Sea Interactions Mediated by Mesoscale Sea Surface Temperature and Surface Current in the Arabian Sea[END_REF] and eddy propagation [START_REF] Seo | Distinct Influence of Air-Sea Interactions Mediated by Mesoscale Sea Surface Temperature and Surface Current in the Arabian Sea[END_REF]. The TFB effect at the submesoscale should be studied using a similar approach as Seo (2017), i.e., by smoothing the SST sent to the atmospheric model by the ocean model; it may have an effect on the baroclinic conversion.

The approach used in this study has some limitations. Both TFB and CFB are considered; however, the oceanic surface waves that are neglected here (by use of the bulk formula for stress) can have other feedbacks with the ocean and the atmosphere. In particular, the Stokes vortex force [START_REF] Craik | A rational model for Langmuir circulations[END_REF]) can directly impact SMCs, and the loss of momentum flux and energy due to wave generation [START_REF] Janssen | On the interaction of wind and waves[END_REF] can alter the exchange of energy between SMCs and the atmosphere and thus the intensity of the SMCs. In addition, the bulk formula used in this study [START_REF] Fairall | Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm[END_REF] may not be accurate at the submesoscale because it was developed mainly with attention to larger scales. Overall, the results presented here are only valid for the CCS during the upwelling season. The CFB to the atmosphere should have an influence on the SMCs ev-erywhere in the world ocean and for other time periods; however, the SMCs could have different local responses. For the CCS, during the upwelling season, the main drivers that explain the alteration of the SMCs variability are the mixed-layer baroclinic conversion and the negative submesoscale wind-work. During the non-upwelling season the wind is weaker than during the upwelling season and the SMCs has roughly the same intensity (Gula, personal communication). As s τ depends on the wind (Renault et al., 2017a), on one hand, this should weaken the sink energy. On the other hand, the induced Ekman pumping velocities should also be diminished, reducing the additional baroclinic instability. In other regions, the dampening of the SMCs could cause a reduction in the density restratification process caused by the submesoscale [START_REF] Fox-Kemper | Parameterization of mixed layer eddies. Part I: Theory and diagnosis[END_REF], thus further induce a deepening of the mixed layer; this might counteract the reduction of the mesoscale APE by the weakening of the mesoscale buoyancy horizontal gradients. Near western boundary currents, as the Gulf Stream or the Agulhas Current, the SMCs can be generated by both mixed-layer baroclinic and barotropic instabilities [START_REF] Gula | Submesoscale cold filaments in the Gulf Stream[END_REF].

The CFB also causes a slow-down of the western boundary currents (Renault et al., 2016c(Renault et al., , 2017b) and a reduction of the mean wind-work. It could in turn reduce the submesoscale activity generated by baroclinic conversion from the mesoscale eddies and boundary currents. Futures studies are needed for the SMC response to the CFB in other regions and other or longer time-period.

Conclusion of the Chapter

Using oceanic and atmospheric coupled simulations, we assess how the current feedback to the atmosphere modulates the transfer of energy between the atmosphere and the ocean (wind work), and how it alters the oceanic circulation, including the large scale, the mesoscale, and also the submesoscale. My results on the modulation of the wind work by the current feedback from my different papers can be compared. For the Agulhas Current, the current feedback attenuates the mean transfer of energy from the atmosphere to the ocean (mean wind work) by 12%. This is less than the weakening for the north Atlantic (Renault et al. 2016c, 30%) to the current vorticity that deflects energy from the geostrophic current into the atmosphere and dampens eddies. It induces a mean pathway of energy from the ocean to the atmosphere over all the AC. As a result, the EKE is drastically reduced by 25% over the whole domain. The deflection of energy can be between two and three times larger over the Agulhas Basin region and the Gulf Stream compared to the U.S. West Coast (Renault et al., 2016d,c). There is a strong correlation between eddy windwork and EKE: the larger the EKE is, the larger the sink of energy is. Note, the mean wind work could be further more reduced by including the full Indian Ocean Gyre in the Greater Agulhas domain.

As previously shown, this could slow down the mean circulation, reduce the mean wind work and the generation of Natal Pulses over the Madagascar Channel by barotropic conversion of energy from mean to eddy, and, thus, diminish furthermore the EKE.

I also assessed the impact of the current feedback on Submesoscale Currents (SMCs) using high-resolution ocean-atmosphere coupled models carried out over the Central California region during the summer. I demonstrated the main effect of the current feedback is to cause a dampening of the Submesoscale Kinetic Energy (SKE) by roughly 17%. As at the mesoscale, the current feedback induces a sink of energy from SMCs to the atmosphere that can also involves additional Ekman pumping in the ocean (w τ ). The reduction of the mesoscale activity causes a weakening of the APE; however, the injection of energy by baroclinic conversion is not reduced, as might be expected, but rather enhanced. The Near western boundary currents, as the Gulf Stream or the Agulhas Current, the SMCs can be generated by both mixed-layer baroclinic and barotropic instabilities [START_REF] Gula | Submesoscale cold filaments in the Gulf Stream[END_REF]. The current feedback also causes a slow-down of the western boundary currents (Renault et al., 2016c(Renault et al., , 2017b) and a reduction of the mean wind-work. This could in turn reduce the submesoscale activity generated by baroclinic conversion from the mesoscale eddies and boundary currents. Futures studies are needed for the SMC response to the current feedback in other regions.

The current feedback is crucial to represent in numerical model, as it partly determines the large-scale, mesoscale, and submesoscale circulations. It reduces the mean input of energy from the atmosphere to the ocean, and induces sink of energy from mesoscale and submesoscale currents to the atmosphere. However, in the next chapter, I will demonstrate the eddy killing effect has an upscaling effect that is crucial to represent in numerical models as it reduces the eddy-mean flow interactions and, thus, the Western Boundary Currents Dynamic.

Chapter 3

Control of the Western Boundary

Currents by the Current Feedback There are still major gaps in our knowledge of ocean dynamics, despite numerous international programs of observation and modeling. The separation of WBCs was associated early on with strong bathymetry-induced inertial dynamics, with some control (for the GS) from counterflowing deep western boundary currents [START_REF] Spall | Dynamics of the Gulf Stream/ Deep Western Boundary Current crossover[END_REF]. More recently, emblematic features of WBCs appeared tied in ocean models to the resolution of mesoscale activity through eddy-mean flow interaction [START_REF] Mcwilliams | The nature and consequences of oceanic eddies[END_REF] and a spatial resolution of 1/10 o was suggested as a minimum for properly representing the Gulf Stream separation [START_REF] Bryan | Resolution convergence and sensitivity studies with North Atlantic circulation models. Part I: The western boundary current system[END_REF][START_REF] Chassignet | Gulf Stream separation in numerical ocean models[END_REF]. Therefore, large improvements were expected from the increase of computing power and grid resolution. If this was verified to an extent, the simulated eddy energy has now become excessive in WBCs. Specifically, according to [START_REF] Özgökmen | Dynamics of two-dimensional turbulent bottom gravity currents[END_REF], an excess of mesoscale activity at the separation point leads to unrealistic WBC separation from the coastline. An energy sink is thus needed in high-resolution, mesoscale resolving models.

This can be provided by dissipation terms used as turbulence closure model (e.g., [START_REF] Bryan | On the midlatitude circulation in a high-resolution model of the North Atlantic[END_REF][START_REF] Bryan | Resolution convergence and sensitivity studies with North Atlantic circulation models. Part I: The western boundary current system[END_REF][START_REF] Chassignet | Viscosity parameterization and the Gulf Stream separation[END_REF][START_REF] Chassignet | Gulf Stream separation in numerical ocean models[END_REF][START_REF] Chassignet | Impact of horizontal resolution (1/12 to 1/50) on gulf stream separation, penetration, and variability[END_REF]). However, this approach is inconsistent with geostrophic turbulence, which is characterized by an inverse cascade of energy towards larger scale. A direct energy transfer toward dissipation is still possible due to loss of balance at submesoscale (see [START_REF] Gula | Topographic generation of submesoscale centrifugal instability and energy dissipation[END_REF] for the GS), but theoretically limited.

In parallel to improved resolution and more accurate numerical techniques, supercomputers also favored the emergence of regional coupled models, and a growing interest in fine-scale air-sea interactions. At first, attention was essentially given to the feedback of sea surface temperature (SST) on the air flow (e.g., [START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF][START_REF] Minobe | Influence of the Gulf Stream on the troposphere[END_REF][START_REF] Ma | Western boundary currents regulated by interaction between ocean eddies and the atmosphere[END_REF]. Progressively, the issue of stress interaction has emerged, i.e., the feedback effect of surface currents on the stress and overlying winds (process called current feedback or top drag; see [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF][START_REF] Dewar | Some effects of the wind on rings[END_REF][START_REF] Luo | Reducing climatology bias in an ocean-atmosphere CGCM with improved coupling physics[END_REF][START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF][START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF][START_REF] Mcclean | A prototype two-decade fully-coupled fine-resolution CCSM simulation[END_REF]Renault et al. 2016d). Quite unexpectedly, the latter happens to correct some long-standing modeling biases in eddy-mean flow interaction, providing an undeniable energy sink mechanism with no need for large internal dissipation.

As shown in the previous Chapter (Chapter 2), there are two main effects on the ocean circulation: a large-scale and a local effect. At the large-scale, neglecting the current feedback leads to an overestimation of the energy input from the atmosphere to the ocean (e.g., [START_REF] Scott | An update on the wind power input to the surface geostrophic flow of the World Ocean[END_REF]Renault et al. 2016c), e.g., a circulation slowdown of the GS and Agulhas Current [START_REF] Pacanowski | Effect of equatorial currents on surface stress[END_REF][START_REF] Luo | Reducing climatology bias in an ocean-atmosphere CGCM with improved coupling physics[END_REF]Renault et al., 2016cRenault et al., , 2017b)). The local effect was less intuitive and was only recently confirmed by the advent of "eddy-rich" coupled models. It consists of a drastic reduction (by roughly 30%) of oceanic mesoscale activity (e.g., [START_REF] Dewar | Some effects of the wind on rings[END_REF]; [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF]; [START_REF] Dawe | Effect of ocean surface currents on wind stress, heat flux, and wind power input to the ocean[END_REF]; [START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF]; Renault et al. (2016dRenault et al. ( ,c, 2017a))). The sink of mesoscale energy to the atmosphere is generally ignored in WBC simulations. The excess mesoscale energy then feeds the large-scale circulation as part of eddy-mean flow interaction -the inverse energy cascade. Because mesoscale eddies contain the largest reservoir of oceanic energy, the inverse cascade operates a tight control on the general circulation and on the WBCs. Confirmation and quantification came about in two papers I published recently (Renault et al., 2016c(Renault et al., , 2017b)). As detailed in the next sections, the energy sink, or "eddy killing", controls important aspects of WBCs and largely corrects two long-lasting biases in oceanic models: the representation of the Agulhas Current retroflection and the GS separation and penetration in the North Atlantic Basin. In this Chapter, Sec. 3.1 illustrates the control of the GS by the current feedback, whereas Sec. 3.2 shows the case of the AC.

Sec. 3.4 concludes this chapter.

The Case of the Gulf Stream

The Gulf Stream (GS) is known to have a strong influence on the climate and the transport of heat from the tropics to middle and high latitudes. shown [START_REF] Spall | Dynamics of the Gulf Stream/ Deep Western Boundary Current crossover[END_REF], and a minimum resolution of 1/10 o (Bryan et al. 2007, Chassignet and[START_REF] Chassignet | Gulf Stream separation in numerical ocean models[END_REF]) is deemed to be required for proper separation dynamics.

GS_NOCRT, as the simulations in [START_REF] Schoonover | North Atlantic Barotropic Vorticity Balances in Numerical Models*[END_REF], is able to represent the GS separation at Cape Hatteras, however, it is characterized by the presence of a standing eddy making its separation convex. Additionally, the post separation region is characterized by a too large EKE (Figure 3.1) that induces a spatial spread of mean circulation (Figure 3.2) with respect to the observations. The current feedback strongly improves the GS separation and post separation characteristics. In GS_CRT, the GS has a concave separation at Cape Hatteras as in the observations (Fig. 3.2). The current feedback large scale and mesoscale (i.e., the eddy killing) effects are potentially the two main drivers that explain the stabilization of the GS path and separation. In Renault et al. (2016c), I demonstrate the eddy killing effect is the main driver of such a stabilization. From satellite observation, we know that the GS has a unique very stable mode of separation (Figure 3.2). By contrast, simulated eddies without the current feedback and the associated "eddy killing" effect are steadily advected along the current path, then detach and propagate back to the coast where they merge, causing standing eddies and a bimodal GS separation. With "eddy killing", eddy activity is more realistic and the GS representation is more stable and very similar to observations.

The Case of the Agulhas Current

The Agulhas Current (AC) is the western boundary current of the South Indian Ocean subtropical gyre (e.g., [START_REF] Lutjeharms | The Agulhas current[END_REF], and it is known to have a strong influence on the climate and on transports of heat and salt from the Indian Ocean to the Atlantic Ocean and the Southern Ocean. The sources of the AC are from the Mozambique Channel and from south of Madagascar; it flows along the southeastern coasts of Africa, transporting about 77 Sv (1 Sv = 10 6 m 3 s -3 ) [START_REF] Beal | Capturing the transport variability of a Western Boundary Jet: Results from the Agulhas Current Time-series experiment (ACT)*[END_REF] towards the south in a narrow band about 50 km wide with velocities often above 2 ms -1 (e.g., [START_REF] Boebel | Float experiment studies interocean exchanges at the tip of Africa[END_REF][START_REF] Lutjeharms | The Agulhas current[END_REF]). The AC is characterized by the presence of a retroflection at the south of the African continent, around 17 • E, where the flow turns back on itself to return to the Indian Ocean (Lutjeharms and Van Ballegooyen, 1988b).

Although regional models can simulate some properties of the AC [START_REF] Biastoch | Mesoscale perturbations control inter-ocean exchange south of Africa[END_REF][START_REF] Loveday | Decoupling of the Agulhas leakage from the Agulhas Current[END_REF], the oceanic mesoscale turbulence in the region is difficult to model satisfactorily, e.g., an AC retroflection further east (upstream) and Agulhas Rings in a straight line in the south Atlantic [START_REF] Lutjeharms | Modelling the Agulhas current system with FRAM (fine resolution antarctic model)[END_REF][START_REF] Maltrud | An eddy resolving global 1/10 ocean simulation[END_REF]Barnier et al., 2006;[START_REF] Thoppil | Energetics of a global ocean circulation model compared to observations[END_REF]. With the exception of regional models where specific treatments are applied (e.g., large smoothing of the bathymetry or large value of diffusivity in [START_REF] Biastoch | Mesoscale perturbations control inter-ocean exchange south of Africa[END_REF][START_REF] Loveday | Decoupling of the Agulhas leakage from the Agulhas Current[END_REF]), a large majority of simulation models have persistent biases in representing the AC retroflection. Those issues persists even with high-resolution models [START_REF] Thoppil | Energetics of a global ocean circulation model compared to observations[END_REF]. 1985) toward Port Elizabeth where they can die, merge, and/or recirculate. This process is thought to induce upstream retroflection of the AC (Lutjeharms and Van Ballegooyen, 1988a). The western standing eddy induces a southern location of the AC retroflection with respect to AVISO. AGH_CRT, the dampening of the EKE by negative F e K e (eddy killing) and also by the reduction of K m K e (that reduces the generation of the Natal Pulses)

Agulhas Retroflection

weakens the persistence of the two standing eddies, improving the realism of the AC mean path and its retroflection with respect to AVISO. In particular, the retroflection is shifted toward the north, improving its realism (See Fig. which merge near Port Elizabeth and cause a short-cut of the AC [START_REF] Biastoch | Mesoscale perturbations control inter-ocean exchange south of Africa[END_REF][START_REF] Rouault | New perspectives on Natal Pulses from satellite observations[END_REF]. It could also be due to eddies from the ARC, which detach and propagate westward [START_REF] Mcwilliams | Submesoscale, coherent vortices in the ocean[END_REF] toward Port Elizabeth where they can die, merge, and/or recirculate. The too strong mesoscale activity in AGH_NOCRT reinforces the eastern category (i.e., the upstream AC retroflection).

In AGH_CRT, the weakening of the mesoscale activity improves the representation of the AC retroflection, despite some persistent biases. The mean AC position is very close to the observations, around 15.3 • E but, as in NOAGH_CRT, it has a too large variability.

The current feedback in AGH_CRT dampens the EKE and, in particular, the Natal Pulses and their influence on the EKE over the Agulhas Basin. This diminishes the importance of the eastern retroflection regimes, allowing a shift toward the west of the retroflection distribution. Indeed, in AGH_CRT, the main regime of variability is the eastern retroflection that, as in NOAGH_CRT, also includes the Central retroflection detected from the observations (between 13 • E and 16 • E). The other western retroflection is centered at 6.5 • E and is slightly over-represented (4%). The remaining over-representation of the eastern retroflection is likely due to an overestimation of the EKE in AGH_CRT that may be the consequence of the biases in F m K mg , and too large a K m K e (Fig. 2.1 and 2.6). As shown by Renault et al. (2017b), this has further implications for the Agulhas Current

Leakage and water masses over the Benguela Upwelling System.

Reduction of the Eddy-Mean Flow Interactions

This is part of a study that has been recently accepted for publication in GRL (Renault et al., 2019a). In the ocean mesoscale energy feeds back to the large-scale circulation through eddy-mean flow interaction -the inverse energy cascade (e.g., Capet et al. 2008b;[START_REF] Lacasce | Surface quasigeostrophic solutions and baroclinic modes with exponential stratification[END_REF]Arbic et al. 2013). Because mesoscale eddies compose a huge reservoir of oceanic energy, the inverse cascade operates a tight control on the general circulation.

Stabilization of the GS and improvement of the AC retroflection may be explained by a reduction of the inverse energy cascade, as we now show. To quantify the transfer of energy, the spectral fluxes π of surface ocean geostrophic kinetic energy in the isotropic horizontal wavenumber k domain is estimated from the coupled simulations and from AVISO 1 gridded altimeter data [START_REF] Ducet | Global high-resolution mapping of ocean circulation from TOPEX/Poseidon and ERS-1 and-2[END_REF]. The analysis is done over a sub-region of GS and AC domains (Figure 3.6, see 1). From a wavelength of about 100 km, both forward and inverse energy transfers are identified by positive and negative lobes, respectively.

Following e.g., Arbic et al. (2013), the relative size of the forward and inverse cascades is Spectral energy fluxes can also be computed from satellite SSH data, which provides a validation for our analysis of WBC dynamics. However, AVISO has a coarse spatial Accounting for eddy killing effect and associated sink of energy in CFB simulations leads to better agreement with AVISO data.

Conclusion of the Chapter

We conclude that a poor representation of GS separation/penetration and AC retroflection position in uncoupled models can be explained by the missing eddy killing process.

Most research studies in the recent past have relied on dissipation processes to correct simulation biases, but only few improvements were reported on other missing dynamical processes. One relevant finding in the last two decades is the key role played by topographic steering in WBC dynamics [START_REF] Couvelard | Barotropic zonal jets induced by islands in the southwest Pacific[END_REF][START_REF] Gula | Gulf Stream dynamics along the southeastern US seaboard[END_REF], that goes far beyond the idealized representation of western boundaries as solid walls.

However, higher resolution and improved topographic treatment did not solve the energy budget issue because oceanic mesoscale energy was then produced in excess and requires an energy sink to stabilize and accurately position the mean current paths. In [START_REF] Chassignet | Impact of horizontal resolution (1/12 to 1/50) on gulf stream separation, penetration, and variability[END_REF], a subgrid-scale eddy viscosity is added to numerical hyperviscosity (used for selective damping of numerical dispersion generated by centered advection schemes, akin to the implicit diffusion part of the third-order upstream-biased advection scheme in CROCO; see Marchesiello et al. 2009). The added dissipation is rationalized by mesoscale damping processes that are not resolved by the model [START_REF] Chassignet | Viscosity parameterization and the Gulf Stream separation[END_REF]. It allows to produce a correct mean GS path with an uncoupled 1/50 • resolution HYCOM setup. However, even though the simulated mesoscale variability at the separation point (Cape Hatteras) compares favorably with AVISO data, there is still too large a spread of mesoscale activity after separation (Fig. 14 found that GS interaction with topography can generate submesoscale centrifugal instability and some amount of energy dissipation, but only near the continental slope. An interior route to dissipation associated with submesoscale instabilities at the ocean surface is also proposed [START_REF] Molemaker | Balanced and unbalanced routes to dissipation in an equilibrated Eady flow[END_REF]Capet et al., 2008b), but cannot account for large offshore dissipation past the separation point, where even numerical dissipation needed to damp numerical dispersion errors appears to be in excess [START_REF] Marchesiello | Submesoscale dynamics in tropical instability waves[END_REF][START_REF] Soufflet | On effective resolution in ocean models[END_REF]. While the route to dissipation in the ocean is being debated, mesoscale air-sea coupling offers a unambiguous physical process for the required sink of energy to achieve proper equilibrium in WBC systems and elsewhere.

The role of fine-scale ocean-atmosphere coupling modifies the usual conception of wind-driven currents. The wind is not just a large-scale energy source that initiates a turbulent cascade; it also interacts at fine scale and directly affects the entire oceanic spectrum. High-resolution coupled models have thus become essential tools that are now more easily accessible -at least regional models. Alternatively for uncoupled ocean models, new formalisms should be designed to account for atmospheric adjustments and provide accurate oceanic energy sink. A major step will then be expected in the representation of currents, water masses, overturning circulation, oceanic ventilation, carbon uptake, etc. In particular, the boosting effect of oceanic eddies on marine productivity in nutrient-poor regions should be revisited through the lenses of eddy-wind interaction, as initiated by [START_REF] Mcgillicuddy | Eddy/wind interactions stimulate extraordinary mid-ocean plankton blooms[END_REF]. Anticyclonic eddies could sustain primary production over long distances due to surface Ekman pumping induced by the same eddywind interaction that dampens the eddy energy. This effect is again missing in usual oceanic model simulations.

Overall, the results presented here call for a change of paradigm in our representation of the ocean interface. The uncoupled approach is no longer suitable for continued ocean model improvement, unless new formulations can be devised that better account for air-sea interactions. Those should replicate a partial re-energization of the ocean by winds that are modified by surface currents -avoiding redundant energy sink in uncoupled models if fully using Eq. ??. Different approaches are possible. One consists of correcting the relative wind using a current-wind coupling coefficient s w defined by (Renault et al., 2016d), or the surface stress using a current-stress coupling coefficient s τ defined by τ = τ a + s τ U o (Renault et al., 2017a); s w and s τ can be estimated from a coupled simulation although s τ can also be parameterized as a function of the large-scale wind. Yet another approach would be based on the coupling of a simple atmospheric boundary layer model (a slab model for the lower atmosphere; e.g., [START_REF] Lemarié | Toward an improved representation of air-sea interactions in high-resolution global oceanic forecasting systems[END_REF], in place of a full atmospheric model. In all cases, the results should be compared with fully coupled simulations, specifically looking at the sink of energy from eddy-wind interaction, and more generally at mesoscale activity and large scale currents.

U = U a -(1 -s w )U o
As shown in the previous chapters, the current feedback to the atmosphere has a large impact on the ocean dynamic. In Chapter 2, I briefly mentionned the atmospheric response to the current feedback causes a partial re-energization of the ocean. In this chapter, I will synthetize my work on that topic: In Sec. 4.1, the stress response to the current feedback is assessed from both observations and models. I will define a new coupling coefficient between surface current vorticity and surface stress curl. Section 4.2 addresses the corresponding wind adjustment and a coupling coefficient between surface current vorticity and wind curl will be defined and characterized. In Sec. 4.3, as an indirect effect of the current feedback on the atmosphere, the precipitation response will be addressed by focusing over the Agulhas Current. I will conclude this Chapter in in Sec. 4.4.

Coupling Coefficient between Current and Stress

The surface stress can be represented in a bulk formulae by using the difference of the wind relative to the current:

τ = ρ a C D (U a -U o )|U a -U o | , (4.1)
where τ is the surface stress, ρ a is the density of the air, C D is the drag coefficient, and U a and U o are the 10 m wind and the surface current, respectively. When neglecting the current feedback, under the same assumptions the stress is estimated as

τ a = ρ a C D U a |U a | . (4.2)
Following [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF]; [START_REF] Rooth | Air-sea boundary layer dynamics in the presence of mesoscale surface currents[END_REF]; [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF]

τ di f f ∼ - 3 2 ρ a C D |U a | U o . (4.3)
where U o represents the mesoscale oceanic currents. Recently, focusing on the U.S.

West coast with ocean-atmosphere coupled simulations, Renault et al. (2016d) show at mesoscale the surface stress response to the current feedback can also be expressed through a regression coefficient s τ as

τ di f f = s τ U o , (4.4)
Equating these two expressions gives a relation where s τ is a linear function of the wind:

s τ ∼ - 3 2 ρ a C D |U a | (4.5)
Assuming nominal values of the constants in (4.5) with a C D = 1.2 10 -3 and a ρ a = 1.225 kg m -3 :

s τ ∼ -2.20 10 -3 N m -4 s 2 |U a |. (4.6)
The use of derivatives of surface stress and currents allows to efficiently isolate the current feedback effect on the surface stress from the SST feedback (Renault et al., 2016d).

Similar to [START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF], the statistical relationship between surface stress curl and oceanic current vorticity is evaluated by bin-averaging the 1-month running means of the stress curl as a function of the 1-month running means of the oceanic current vorticity over the full simulated period for the three experiments. Bin sizes of 1 ms -1 per 100 km and 1 Nm -2 per 10 5 km are used for surface current vorticity and the stress curl, respectively. The large scale signal is removed using a high-pass Gaussian spatial filter with a 150 km cut-off. The analysis domain is 30 • N -45 • N and (150 km < d < 500 km), i.e., offshore of the wind drop-off region where the current feedback effects are partly masked by the orographic, coastline, and SST effects on the wind [START_REF] Perlin | Coastal atmospheric circulation around an idealized cape during wind-driven upwelling studied from a coupled oceanatmosphere model[END_REF]Renault et al., 2016b). smoothed (over 50 km) to diminish sampling noise due to the relatively short analysis period (9 years). The mesoscale surface currents systematically induce persistent surface stress anomalies everywhere (Fig. The linear relationship between wind magnitude and s τ is confirmed by analyzing the s τ global values in Fig. 5.1a and by comparing it to a mean 10m-wind map (not shown).

Regions characterized by a mean large wind have an strong imprint of the current on the surface stress, and, thus, have a large s τ . The primary dependence of s τ on the wind is furthermore corroborated by analyzing the statistical relationship between mean 10mwind and s τ . Global bin-averaged values of 10m-wind magnitude (bins of 0.1 m s -1 ) and s τ are computed over the whole period [START_REF] Penven | A numerical study of the southern Benguela circulation with an application to fish recruitment[END_REF]( -2008, Fig. 5.1b), Fig. 5.1b). They have a clear negative linear relationship (σ > 0.95 using a t-test) :

s τ = -2.5 10 -3 Nm -4 s 2 |U a | + 0.013 N m -3 s, (4.7)
The expression in (4.6) has implicit further dependencies in C D on U a and on wave age [START_REF] Janssen | Effect of atmospheric stability on the growth of surface gravity waves[END_REF][START_REF] Komen | Dynamics and modelling of ocean waves[END_REF][START_REF] Sullivan | Turbulent flow over water waves in the presence of stratification[END_REF] so that imperfections in the observational regression fit of (4.7) can partly be attributed to these other dependencies, to the θ approximation (see Renault et al. 2017a), and also to a possible partial re-energization of the eddies by the wind response to the current feedback (Renault et al., 2016d). Interestingly, a similar relationship has been found by ONeill et al.

(2012) for the SST coupling coefficient that also primarily depends on the mean wind distribution.

A predicted s τ is then computed in Fig. 5.1c using (4.7). The mean 10m-wind magnitude appears to be a fair predictor of s τ , indicating its primary role in determining its spatial variation. s τ is characterized by a seasonal cycle that is mainly driven by the 10mwind seasonal cycle (not shown). The surface stress response to the current feedback can have furthermore dependencies. For example, in (4.1), a second order term (because

U a >> U o ) can be derived as: ρ a C D U 2 o .
The secondary importance of this term is confirmed by the less obvious relationship that can be found between the logarithm of the EKE and s τ : the larger a log[EKE], the larger a s τ (not shown). However, the statistical relationship between EKE and s τ represents only s τ values between -0.8 10 -2 and -1.5 10 -2 N s m -3 and has a large spread. Additionally, as a second order effect of the current feedback, the wind response to the current feedback partially damps the surface stress changes and thus weakens s τ (Renault et al., 2016d). The wind response depends on the marine boundary layer height h: the shallower h, the larger a wind response (Renault et al., 2017b), and, thus, the weaker s τ . However, no significant relationship between the mean h from ERA interim [START_REF] Dee | The ERA-Interim reanalysis: Configuration and performance of the data assimilation system[END_REF] and s τ has been found.

In light of the coupling coefficient between the surface current and the surface stress s τ and eq. ( 4.4), a predicted F e K ep is estimated as the product of the seasonal values of s τ and EKE (Fig. 4.3b):

F e K ep = 2 ρ o s τ EKE (4.8)
The sink of energy from the geostrophic current to the atmosphere mainly depends on the EKE, however it is modulated by s τ : the more negative a s τ , the more efficient an eddy killing effect and, hence, larger a sink of eddy energy. s τ can be interpreted as a measure of the efficiency of the current feedback. Regions characterized by a weak EKE (e.g., center of North Pacific) may have a large s τ , but their sink of energy remain very weak. The WBC and in particular the ACC, characterized by both an important mesoscale activity and a large mean wind, are regions with the largest sink of energy. Eastern boundary currents are characterized by a weaker sink of energy than WBC because of their milder EKE.

The total predicted F e K ep away of the tropics is ≈ -48GW, which is much larger than an estimate based on Fig. 4.3a. This estimate can be interpreted as a direct measure of the transfer of energy from the mesoscale geostrophic currents to the atmosphere induced by the current feedback whereas an estimate based on a Reynolds decomposition does not capture only the atmospheric response to the current feedback but all kind of "eddy windwork" (e.g., wind-driven currents). F e K e can furthermore be estimated by considering the current and stress anomalies using a high-pass Gaussian spatial filter with a 250 km cut-off (see Chapter 1). This estimate is closer to the predicted F e K ep (not shown) and represents a total sink of energy away of the tropic by ≈ 70GW, confirming the difference between a Reynolds decomposition estimate of F e K e and the predicted F e K ep . F e K e estimated using a spatial filter is larger than the other F e K e estimates because 1) wind driven currents (that induces positive F e K e ) have a larger scale than the oceanic mesoscale and, thus, are not included when estimating the wind work using a spatial filter; and 2) the F e K e estimated using a spatial filter also includes the effect of strong currents (such as the Gulf Stream) on the surface stress that causes an additional sink of energy from the ocean The F e K e sink from the ocean to the atmosphere results in a slightly larger TKE in US_CRT compared to US_NOCRT. In the near-shore region there is a larger wind enhancement that is likely partly explained by the presence of the steady oceanic geostrophic jet that flows in the same direction as the wind. Figure from Renault et al. (2016d).

to the atmosphere.

Coupling Coefficient between Current and Wind

The oceanic surface currents partially drive the atmosphere. When coupling the atmosphere to the oceanic currents, the reduction in air-sea velocity difference reduces the stress acting on the wind and allows it to accelerate. Figure 4.4 depicts the mean crossshore profiles of surface wind Turbulent Kinetic Energy (TKE) at 30 • N and 45 • N. TKE is always larger in US_CRT than in US_NOCRT, which reflects the changes in surface stress. Interestingly, the nearshore region (d ≤ 80 km) has a higher TKE difference than the offshore region. This is likely partly explained by the presence of the steady oceanic geostrophic jet that flows in the same direction as the wind, reducing the surface stress near the coast.

Binned scatter-plots of 1-month running means of wind curl and surface current vorticity over the domain 30 • N -45 • N and (150 km < d < 500 km) are calculated for US_NOCRT and US_CRT. US N OCRT, as expected, does not have any significant relationship between wind curl and surface current vorticity (not shown). US_CRT has a clear linear relationship between them (Fig. 4.5a). A non-dimensional coupling coeffi-cient s w is defined from the slope of the linear regression estimated from the scatter-plot.

The positive s w indicates a positive forcing of the currents on the wind, a positive (negative) current vorticity inducing a positive (negative) wind curl. The wind changes are explained by the surface stress changes: a weaker surface stress allows the wind to accelerate. s w counteracts the effect expressed in s st and hence acts to reduce s st from US_CRTF to US C RT. The positive s w is also consistent with Fig. 2.9, the currents inducing a positive wind curl in the center of an anticyclonic eddy, which counteracts the current-induced negative surface stress curl. Fig. 4.5b depicts the vertical structure of the coupling coefficient s w . The current feedback mainly shapes the surface wind, however, its effect can be felt up to 300m. Finally, a spectral analysis reveals the current feedback mainly affects the wind at eddy-scale (but can be felt slightly over several hundreds of km.), and over the timescale between 30-days -1 and 300-days -1 (not shown). To our knowledge this is an entirely new phenomenon that has not previously been pointed out. Finally, although the wind changes have an important effect on the oceanic response, from the atmospheric point of view the changes are rather small. The Planetary Boundary Layer Height is not changed, nor the mean overlying circulation, clouds or the precipitation. For more dynamical regions we expect a larger large-scale effect. I also estimate s w over the Agulhas Current in Renault et al. (2017b) at each grid point using the fully coupled experiment (AGH_CRT) over the period 2000-2004, only the s w with a σ > 0.95 using a F-test is used. As in Renault et al. (2016d), the coastal band (150 km wide) is not taken into account because of the strong influence of the orography and coastline meandering on the wind that can hide the influence of the currents (Renault et al., 2016b). Figure 4.6a depicts the s w spatial distribution smoothed over 100 km. It shows s w is not constant and varies from 0.1 to 0.5 (Nondimensional). Figure 4.6b depicts the structure of the coupling coefficient s w over the Agulhas Return Current (similar behavior is found over other regions). There is a sharp vertical decay of the influence of the current on the wind: the current feedback mainly acts on the surface wind but consistent with Renault et al. (2016d); its effect can be felt up to 350 m. However, it remains weak with respect to the wind velocities (e.g., at 350m, a s w of 0.05 induces a wind response of 5 cm s -1 , which is weak compared to wind velocities of 15 m s -1 ). s w depends on the currents magnitude and on the background wind (Renault et al., 2016d;[START_REF] Gaube | Satellite observations of mesoscale eddy-induced Ekman pumping[END_REF]. It also depends on the Marine Boundary Layer Height. To highlight it, a binned scatterplot of the mean Marine Boundary Layer Height and s w is estimated over the whole domain using bins of 50m for the Marine Boundary Layer Height (Fig. 4.6c). It shows a clear linear relationship (σ > 0.95 using a f-test) between the Marine Boundary Layer Height and s w : a deeper Marine Boundary Layer induces a weaker s w . This is consistent with Fig. 10 from Renault et al. 2016d that shows the energy deflected from the ocean to the atmosphere by the current feedback that is distributed over the entire Marine Boundary Layer.

Indirect Effect on the Precipitation over the Agulhas Current

From an atmospheric point of view, the current feedback induced changes remain weak with respect to the wind velocities. However, the atmosphere can be influenced by indirect effects of the current feedback. As discussed in the previous section, from AGH_NOCRT to AGH_CRT, the SST over the AC retroflection and the southern Benguela ). s w is characterized by a complex spatial pattern that depends on the Marine Boundary Layer Height.

The deeper is the Marine Boundary Layer, the weaker is s w . The current feedback to the atmosphere mainly acts on the surface wind. Figure from Renault et al. (2017b).

Conclusion of the Chapter

The atmospheric response to the current feedback is crucial to represent in oceanic models as it induces a partial re-energization of the ocean. This response could be ignored under the assumption the wind anomalies induced by the current feedback are much weaker than the background wind, which is generally true, as e.g., a current of 1 m s -1 will cause a wind anomalie of roughly 0.3 m s -1 . However, such an assumption has been made during years to justify to ignore the whole current feedback. We clearly demonstrated this was not correct as it induces stress and wind curl that are persistent and collocalized right over the eddies or the mean currents. By ignoring the wind response, the weakening of the mean input of energy from the atmosphere to the ocean would be overestimated, resulting in a too weak a mean circulation. More importantly, the eddy killing effect would be too strong, causing too large a dampening of the mesoscale activity.

The substantial current feedback effect on the currents should change the paradigm of how to force an regional high resolution uncoupled oceanic model. However, regional models and even global reanalysis (NCEP or ERA) generally still ignore this feedback.

When forcing an ocean model with an atmospheric product that does not contain the atmospheric response to the current feedback (as e.g., NCEP but not as QuikSCAT), this effect could be incorporated by using in the bulk formulae the relative wind to the current (instead of the wind alone) but with a parameterization of the wind response that will partially re-energizes the ocean. As discussed in Chapter 6, in Renault et al. (2016d) and Renault et al. (2017b), I suggest two simple parameterizations of the atmospheric response to the current feedback that aim to mimic the wind coupled response in an uncoupled oceanic model. The test of those parameterization are part of my on-going research (see Chapter 6. Those results also raise the question on how to disentangle at the mesoscale the thermal feedback from the current feedback. I will try to answer to that question in the next chapter.

In the past decades, air-sea interactions at the oceanic mesoscale (i.e., scales of tens to hundreds of km and tens to hundreds of days, e.g., [START_REF] Wunsch | The global frequency-wavenumber spectrum of oceanic variability estimated from TOPEX/POSEIDON altimetric measurements[END_REF][START_REF] Stammer | Global characteristics of ocean variability estimated from regional TOPEX/POSEIDON altimeter measurements[END_REF][START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF][START_REF] Mcwilliams | The nature and consequences of oceanic eddies[END_REF] have received a growing interest from the scientific community [START_REF] Chelton | Coupled ocean-atmosphere interaction at oceanic mesoscales[END_REF] and have been shown to have a large influence on both wind and surface stress [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF][START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF][START_REF] Oneill | Covariability of surface wind and stress responses to sea surface temperature fronts[END_REF][START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF][START_REF] Gaube | Satellite observations of mesoscale eddy-induced Ekman pumping[END_REF]Renault et al., 2016d). In the literature, two main interactions have been assessed: the influence of the Sea Surface Temperature (SST) on the atmosphere, i.e., the Thermal Feedback (TFB), and the influence of the surface oceanic currents on the surface stress and wind, i.e., the Current FeedBack (CFB).

The TFB has a "top-down" effect: it modifies the Atmospheric Boundary Layer (ABL) turbulence and the wind, which consequently alter the surface stress. In that case, the surface stress induced anomalies are directly related and positively correlated to the wind induced anomalies [START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]. [START_REF] Small | Air-sea interaction over ocean fronts and eddies[END_REF] provide a review of the different processes involved. The TFB has a linear effect on the stress and the wind curl, divergence, and magnitude [START_REF] Small | Damping of tropical instability waves caused by the action of surface currents on stress[END_REF][START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF][START_REF] Chelton | Coupled ocean-atmosphere interaction at oceanic mesoscales[END_REF]. This has been quantified by coupling coefficients [START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF][START_REF] Chelton | Global observations of nonlinear mesoscale eddies[END_REF][START_REF] Oneill | Covariability of surface wind and stress responses to sea surface temperature fronts[END_REF][START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF][START_REF] Desbiolles | Response of the Southern Benguela upwelling system to fine-scale modifications of the coastal wind[END_REF][START_REF] Wang | Variability in the coupling between sea surface temperature and wind stress in the global coastal ocean[END_REF][START_REF] Oerder | Mesoscale SST-wind stress coupling in the Peru-Chile current system: Which mechanisms drive its seasonal variability?[END_REF] defined between (See Sec. ?? and Table ?? for a complete description):

wind/stress curl and cross-wind/stress SST gradient (s Cu /s Cstr ); wind/stress divergence and down-wind/stress SST gradient (s Du /s Dstr ); wind/stress speed anomalies and SST anomalies (S u /S str ). On the oceanic side, [START_REF] Hogg | The effects of mesoscale ocean-atmosphere coupling on the large-scale ocean circulation[END_REF], using a high-resolution quasigeostrophic ocean model, suggest that the mesoscale TFB could slow down the large-scale currents. More recently, [START_REF] Ma | Western boundary currents regulated by interaction between ocean eddies and the atmosphere[END_REF] and [START_REF] Seo | Distinct Influence of Air-Sea Interactions Mediated by Mesoscale Sea Surface Temperature and Surface Current in the Arabian Sea[END_REF] suggested that the TFB generates wind velocity and turbulent heat fluxes anomalies that could impact the Western Boundary Currents (WBCs).

The surface oceanic currents are generally much weaker than the winds, but their interactions with the surface wind and stress (the CFB) influence both the atmosphere and the ocean (e.g., [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF]; [START_REF] Rooth | Air-sea boundary layer dynamics in the presence of mesoscale surface currents[END_REF]; [START_REF] Dewar | Some effects of the wind on rings[END_REF]; [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF] 2018)). As largely presented in this manuscript, contrarily to the TFB, the CFB modifies directly the surface stress [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF][START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF] and has a "bottom-up" effect on the wind: a positive current anomaly creates a negative stress anomaly, which in turn causes a positive wind anomaly (Renault et al., 2016d;[START_REF] Takatama | The Role of Back Pressure in the Atmospheric Response to Surface Stress Induced by the Kuroshio[END_REF]. Therefore, wind and stress anomalies induced by the CFB are anti-correlated. Although the CFB modifies directly the surface stress, it does not have statistically a systematic effect on the stress (wind) magnitude as a current anomaly can induce an positive or a negative stress (wind)

anomaly depending on the wind direction. At the mesoscale, the ocean currents are very nearly geostrophic and mainly non-divergent, so that the mesoscale CFB mainly affects the stress (wind) curl but not its divergence [START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]Renault et al., 2016d;[START_REF] Oerder | Impacts of the Mesoscale Ocean-Atmosphere Coupling on the Peru-Chile Ocean Dynamics: The Current-Induced Wind Stress Modulation[END_REF]. Renault et al. (2016dRenault et al. ( , 2017a) ) demonstrate that the CFB causes surface stress/wind curl anomalies that are both linearly related to the current vorticity. They define two additional coupling coefficients: one between surface current vorticity and stress curl (s τ ); and one between surface current vorticity and wind curl (s w ). The CFB slows down the mean oceanic currents (e.g., [START_REF] Pacanowski | Effect of equatorial currents on surface stress[END_REF]; [START_REF] Luo | Reducing climatology bias in an ocean-atmosphere CGCM with improved coupling physics[END_REF]) and induces a dampening of the eddy mesoscale activity by ≈ 30% by acting as an "eddy killer", i.e., by causing a sink of energy from the eddies to the atmosphere (e.g., [START_REF] Bye | Large-scale momentum exchange in the coupled atmosphere-ocean[END_REF][START_REF] Rooth | Air-sea boundary layer dynamics in the presence of mesoscale surface currents[END_REF][START_REF] Dewar | Some effects of the wind on rings[END_REF][START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF][START_REF] Xu | Subtleties in forcing eddy resolving ocean models with satellite wind data[END_REF][START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF][START_REF] Mcclean | A prototype two-decade fully-coupled fine-resolution CCSM simulation[END_REF][START_REF] Hutchinson | Southern Ocean response to relative velocity wind stress forcing[END_REF]Anderson et al. 2011;Renault et al. 2016dRenault et al. , 2017a;;[START_REF] Oerder | Impacts of the Mesoscale Ocean-Atmosphere Coupling on the Peru-Chile Ocean Dynamics: The Current-Induced Wind Stress Modulation[END_REF]). It appears crucial to represent the CFB in numerical oceanic models as it partly controls the WBCs dynamics (Renault et al., 2016c(Renault et al., , 2017b(Renault et al., , 2019a)). Characterizing and modeling the mesoscale air-sea interactions and their consequences on the ocean dynamics and biogeochemistry is therefore of uttermost importance. [START_REF] Ross | Oceanic surface winds[END_REF], see Sec. ??). Based on in situ data analysis, the ENW has been shown to overestimate U a and its mesoscale response to the TFB from 10% to 30% [START_REF] Liu | Equivalent neutral wind[END_REF][START_REF] Liu | Ocean-atmosphere interaction over Agulhas extension meanders[END_REF][START_REF] O'neill | The effects of SST-induced surface wind speed and direction gradients on midlatitude surface vorticity and divergence[END_REF][START_REF] O'neill | Wind speed and stability effects on coupling between surface wind stress and SST observed from buoys and satellite[END_REF]. Moreover, as suggested by e.g., [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF]; [START_REF] Kelly | Ocean currents evident in satellite wind data[END_REF]; [START_REF] Cornillon | Warm core ring velocities inferred from NSCAT[END_REF]; [START_REF] Plagge | Examining the impact of surface currents on satellite scatterometer and altimeter ocean winds[END_REF], scatterometers winds represent the ENW (U ENWr ) relative to the surface currents rather than the absolute ENW. Scatterometers may therefore induce errors in the characterization of the TFB and CFB effects on the wind.

Scatterometers such as

Both TFB and CFB affect the stress and the wind but because the mesoscale currents are very nearly geostrophic (thus very often proportional and perpendicular to the SST gradients), the stress mesoscale anomalies induced by the CFB can also be proportional and perpendicular to the SST gradients [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF]. [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF] suggest that the TFB effect on wind stress curl observed by scatterometers could be contaminated by the CFB effect. So far, it is still unclear how to unravel the TFB effect from that due to the CFB and, thus, whether the defined coupling coefficients allow to properly separate the mesoscale TFB and CFB effects on wind and surface stress. Without consistent measurements of surface ocean velocity, it is not possible to separate the effects of TFB and CFB on the curl fields. So far, only coupled models can be used to separate the CFB effect from the TFB effects. Using a numerical model off California, Renault et al. (2016d) recently showed that the coupling coefficients s τ and s w allow to distinguish the CFB from the TFB effect on the surface stress and on the wind. However, this has not been yet demonstrated globally.

In this Chapter, a set of three realistic mesoscale resolving ocean and atmosphere coupled simulations are carried out over the region 45

Disentangling The Current Feedback

As stated in the introduction, the CFB has only a systematic effect on the stress and wind curl, which will be explored in this section.

Effect on the Surface Stress Curl

The coupling coefficient between the current vorticity and the stress curl (s τ ) is estimated from satellite altimeter data (AVISO and a QuikSCAT product, as in Renault et al.

(2017b),) and compared to PULS_CTRL and PULS_NOCRT (Figure 5.1). In the observations and in PULS_CTRL, s τ is negative almost everywhere (Figure 5.1ab): a positive surface current vorticity anomaly causes a negative surface stress curl anomaly. s τ can be interpreted as a measure of the CFB efficiency: the more negative a s τ , the more efficient an eddy killing. It primarily depends on the large-scale wind: the larger the wind speed, the more negative s τ (Renault et al. (2017b) and Eq. 17 from [START_REF] Gaube | Satellite observations of mesoscale eddy-induced Ekman pumping[END_REF]). s τ therefore partially determines the sink of energy induced by the CFB [START_REF] Xu | Subtleties in forcing eddy resolving ocean models with satellite wind data[END_REF]Renault et al., 2016c;[START_REF] Xu | Work done by atmospheric winds on mesoscale ocean eddies[END_REF] as a large sink of energy needs the presence of an important mesoscale activity and of a negative s τ (Renault et al., 2017a). s τ in PULS_CTRL is overestimated by ≈ 50% with respect to the observations. While part of that discrepancy is certainly due to model biases, there are important sampling differences between AVISO and QuikSCAT that can have a large influence on the s τ estimate (See Fig. 2 of Supplemental Information of Renault et al. (2017a)). In PULS_NOCRT, where only the TFB still active, s τ strongly reduces (by more than 96%), becoming very weak everywhere (Figure 5.1c), indicating that the mesoscale surface current vorticity is not correlated with the mesoscale surface stress curl. Thus, at the mesoscale, s τ efficiently unravels the CFB effect on the surface stress from that due to the TFB. This result is further confirmed by estimating s τ from PULS_SMTH where the CFB is active and the mesoscale SST ignored by the atmosphere. In such an experiment, s τ is very similar to that estimated from PULS_CTRL (not shown).

Effect on the 10-m Wind Curl and Scatterometers Limits

To characterize globally the wind curl response to the CFB, the coupling coefficient between the surface current vorticity and the wind curl (s w ) is first computed from PULS_CTRL using U a . s τ and s w have the opposite sign (Figures 5.1b and 5.2c), i.e., a positive surface current anomaly induces a negative surface stress anomaly, which in turn causes a positive wind anomaly (Renault et al., 2016d). s w varies from 0 to 0.5 with a mean value of ≈ 0.3. For example, it means a mesoscale eddy with a velocity of 1 m s -1 will induce on average a wind velocity anomaly of 0.3 m s -1 . From an atmospheric point of view, the wind response to the CFB remains weak. However, s w can be interpreted as a measure of the efficiency of the partial re-energization of the ocean by the CFB induced wind anomalies (Renault et al., 2016d): the larger s w , the larger the partial re-energization of the mesoscale currents. For the US West Coast a s w of 0.23 causes a partial re-energization by ≈ 25% of the present mesoscale activity. In PULS_NOCRT, consistent with the previous result on s τ , s w becomes very weak (not shown) and appears to be a good metric to characterize the CFB wind response.

Figure 5.2b shows that s w evaluated from the observations and from PULS_CTRL are of opposite sign, observed s w from satellite being negative everywhere with a mean value of ≈ -0.54. This is because QuikSCAT scatterometers winds represent U ENWr (e.g., [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF]) rather than U ENW or U a , so s w is strongly positively correlated to s τ (r > 0.8). To confirm it, s w is estimated from PULS_CTRL mimicking scatterometer winds by using the relative ENW (s wENWr , Figure 5.2b), and by using U r (s w r). s wENWr and s wr are very alike (not shown) and are a mirror of s τ . This confirms that scatterometers can characterize the relative wind (U r ) response to the CFB, however, it would be overestimated (i.e., more negative) by ≈ 10% because of the use of U ENWr instead of U r (not shown). Difference between U a and U ENW can be large for atmospheric stratifications that deviate greatly from neutral conditions [START_REF] Song | Coupling between sea surface temperature and low-level winds in mesoscale numerical models[END_REF]. This is consistent with [START_REF] Song | Coupling between sea surface temperature and low-level winds in mesoscale numerical models[END_REF] and [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF] that shows the wind curl response to the TFB can be overestimated by ≈ 10% when using the ENW instead of the 10m-wind.

Scatterometers limits to capture the 'bottom-up' effect of the CFB is further confirmed by computing the correlation between the curls of the surface stress and low levels winds at mesoscale. Consistent with eq. 1, Fig. 5.3a shows that at the mesoscale, scatterometerslike UENWr curl is positively correlated everywhere to the surface stress curl (similar results are found using Quikscat). This is because the wind is determined from the surface stress curl. On the other hand, Fig. 5.3b shows much weaker values for the correlation between U a and the stress curls, with even null or negative values over the western and eastern boundary currents areas. These negative correlations indicate regions where, at the mesoscale, the currents force the lower atmosphere and dominate the TFB and the atmospheric internal variability. This suggests that the mesoscale stress and wind curl are mainly driven by the atmospheric internal variability or by TFB unless the ocean presents a large mesoscale activity that can, through the CFB, induces a negative correlation between U a curl and stress curl. To confirm it, Fig. 5.3c shows the same correlations but using the PULS_SMTH simulation, in that case, the SST mesoscale signal is not sent to the atmosphere. In regions characterized by a weak mesoscale activity, it is not the TFB but the atmosphere that determines the sign of the mesoscale wind and stress curl. Regions characterized by a large mesoscale activity (as WBCs or eastern boundary current)

have correlations between stress curl and wind curl even more negative as the TFB is removed. Those features can not be monitored by scatterometers. Therefore, this confirms that when using scatterometers, the stress seems more appropriate to assess the atmospheric response to the air-sea interactions.

Disentangling The Thermal Feedback

Effects on the Mesoscale Stress and Wind Curl

The coupling coefficient between the surface stress curl and the crosswind SST gradient (s Cstr , [START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]) is estimated from the observations and PULS_CTRL for the summer period of each hemisphere (Figure 5.4ab, as in [START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF]; [START_REF] Wang | Variability in the coupling between sea surface temperature and wind stress in the global coastal ocean[END_REF], see Methods). Consistent with, e.g., [START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF]; [START_REF] Wang | Variability in the coupling between sea surface temperature and wind stress in the global coastal ocean[END_REF], in the observations, s Cstr has overall values varying from 0 to 0.03 N m -2 • C -1 , and is larger where the wind is more intense [START_REF] Oneill | Covariability of surface wind and stress responses to sea surface temperature fronts[END_REF]. Offshore, in regions of weak EKE, s Cstr is close to zero or not significant. In regions of intense at- mospheric convection (e.g., Intertropical Convergence Zones), the atmospheric mesoscale is characterized by vortices generated by the synoptic convergent circulation, and wind gusts, which force the ocean even at the mesoscale, resulting in negative s Cstr . The spatial distribution of s Cstr estimated from PULS_CTRL (Figure 5.4b) is in agreement with the observations, but its intensity is underestimated. While no doubt some of these are due to model biases such as the ABL or the coastal wind representations [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF]Renault et al., 2016a), the estimation of s Cstr also suffers from uncertainties due to the effective resolution and the sampling of the observations (Renault et al., 2017a). For instance, despite a larger s Cstr , the correlations between stress curl and cross-stress SST gradients are weaker in the observations than in the simulations.

Scatterometers not only integrate the TFB effect on the stress but also the CFB effect.

Thus, s Cstr may not properly distinguish the TFB effect on the stress (and wind) from that due to the CFB. s Cstr is estimated from PULS_NOCRT, i.e., the coupled simulation s Cstr in PULS_SMTH_NOCRT is weaker than s Cstr estimated from PULS_SMTH, however, the residual of SST signal can account up to 25 -30% of the s Cstr estimated from PULS_SMTH. This means the CFB effect represents on average ≈ 27% of s Cstr as estimated from PULS_CTRL. Overall, this confirms s Cstr can not fully disentangle the TFB effect and the CFB effect on the surface stress. Finally, in all the simulations, the negative values of s Cstr remain roughly the same, confirming that the atmosphere forced the ocean even at the mesoscale in those regions.

Similar results are found for U a (by estimating s Cu , not shown). Additionally, using U ENWr in PULS_CTRL rather than U a , like in the case of scatterometers winds, s Cu can be increased by up to 25% when using U ENWr instead of U a (not shown). This overestimation is due to the use of the relative wind: geostrophic currents tend to follow isotherms and can, thus, contaminate the wind curl response [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF]. Moreover, large difference between ENW and 10-m wind occur when atmospheric stratifications deviate greatly from neutral [START_REF] Song | Coupling between sea surface temperature and low-level winds in mesoscale numerical models[END_REF]. The overestimation is larger that the previous estimate by [START_REF] Song | Coupling between sea surface temperature and low-level winds in mesoscale numerical models[END_REF] and [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF] that report for the Agulhas Return Current an overestimation of s Cu by 10-15% . To sum up, coupling coefficients based on stress or wind or surface stress curl should be used with caution when evaluating the impact of the TFB on the wind and surface stress curl. Finally, because the mesoscale currents are very nearly geostrophic and, thus, non-divergent, the CFB has little influence on the coupling coefficients s Du and s Dstr .

Mesoscale Wind and Surface Stress Magnitude

ONeill et al. ( 2012) demonstrate that the mesoscale stress magnitude perturbations are characterized by a roughly linear dependence on the mesoscale SST perturbations has larger values at the mid-latitudes, the Eastern Boundary Currents, and some WBCs.

Consistent with the previous results, s str has negative values over regions of important atmospheric convection. PULS_CTRL fairly represents the s str spatial distribution (Figure 5.6b) although it underestimates its strength in particular over the Antarctic Circumpolar Current likely because of the ABL parameterization. In PULS_NOCRT, s str has a very alike spatial distribution and intensity, suggesting the CFB does not have a significant influence on mesoscale surface stress and, thus, on s str (Figure 5.6c). This is furthermore corroborated by the probability density function of the ratio between s str as estimated from

PULS_NOCRT and PULS_CTRL (Figure 5. 7), that shows difference between both experiments of ≈ 6%. In PULS_SMTH, s str is very weak, confirming the CFB does not influence its intensity. Although geostrophic currents tend to follow isotherms, the CFB does not have a systematic statistic effect on the stress magnitude as a current anomaly can induce an positive or a negative stress (wind) anomaly depending on the wind direction. This is finally confirmed by the comparison between PULS_SMTH and PULS_SMTH_NOCRT. The ratio between s str as estimated from PULS_SMTH and PULS_SMTH_NOCRT are very similar (not shown). This confirms the remaining s str signal in PULS_SMTH is not induced by the CFB but rather by residual SST signal. Similar results are found when using U a instead of the surface stress to estimate s u . However, the use of U ENWr instead of U a can overestimate the TFB effect on the wind by ≈ 25% (not shown) because U a and U ENWr can differ when the atmospheric stratification deviate greatly from neutral conditions. This is consistent with ONeill et al. ( 2012) that report an overestimation by 10 -30% based on in situ buoys.

Conclusion of the Chapter

Both Current FeedBack (CFB) and Thermal FeedBack (TFB) exert an influence on the wind and surface stress. While the CFB has a "bottom-up" effect on the surface stress and the wind, the TFB has a "top-down" effect from the ABL and the 10-m wind to the surface stress. The CFB mainly affects the stress and wind curl, whereas the TFB can have an influence on their curl, divergence, and magnitude. In the last decade, coupling coefficients have been defined to evaluate the importance of the mesoscale air-sea interactions on the wind and surface stress. We show that coupling coefficients based on curl of current and stress (s τ ) or wind (s w ) efficiently allow to disentangle and characterize the influence of the CFB on 10-m wind and surface stress curl. The TFB influence on stress (wind) curl is often characterized by estimating coefficients between stress (wind) curl and cross-stress (cross-wind) SST gradients (e.g., [START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF]). However, those TFB coupling coefficients cannot properly unravel the TFB and CFB effects. Coefficients based on divergence or mesoscale anomalies of SST and stress (or wind) allow disentangling the TFB effects from those due to the CFB. Scatterometers wind have been very useful to demonstrate the ubiquity of both TFB and CFB effects on surface stress and wind. However, consistent with [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF]; [START_REF] Plagge | Examining the impact of surface currents on satellite scatterometer and altimeter ocean winds[END_REF], we show that because scatterometer winds represent the relative ENW to the oceanic motions, they allow to characterize the relative ENW response to the CFB and TFB and not the absolute wind response. Despite limitations in the estimation of wind and then surface stress by scatterometers [START_REF] Quilfen | The ERS scatterometer wind measurement accuracy: Evidence of seasonal and regional biases[END_REF], as scatterometers are fundamentally stress-measuring instruments, coupling coefficients based on stress appear to be more appropriate to characterize both TFB and CFB effects from scatterometers data.

The approach presented in this study is mainly based on numerical models and, thus, suffers from limitations that can largely affect the surface stress and wind responses to the air-sea interactions. As shown by [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF] and [START_REF] Oerder | Mesoscale SST-wind stress coupling in the Peru-Chile current system: Which mechanisms drive its seasonal variability?[END_REF], of particular concern is the choice of the atmospheric boundary layer mixing parameterization. For the Agulhas Return Current and the Peruvian Upwelling System, the TFB coupling coefficients in numerical models present a sensitivity to such a parameterization. For example, here the YSU parameterization is used. This scheme has been shown by [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF] for the Agulhas Return Current to underestimate the strength of the TFB coupling coefficients with respect to the observations. The coupling coefficient between surface current vorticity and wind curl depends on the atmospheric boundary layer height (Renault et al., 2017b). Therefore, the CFB effects on surface stress and wind may have also have a sensitivity to the choice of the atmospheric boundary layer mixing parameterization. Futures studies similar to [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF] are needed for characterizing such such a sensitivity. Finally, in this study, a 1/4 • atmospheric model has been coupled to a 1/12 • oceanic model. This raises up the question on the atmospheric spatial resolution needed to couple or to force an ocean model. Does an equivalent atmospheric and oceanic spatial resolution is deemed to be required to represent the air-sea coupling coefficients ? We intend to investigate this soon.

Our results have large implications for the understanding of the mesoscale air-sea interactions, and their effects on the ocean. The mesoscale stress anomalies induced by both TFB and CFB cause additional Ekman pumping that can (for the CFB) induce a sink of energy from the ocean to the atmosphere and a large dampening of the mesoscale activ-ity (e.g., [START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF] This Chapter aims to present some of my on-going work. In particular I will discussed how to best force an ocean model, the biogeochemical response to the current feedback, and also, what I call a missing piece of the puzzle: the potential role of the wave feedbacks to the atmosphere and the ocean.

Toward a New Paradigm: Recipes How to Best Force an Ocean Model

The substantial current feedback effect on the currents should change the paradigm of how to force an regional high resolution uncoupled oceanic model. However, regional models and even global reanalysis (NCEP or ERA) generally still ignore this feedback.

When forcing an ocean model with an atmospheric product that does not contain the atmospheric response to the current feedback (as e.g., NCEP but not as QuikSCAT), this effect could be incorporated by using in the bulk formulae the relative wind to the current (instead of the wind alone) with a parameterization of the wind response that partially re-energizes the ocean.

A regional high-resolution atmospheric model is usually very costly compared to an oceanic model. So an important next question is how best to force an uncoupled oceanic model. A simulation that uses prescribed wind stress can not dampen the offshore eddies because the prescribed wind stress is correlated with the eddies. A bulk-forced oceanic simulation, i.e., where the model is forced by the wind, should estimate the surface stress using the relative wind. A distinction is necessary between observations or a fully coupled model, on one hand, and an uncoupled atmospheric wind product, on the other. For non-deterministic variability (such as oceanic eddies), the bulk formulae used to estimate the surface stress should in any case take into account a parameterization of the partial re-energization of the ocean by the atmospheric response. In Renault et al. (2016d), I suggest using a simple wind correction to make to a wind U a to mimic the coupled response in an uncoupled oceanic model. Such a parameterization is based on the current-wind coupling coefficient s w estimated from a coupled simulation. A different parameterization could be based on a stress correction to make a τ that mimics the coupled surface stress response (i.e., that includes the wind adjustment) in an uncoupled oceanic model, viz.,

τ = τ a + s τ U o . (6.1)
When forcing an ocean model, this correction could be applied on a prescribed surface stress or to a surface stress estimated using a bulk formulae and the absolute wind.

For the U.S. West Coast, s w = 0.23 can be derived from Fig. 4.5. However, it remains to be seen how well this modified relative wind parameterization would work for an un-coupled model, and the current-wind coupling coefficient found in this study may not be valid for other regions, pending further investigation. The coupling coefficient depends on several local parameters such as the background wind, the steadiness, and the EKE.

Even for the CCS, the wind coupling coefficient may not be accurate for the near-shore region; there the wind adjustment is stronger, canceling more efficiently the reduction of energy transfer from the atmosphere to the ocean. For deterministic features such an adjustment may not be necessary if the model is forced by observations or some adequate representation of the oceanic currents. For instance, for a U.S. West Coast configuration forced by the QuikSCAT wind stress observations (e.g., Capet et al. 2008a;Renault et al. 2016a), the simulated wind-driven alongshore current perturbations may be correlated to the climatological average currents and hence already contain both the atmospheric adjustment to the current feedback and the reduction of the surface stress perturbations, allowing a realistic EKE close to the coast. However, the eddies generated are not correlated with the reality lying behind the measured stress, so that such simulations can not represent the offshore sink of energy from the ocean to the atmosphere, explaining their offshore EKE overestimation. I am currently working on that thematic that emerged from my previous results. In the following I will present preliminary results I have for the U.S.

West Coast. We are also working with S. Masson to test those parameterizations and more generally to assess how to best force an ocean model using the tropical channel domain (45 • S -45 • N).

Preliminary results on the US West Coast

In this on-going study, the Regional Oceanic Modeling System (ROMS) is implemented over the U.S. West Coast and is forced by an atmospheric forcing derived from a coupled simulation Renault et al. (2016d) that ignores the current feedback to the atmosphere over the period 1995-1999, and also by an uncoupled realistic regional configuration of the Weather and Forecast (WRF) model over the period 1995-2013. The objective of this study is to go a step beyond Renault et al. (2016dRenault et al. ( , 2017b) ) by testing the validity of the proposed parameterizations of the wind response to the current feedback. Here, the parameterization from Renault et al. (2016d) is tested and the results are compared to the simulations from Renault et al. (2016d) and to the satellite observations.

Validation with the Fully Coupled Simulation

We start by comparing the parameterized uncoupled simulation USW4 that is forced using the parameterization of the wind response to the current feedback suggested by Re- US_NOCRT is a thermally coupled experiment without current feedback. US_CRTF is forced by the atmosphere from US_NOCRT and the full surface current to calculate the surface stress. US_CRTF neglects the atmospheric response to the current feedback, whereas US_CRT is a coupled experiment that takes into account both thermal and mechanical coupling. Thus, USW4 is configured similar to US_CRTF except that the surface stress is estimated using the parameterized U r .

The numerical outputs from the solution are daily averages. The mean is defined in respect to long-term averaging, and the prime denotes deviation from the long-term mean.

The temporal evolution of the domain-averaged surface EKE from the different experiments is plotted in Fig. 6.1a. As shown by Renault et al. (2016d), from US_NOCRT to US_CRTF, the EKE is reduced by 55% by the current stress feedback. In the fully coupled experiment (US_CRT), the wind can adjust to the surface stress induced by the current feedback. It re-energizes partially the ocean (Renault et al., 2016d), therefore, the EKE is reduced by only 40%. USW4 is uncoupled, as US_CRTF, but estimates the surface stress by taking into account the surface current and the current-wind coupling coefficient (s w ). The inclusion of the parameterization of the atmospheric response in USW4 allows a partial re-energization of the ocean and, therefore, leads to a fair approximation of the EKE reduction induced by the current feedback from US_NOCRT to US_CRT; As shown by Renault et al. (2016d), a simulation that ignores the atmospheric response to the changes in surface stress (as in US_CRTF), systematically neglects the partial re-energization of the atmosphere, with the consequence of strengthening the currents. It may overestimate the coastal reduction of the geostrophic eddy wind work F e K eg (= τ • u go ) and the offshore deflection of energy from the oceanic geostrophic currents to the atmosphere. This is seen in the EKE temporal evolution and in Table 6.1, which lists F e K eg from all the simulations. Following Fig. 3 of Renault et al. (2016d), two regions are considered: a coastal region where F e K eg is positive (d < 300 km), and an offshore region where F e K eg is negative (500 < d < 300 km), and d is cross-shore distance from the coast. For all the experiments, in the nearshore region, F e K eg is positive because the wind fluctuations induce geostrophic coastal jets (e.g., Renault et al. 2012Renault et al. , 2016d)). US_NOCRT, due to its lack of current feedback, has an offshore F e K eg close to zero: over an eddy, the input of energy has roughly the same magnitude as the deflection of energy. All the experiments with current feedback have a reduction of the coastal F e K eg in the coastal area and a negative F e K eg offshore compared to US_NOCRT. Consistent with Renault et al. (2016d), US_CRTF overestimates the reduction of energy transfer from the atmosphere to the ocean in the coastal region, drastically reducing the reservoir of energy of the ocean.

For that reason, although the wind response is neglected in US_CRTF, the offshore F e K eg is less negative in US_CRTF than in US_CRT and USW4 (Renault et al., 2016d). USW4 approximately reproduces the coastal F e K eg reduction and the offshore deflection of energy from US_CRT (Table 6.1). The differences between US_CRT and USW4 may be partly due to the different open boundary conditions used, but also due to an incorrect s w value that can not be accurately estimated in the nearshore region due to the dominant effect of the orography and coastline meandering on the wind (Renault et al., 2016b,d). s w is taken as spatially constant in USW4; however, in the coastal region it may be larger due to the shallower marine boundary layer, yet it may also be smaller because of the slackening of the wind toward the coast (Renault et al., 2016d). s w is also taken as temporally constant, although it may have seasonal and interannual variations related to the marine boundary layer and the wind magnitude. STAU only approximate -> error too. This may explain the slight overestimation of the coastal F e K eg (Table 6.1) and the small EKE discrepancy between US_CRT and USW4 (Fig. 6.1a). -3 ] is estimated as the statistical regression slope between surface stress curl and oceanic surface current vorticity using USW4; it is then compared to s st from US_NOCRT, US_CRTF and US_CRT in Fig. 6.1b. Renault et al. (2016d) show s st is overestimated when neglecting the wind response to the current feedback, hence it induces an excessive deflection of energy from the ocean to the atmosphere, and then excessive eddy killing. A realistic s st value allows a realistic dampening of the eddies by the current feedback. As shown by Renault et al. (2016d), the s st value in US_NOCRT is insignificant (it ignores the surface currents). US_CRT and USW4 show a similar negative linear relationship, with s st = 1.2 ± 0.35 × 10 -2 N s m -3 and s st = 1.3 ± 0.30 × 10 -2 N s m -3 , respectively.

USW4 has a slightly lower s st (i.e., eddy killing is more efficient) than US_CRT, but the difference is within the error estimate. US_CRTF, which neglects the atmospheric coupling response, has a significant lower s st that induces more efficient dampening of the eddies. To sum up, relative to the fully coupled US_CRT, the parameterized USW4 has a slight positive bias in F e K eg in the nearshore region (too much energy by 2%) that is compensated by a too large deflection of energy offshore: the eddy killing is too efficient and induces a F e K eg that is too negative (by 3%). Despite those small biases, overall the parameterization of the wind response allows a more realistic EKE and s st coupling coefficient by incorporating the partial re-energization of the ocean by the wind response to the current feedback.

Validation with Observations

The geostrophic EKE is estimated over the period 1995-2010 from AVISO [START_REF] Ducet | Global high-resolution mapping of ocean circulation from TOPEX/Poseidon and ERS-1 and-2[END_REF] and from USW4. For the model the EKE is computed using low-pass filtered geostrophic velocities (Gaussian spatial filter with 36-km half-width) as an approximation to AVISO resolution [START_REF] Chelton | The accuracies of smoothed sea surface height fields constructed from tandem satellite altimeter datasets[END_REF]. (More rigorous comparisons could be done using numerical solutions processed in the same way as altimetric observations.)

For USW4 Fig. 6.2 shows that the simulated EKE has its largest values not too far offshore and exhibits a wide decay further offshore, which is due to the combined influences of Ekman transport, eddy diffusion, and to the current feedback, with an overall general similarity with AVISO and the literature [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF]Capet et al., 2008a).

The pattern similarity is better with USW4 and US_CRT than it is with US_NOCRT and US_CRTF (Renault et al., 2016d). There are some biases in the USW4 spatial pattern, mainly that EKE is too large in the near-coastal region, where the s w estimates are less certain , and that EKE is too large in the Southern California Bight, which seems most likely due to errors in the atmospheric forcing.

Figure 6.3a depicts several relevant EKE rates in USW4 over the period 1995-2013, and Fig. 6.3b is the cross-shore profile for each term averaged between 30 • N and 45 • N. The geostrophic eddy wind work F e K eg profile is also estimated using a QuikSCAT product [START_REF] Bentamy | Compatibility of C-and Ku-band scatterometer winds: ERS-2 and QuikSCAT[END_REF] and AVISO but only over the available QuikSCAT period (2000QuikSCAT period ( -2009)). (Due to the QuikSCAT and AVISO coastal accuracy issues, the F e K eg value over the first 50 km off the coast is not shown.) Consistent with [START_REF] Marchesiello | Equilibrium structure and dynamics of the California Current System[END_REF] and Renault et al. (2016d), the main sources of EKE are the eddy wind work and the baroclinic conversion. Both of them have large positive values in the nearshore region. K m K e is a secondary term. Consistent with the observations, F e K eg is positive in the nearshore region and then becomes negative offshore, deflecting energy from the oceanic geostrophic currents to the atmosphere and dampening the offshore eddies. USW4 deflects slightly more energy offshore than the observations (by 10% over the offshore area). This could be due to the errors in the observations, but might also be due to biases in the atmospheric and oceanic simulations, with an overestimation of the EKE reservoir (more energy to be deflected) and a biased estimation of s w and s st . For example, s w may depend on the atmospheric parameterization of the marine boundary layer (Renault et al., 2016d). This may explain the slight overestimation of the offshore EKE and the overestimation of the eddy life in US_CRT shown by Renault et al. (2016d). Overall, however, the parameterization of the wind response to the current feedback in USW4 fairly reproduces the observed EKE and F e K eg . is the main energy conversion term. F e K eg is positive nearshore and deflects energy from the ocean to the atmosphere offshore while damping the mesoscale activity.

Summary and Discussion

In this on-going study we test over a long time period (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) the parameterization of the wind response to the current feedback suggested by Renault et al. (2016d) for the U.S. West Coast. We show the parameterized uncoupled simulation successfully replicates the EKE, F e K eg , and s st in a fully coupled simulation. As in a coupled simu- Paradoxically, global wind reanalyses without current feedback are the best choice (in the absence of regional atmospheric uncoupled or coupled models without current feedback)

when combined with the stress feedback parameterization I proposed.

On the Biogeochemical Response

I am also interested by the biogeochemical response to the air-sea interaction. In particular, I aim to understand the role of the mesoscale and submesoscale processes (and their links with the air-sea interactions) in determining the variability and the mean state of the net primary production and of the oxygen. A middle-term goal is to better understand the on-going deoxygenation of the ocean. I illustrate here one study we are doing with Faycal Kessouri (post-doc, UCLA, see Chapter 8) on the primary production response of the California Upwelling System to the current feedback.

Seasonal wind-driven upwelling sustains high productivities along the coastal California Current System (CCS), supporting in turn a rich and diverse ecosystem. High productivities arise by a complex interplay of nutrient supply by upwelling and removal by subducting eddies, which is highly sensitive to the details of wind forcing, topography and circulation, and is difficult to predict with simple indices. Using regional numerical simulations, we show that mechanical coupling between the ocean and the atmosphere ("current feedback") drastically dampens the eddy activity by deflecting energy from geostrophic currents to the atmosphere, but also induces fine scale spatial structures on the wind itself, inducing a partial re-energization of the ocean, and leading to more realistic eddies characteristics. The subsequent reduction of the EKE reduces the eddydriven offshore subduction of nutrients and organic material, increasing phytoplankton production on the shelf by between 10 to 30%, and decreasing it offshore. The offshore NPP reduction is accompanied by a change in the dominant phytoplankton groups, and also on the oxygen distribution. These complex ocean-atmosphere-land interactions imply that simple wind-based indices are incomplete predictors of productivity in the CCS, and that effective predictors will require inclusion of the effects of eddies. first quantify the importance of SST gradients on regional atmospheric conditions. Agulhas eddies and meanders influence the vertical air column up to the troposphere, and mesoscale ocean patterns significantly modify incoming landward moisture fluxes. The austral summer mean state is then modified in terms of air-temperature, cloud cover and mean rainfall, with notable differences in tropical rainbands over southwestern Africa.

Control of the Precipitation by Mesoscale Air-Sea Interactions

Mesoscale SST variability favors tropical-extra-tropical interactions and cloudband de-velopment over the continent. These results stress the importance of high resolution ocean forcing for accurate atmospheric simulations.

Role of the oceanic vertical thermal structure in the modulation of heavy precipitations over the Ligurian Sea

The importance of the upper ocean thermal vertical structure (mixed layer depth and stratification) in the control of the precipitation during a heavy-rain-producing mesoscale convective system is investigated by means of numerical simulations. In particular, the fully compressible, non-hydrostatic Euler equations for the atmosphere and the hydrostatic Boussinesq equations for the ocean are numerically integrated to study the effect of the ocean-atmosphere coupling both with realistic initial and boundary conditions and with simpler, analytical vertical temperature profile forcing. It is found that the action of the winds associated with the synoptic system, in which the heavy precipitation event is embedded, can entrain deep and cold water in the oceanic mixed layer, generating surface cooling. In the case of shallow mixed layer and strongly stratified water column, this decrease in sea surface temperature can significantly reduce the air column instability and, thus, the total amount of precipitation produced. on the Thermal Feedback. Another possible interaction between the ocean and the atmosphere is the wave feedbacks to the atmosphere and the ocean (WAO). Both the AC and the GS are characterized by the presence of locally generated wind wave (Figure 6.4) and swell (i.e., wind-generated waves that are not-or are hardly-affected by the local wind).

The role of the WAO in determining the energy budget and the dynamic of the WBCs is still an open question. The conventional representation of the air-sea interface and the roughness effects due to the waves is based on the parameterization of fluxes by exchange coefficients (e.g., [START_REF] Charnock | Wind stress on a water surface[END_REF]). The use of these empirical formulations for the assessment of strongly coupled and small-scale phenomena violates most of the assumptions on which they are based: moderate wind conditions, fully developed waves, large spatial scales, and daily frequency. In extreme wind conditions and/or young, strong and complex sea (cross swells, spray, foam banks), the waves are not in balance with the forcing of the wind. The exchanges between the ocean and the atmosphere are then considerably impacted at high frequency and spatially heterogeneous.

As illustrated in Fig. 6.5, WAO may have an impact on the WBCs energy and dynamic It can deepen the oceanic mixed layer more rapidly than wind-forcing and distribute efficiently the momentum and heat fluxes vertically in the surface oceanic mixed layer (e.g., [START_REF] Mcwilliams | Langmuir turbulence in the ocean[END_REF]; [START_REF] Kantha | On the effect of surface gravity waves on mixing in the oceanic mixed layer[END_REF]; [START_REF] Kumar | Implementation of the vortex force formalism in the coupled ocean-atmosphere-wave-sediment transport (COAWST) modeling system for inner shelf and surf zone applications[END_REF]). This could alter the energy budget of the WBCs and modify their thermal feedback. The main objective of TACOS is to improve our understanding of the dynamics at play in determining the WBCs dynamics; in particular the processes linked to the wave feedbacks that alter the energy budget and the dynamic of the AC and the GS. The AC and GS have their own specificities and numerical biases. The GS is characterized by a separation near Cape Hatteras and a penetration to the North Atlantic basin. To the south of Africa, although most of the subtropical warm and salty water masses carried by the AC retroflect back to the Indian Ocean, some penetrate westward in the South Atlantic.

This salient feature, known as the Agulhas leakage, is a potential driver of variability of the meridional overturning circulation in the Atlantic. The representation of those features is a long-standing challenge for modelers.

Our main hypothesis is that the wave feedbacks can partly control the WBCs by altering the turbulent fluxes (e.g., by a change of sea surface roughness), the energy exchange between the ocean and the atmosphere (e.g., lose of energy due to the wave generation), the ocean mixing (e.g., Langmuir circulation), and the currents and the SST (and, thus, their respective feedbacks to the atmosphere). We will perform coupled (activating or not different wave feedbacks) high-resolution simulations over a time period spanning 10 years with an oceanic mesoscale resolving resolution (see Chapter 1). With this methodology, TACOS aims to address specifically three principal scientific questions:

1. To what extent the different WAO interactions can alter the energy budget of the AC and the GS?

2. How the WAO interactions can modulate the mesoscale activity of WBCs?

3. How can they alter the AC and GS dynamics, such as e.g., the AC retroflection and the GS separation and post-separation?

From a modeling perspective, TACOS will aim to improve two main aspects of the WAO coupling:

1. The coupling interface: The Ocean, Wave, and Atmospheric models should use a single bulk to ensure a conservation of the momentum flux across the WAO models. We also propose to integrate the lower atmosphere-wave coupling through effects of waves on wind stress. This will also allow taking into account the spatial and temporal redistribution of the momentum flux and the filtering of its highfrequency component by wave generation and breaking (white-capping).

2. The vertical mixing scheme: Current parameterizations of the oceanic turbulent mixing in ocean models are missing or at least misrepresenting key surface-wave processes that force Langmuir turbulence. This wave feedback to the ocean can deepen the mixed layer depth, affecting the sea surface temperature, and, thus the heat fluxes. Such an incorporation in the ocean model will ensure the complete inclusion of all ocean-waves processes Finally, TACOS also aims to develop diagnostics that will be shared to the modeling community (online and offline, including all terms contributing to the energy cycle).

These diagnostics will allow a clear investigation of where and how energy is dissipated in the AC and the GS and of the role of the waves.

Expected Results

At a minimum, TACOS will improve our knowledge on the different wave feedbacks and on their role in determining the ocean energy budget and on their impact on the WBCs dynamics. It will allow to disentangle the different wave feedbacks at play and to highlight the most important ones that should be taken into account or parameterized in global models. TACOS will also participate to the development of the coupled platform in ocean models by improving the air-sea interface and by implementing and testing a Langmuir Turbulence parameterization in the ocean model. TACOS will participate to the development of CROCO, i.e., a community ocean model widely used in regional oceanography, by working closely with its developer, and by sharing all the developments and the results with them. TACOS will foster collaborations between experts

Chapter 7 Conclusion

As a brief conclusion, I demonstrated in this manuscript fine-scale air-sea coupling leads to a restructuring of the ocean circulation from fine to large scales. The current feedback has 3 main direct effects: (1) it slows down the mean current by reducing the mean input of energy from the atmosphere to the ocean; (2) it creates route of energy from the mesoscale oceanic current to the atmosphere. This process, tentatively called "eddy killing", strongly dampens the mesoscale activity; (3) it also reduces the submeososcale atcivity over the U.S. West coast, although this results should be confirmed in other regions. As an indirect upscaling effect, I demonstrated the current feedback controls to a large extent the Western Boundary Currents by an upscaling effect. The induced sink of energy prevents an excess mesoscale energy that would feed back to the large-scale circulation as part of eddy-mean flow interactions -the inverse energy cascade. In numerical models, taking into account the current feedback and, thus, its eddy killing effect corrects two long-lasting biases in oceanic models: the Agulhas Current retroflection pattern and the GS separation and penetration in the North Atlantic Basin (Renault et al., 2016c(Renault et al., , 2017b)). One of my current goals is to address the biogeochemical response to the air-sea interactions. By shaping the submesoscale and mesoscale activity, fine-scale air-sea interactions may play an important role in explaining the biogeochemical variability and the on-going deoxygenation and acidification.

At the time of my PhD (less than 10 years ago), running high-resolution regional atmospheric models was already possible, but only for limited areas and time-period. Nowadays, high-resolution coupled models are way more easily accessible -at least regional models -. These recent advances have been crucial in my research as it allowed me to run several high resolution coupled simulations over different regions. Climate models and forced ocean models now need new parameterizations in order to take into account the fine scale air-sea interactions. This will allow a major step in the representation of currents, water masses, overturning circulation, ventilation, carbon uptake, etc. Overall, the results presented in this manuscript call for a change of paradigm for what concerns the forcing of ocean models. Should we take into account the current feedback in coupled or forced oceanic simulations ? To my point of view, the answer is positive. Even for say a quarter degree model. For two reasons. First, the current feedback can be seen as a top-drag [START_REF] Dewar | Some effects of the wind on rings[END_REF]. We do not want to ignore the bottom drag nor the top drag as they represent a physical process. To be continued ... The four main Eastern Boundary Upwelling Systems (EBUS) regions, i.e., the U.S. West

Coast, the Humboldt Current, the Canary Current, and Benguela Current, are host to some of the most productive marine ecosystems on the planet. All four are also characterized by large inter-annual to inter-decadal variability and vulnerability to climate change through systematic changes in alongshore winds, upwelling, cloud, and gyrescale ocean currents. Unfortunately, the evolution of these critical environments over the coming decades has received comparatively little attention. This is partly because their essential characteristics (alongshore winds and cloud shaped by local topography and upwelling ribbons) are only tens of km in width and are not well-resolved by current climate models. In addition, processes smaller in scale than the model resolution mediate the relationship between key ecosystem properties and the physical system, making it very difficult to understand consequences of changes in the physical system for marine ecosystems based on model output alone. In this project the team of investigators will address this gap by undertaking an unprecedented suite of high-resolution regional earth system model simulations. The result of this project will be a comprehensive understand-tification and understanding of the key processes shaping variability and change.

The EBUS regions will be compared to one another to understand processes driving upwelling variability and associated biogeochemical responses. The major ecosystem dynamics of interest will include: controls on magnitude and seasonality of upwelling and temperature; controls on magnitude and seasonality of productivity; controls on intensity and spatial scale of hypoxia, and its relationship to circulation and productivity. (2) Include new developments in numerical models: WRF, ROMS , and Simulating Waves Nearshore (SWAN). ( 3) Deliver a 10-year high resolution hindcast product for OSRA and GNOME to conduct oil spill analysis, including hourly surface wind and sea surface currents. ( 4) Deliver a 10-years high-resolution hindcast product for 3D particle transport model to conduct other relevant BOEM supported projects. ( 5) Deliver a 10-years product to BOEM as archives.

CO-PI LEFE AFRICA, 5KE, on-going

We wrote this projet with J. Dehayes and S. Pous from LOCEAN, and P. Penven from LOPS. It aims to assess the Agulhas Current characteristics using different models. Its main goal is to highlight the Agulhas Current sensitivity to the air-sea coupling, the spatial resolution of the models, and the parameterizations used. It will allow us to fund a workshop in South Africa dedicated on the Agulhas Current (October 2018).

ANR JCJC TACOS, 0.2ME, Submitted

After my recent results on the current feedback, a natural step was to include what I think is a missing piece of the air-sea coupling puzzle, i.e., the wave feedback. As summarized in Chapter 6, I recently submitted an ANR JCJC on the influence of the wave feedbacks to the atmosphere and the ocean on the WBCs dynamic and the ocean budget.

This ANR, if funded, will allow me to hire 1 postdoc and 2 Master students to collaborate with me on that topic. Here, it follows a short abstract of the project:

The Agulhas Current (AC) and the Gulf Stream (GS), as WBCs, play a crucial role in global ocean circulation and in determining and stabilizing the Earth's climate. Understanding and modeling their mean paths, variability and alteration by the on-going climate change is of uttermost importance for climate modeling and society as and they can affect the productivity of fishing areas. The AC and GS have their own specificities.

The GS is characterized by a separation near Cape Hatteras and a penetration to the North Atlantic basin, where it acts as the main conduit for the upper branch of the Meridional Overturning Circulation (hereinafter MOC). To the south of Africa, although most of the subtropical warm and salty water masses carried by the AC retroflect back to the Indian Ocean, some penetrate westward in the South Atlantic. This salient feature, known as the Agulhas leakage, is a potential driver of variability of the MOC in the Atlantic. The representation of those features is a long-standing challenge for modelers. The thermal and mechanical interactions between the ocean eddies and the atmosphere have been shown

to partially control the WBCs dynamic. Another possible interaction between the ocean and the atmosphere is the wave feedbacks to the atmosphere and the ocean. This interaction is generally ignored when assessing WBCs although it could have a significant effect on their dynamic. In this project, our main hypothesis is that the wave feedbacks can partly control the WBCs by altering the turbulent fluxes (e.g., by a change of sea surface roughness), the energy exchange between the ocean and the atmosphere (e.g., redistribu-tion of energy due to the wave generation, Stokes drift), the ocean mixing (e.g., Langmuir turbulence), and both currents and sea surface temperature (and, thus, their respective feedbacks to the atmosphere).

Mentoring and Research Team

My main motivations to obtain the HDR lies on the fact I would like to supervise my tried to push my students or post-doc to share their work locally (to the laboratory or the University), nationally, and internationally. I have always used community models and developments, so I think a student should to be encouraged to share her/his development (tools, models, etc) with all the community. This would better fit the scientific community but also, from a personal point of view, it would help the student to develop new collaborations.

In the following, I will briefly sum up my supervising experiences.

- the Mediterranean Sea using a combined approach of in-situ data and numerical models. She also actively participated to the development of an operational model (see next section). Her main results have been published in two articles (Juza et al., 2013(Juza et al., , 2016)).

-Postdoc, Faycal Kessouri, 2016Kessouri, -2017. . Faycal joined UCLA in 2016 thanks to the NOAA Acidification project. I closely co-supervised him during this period and I am still closely collaborating with him from France. His main goal is to assess the role of the mesoscale and submesoscale currents in determining the net primary production and the oxygen concentration over the U.S. West coast. We are currently writing 5 papers based on his results or his contribution to my own research (Kessouri et al., 2018a,b;Renault et al., 2018a;Deutsch et al., 2018;Chen et al., 2018).

-Postdoc, Ru Chen, 2017-2018. Ru joined UCLA in 2017 through my NSF project.

Her main goal is to characterize the California undercurrent and its role in determining the net primary production and the oxygen concentration. She's currently writing a paper synthesizing her results (Chen et al., 2018). She is also closely working with Faycal on the biogeochemical aspects of her research.

-Researcher, Sebastien Masson, 2015-2016. Sebastien has a permanent position at LOCEAN but joined UCLA for 2 years to work with me on my NSF project. His main goal was to develop a realistic coupled configuration of the Humboldt Upwelling System and to characterize the role of the spatial resolution in determining the Stratocumulus cloud deck over this region. Sebastien is still strongly involved in my current research in particular, on the air-sea interactions, but also in my ANR project. See publications (Renault et al., 2016c(Renault et al., , 2017a(Renault et al., , 2019b;;Jullien et al., 2018).

Introduction 1 A 6 Perspectives 6 . 1 1

 16611 Description of the Data, Experiments and Methods 1.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Current Feedback in a Coupled Model . . . . . . . . . . . . . . . . . . . . . . 1.3 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 A Simplified Kinetic Energy Budget . . . . . . . . . . . . . . . . . . . . . . . 1.5 A Full KE budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Spectral Flux of Surface Ocean Geostrophic Kinetic Energy . . . . . . . . . . 1.7 Coupling Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A Direct Control of the Oceanic Circulation, from the Large Scale to the Submesoscale 2.1 A Large Scale Effect: A Slow Down of the Gyre . . . . . . . . . . . . . . . . . 2.2 At the Mesoscale: An "Eddy Killer" . . . . . . . . . . . . . . . . . . . . . . . . 2.3 At the Submesoscale: A Catalizer but Still a Killer, the case of the California Current System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Conclusion of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Control of the Western Boundary Currents by the Current Feedback 3.1 The Case of the Gulf Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Case of the Agulhas Current . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Reduction of the Eddy-Mean Flow Interactions . . . . . . . . . . . . . . . . . 3.4 Conclusion of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 On the Atmospheric Response to the Current Feedback 4.1 Coupling Coefficient between Current and Stress . . . . . . . . . . . . . . . . 4.2 Coupling Coefficient between Current and Wind . . . . . . . . . . . . . . . . 4.3 Indirect Effect on the Precipitation over the Agulhas Current . . . . . . . . . 4.4 Conclusion of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Disentangling the Mesoscale Thermal and Current Feedbacks 5.1 Disentangling The Current Feedback . . . . . . . . . . . . . . . . . . . . . . . 5.2 Disentangling The Thermal Feedback . . . . . . . . . . . . . . . . . . . . . . 5.3 Conclusion of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Toward a New Paradigm: Recipes How to Best Force an Ocean Model . . . 6.2 On the Biogeochemical Response . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Control of the Precipitation by Mesoscale Air-Sea Interactions . . . . . . . . 6.4 A Missing Piece of the Puzzle: the Wave Feedbacks to the Atmosphere and the Ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Implication in Research Project . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Mentoring and Research Team . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Referring activities and outreach . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 :

 1 Figure 1: Mean Biases in Sea Surface Temperature in climate models. Figure from Wang et al. (2014). The black squares represent the regions where at least 19 of the 22 models have the same SST bias sign.

  Stress and Wind from QuikSCAT . . . . . . . . . . . . . . . 1.1.2 AVISO Altimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Sea Surface Temperature . . . . . . . . . . . . . . . . . . . . . . . . . US West Coast configuration . . . . . . . . . . . . . . . . . . . . 1.3.2 A High Resolution Configuration of the US West Coast . . . . . . . 1.3.3 The North Atlantic Configuration . . . . . . . . . . . . . . . . . . . 1.3.4 The Greater Agulhas Region . . . . . . . . . . . . . . . . . . . . . . 1.3.5 The Tropical Chanel Configuration . . . . . . . . . . . . . . . . . . . Feedback Coupling Coefficients . . . . . . . . . . . . . . . 1.7.2 Thermal Feedback Coupling Coefficients based on Derivatives . . 1.7.3 Thermal Feedback Coupling Coefficients based on Mesoscale Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8.1 10-m wind and Equivalent Neutral Wind . . . . . . . . . . . . . . . 1.8.2 Submesoscale characterization . . . . . . . . . . . . . . . . . . . . . 1.8.3 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8.4 Available Potential Energy . . . . . . . . . . . . . . . . . . . . . . . 1.8.5 Surface Stress Induced Ekman Pumping . . . . . . . . . . . . . . . 1.8.6 Spatial Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I sum up in this Chapter the different data, sets of experiments and some methods I used in this manuscript.

Figure 1 .

 1 1 illustrates the domains configuration. To assess the different effects of the current feedback (i.e., from the submesoscale to the large scale), I developped or used configurations over regions characerized by weak mean dynamic but a relatively large mesosale and submesoscale activity (as the US West coast), and over regions characterized by both large mean and mesoscale activities and characterized by the presence of a strong Western Boudary Current (i.e., the Gulf Stream and the Agulhas Current). I finally used the PULSATION (ANR from S. Masson) tropical chanel configuration that helped me to have a quasi-global picture of the CFB effects.

  coordinate model with split-explicit time stepping and with Boussinesq and hydrostatic approximations. ROMS is implemented in a configuration with two offline nested grids. The coarser grid extends from 170 • W to 104 • W and from 18 • N to 62.3 • N along the U.S. West Coast and is 322 x 450 points with a resolution of 12 km. Its purpose is to force the second domain. The second domain grid extends from 144.7 • W to 112.5 • W and from 22.7 • N to 51.1 • N (Fig. 2.5). The model grid is 437 x 662 points with a resolution of 4 km. The boundary condition algorithm consists of a modified Flather-type scheme

  Weather Research and Forecast (WRF)(version 3.6, Skamarock et al. 2008) is implemented in a configuration with two nested grids. The largest domain covers the North American West Coast with a horizontal resolution of 18 km (not shown); the inner domain covers the U.S. West Coast, with a horizontal resolution of 6 km (seeRenault et al. 2016b), which is slightly larger than the ROMS 4 km grid. The coarser grid (WRF18) reproduces the large-scale synoptic features that force the local dynamics in the second grid, each using a one-way offline nesting with three-hourly updates of the boundary conditions.The coarser grid simulation (WRF18) is first run independently. It is initialized with the Climate Forecast System Reanalysis (CFSR) (≈ 40 km spatial resolution;[START_REF] Saha | The NCEP climate forecast system reanalysis[END_REF] from 1st January 1994 and integrated for 6 years with time-dependent boundary conditions interpolated from the same three-hourly reanalysis. Forty vertical levels are used, with half of them in the lowest 1.5 km. The nested domain (WRF6) was initialized from the coarse solution WRF18 on 1st June 1994 and integrated for 5.5 years.

  split-explicit time stepping and with Boussinesq and hydrostatic approximations. The model is implemented from the 4km configuration presented above. The coarser grid extends from 170 • W to 104 • W and from 18 • N to 62.3 • N along the U.S. West Coast and is 322 x 450 points with a resolution of 12 km. Its purpose is to force the second domain. The second domain grid extends from 144.7 • W to 112.5 • W and from 22.7 • N to 51.1 • N (Figure 2.13). The model grid is 437 x 662 points with a resolution of 4 km. Both the third and fourth domain grids encompass the Central California region. The high resolution grid has 1000 x 1520 points with a resolution of 500 m (NOCRT500 and CRT500). As in Capet et al. (2008c), the assumption underlying this approach is that SMCs developing at higher resolutions do not have significant upscaling effects on the mesoscale or mean circulation outside the Central California domain. The model have a similar configuration to Renault et al. (2016d) and to the description of the US West configuration provided above, with 60 vertical levels for the 500 m grid; the vertical grid is stretched for increased boundary layer resolution using stretching surface and bottom parameters of h cline = 250 m, θ b = 1.5, and θ s = 6.5. Initial and horizontal boundary data for T, S, surface elevation, and horizontal velocity are taken from the quarter-degree, daily-averaged Mercator Glorys2V3 product 1.

WRF (version 3 . 7 . 1 ,

 371 [START_REF] Skamarock | A description of the Advanced Research WRF version 3[END_REF]) is implemented in a configuration with three grids. The domains is slightly larger than the ocean domains to avoid the effect of the WRF sponge (4 points). They have a horizontal resolution of 18 km, 6 km, and 2 km. The 18 km and 6 km domains are initialized with the Climate Forecast System Reanalysis (CFSR) (≈ 40 km spatial resolution;[START_REF] Saha | The NCEP climate forecast system reanalysis[END_REF]) from 30th December 1994 and integrated for 5.5 years with time-dependent boundary conditions interpolated from the same six-hourly reanalysis. Forty vertical levels are used, with half of them in the lowest 1.5 km, as inRenault et al. (2016b). The parameterizations used are the same asRenault et al. (2016d). Note WRF has a slight coarser spatial resolution than the ocean model mainly because of the computational cost, which is much higher for an atmospheric model. Moreover, when coupling a 500-m oceanic model, having a 2-km atmospheric model is enough because (1) as shown byRenault et al. (2017a), s τ depends on the large scale wind, and (2) in the atmospheric model, the Planet Boundary Layer (MYNN2.5) response to the current and thermal feedbacks is basically 1D and the CROCO effective resolution is about 4δx (i.e., ≈ 2.5km for a 500m solution), thus, a 2-km resolution in the atmospheric model is enough to reproduce the atmospheric response to the current and thermal feedbacks.

7 . 1 ,

 71 [START_REF] Skamarock | A description of the Advanced Research WRF version 3[END_REF] is implemented in a configuration with one grid. The Climate Forecast System Reanalysis (CFSR) (≈ 40 km spatial resolution; Saha et al. 2010) is used to initialize the model and to force it at the open boundary conditions from June 1, 1999 for 5.5 years. The domain has a horizontal resolution of 18 km and is slightly larger than the ROMS domain to avoid the effect of the WRF sponge (4 points).

Figure 1 . 1 :

 11 Figure 1.1: Illustration of the domains assessed in this manuscript. The color field represents a snapshot of the mesoscale activity as simulated by PULS_CTRL.

Figure 2 . 1 :

 21 Figure 2.1: Mean F m K mg (colors) and surface stress (arrows) estimated from the observations (a), GS_NOCRT (UNCOUPLED) (b), and GS_CRT (COUPLED) (c) for the period 2000-2004. In (c) the arrows represent the difference of mean surface stress between GS_NOCRT and GS_CRT (d) F m K mg averaged over the whole domain (NATL), Gulf Stream (GS), and Center of the domain (CENTER), see black boxes on (a). The current feedback to the atmosphere decreases the surface stress and reduces F m K mg over the whole North Atlantic by 30%. Figure from Renault et al. (2016c).

Figure 2 . 2 :

 22 Figure 2.2: The colors represent the mean surface stress curl from SCOW and from GS_NOCRT (UNCOUPLED) and GS_CRT (COUPLED) (for the period 2000-2004). The black contour shows the negative vorticity of the surface currents from AVISO and the simulations (contour of -3.10 -7 m s -1 ). The current feedback weakens the large scale surface stress curl and improves its realism. Due to the current feedback, the surface stress is decreased along the GS, inducing a positive surface stress curl collocated over the GS. Figure from Renault et al. (2016c).

Figure 2 .

 2 Figure 2.1 depicts the F m K mg as estimated from the observations (using AVISO and SCOW) and the GS and AC simulations. The larger F m K mg values are situated along the westerlies and easterlies winds, where the current is also the strongest. Both GS_CRT and

Figure 2 . 3 :

 23 Figure 2.3: Mean depth-integrated Kinetic Energy from GS N OCRT (UNCOUPLED) (a), and GS C RT (COUPLED) (b). (c) Total depth-integrated KE overall the domain (NATL), and the GS and CENTER boxes indicated in (a) from GS N OCRT (blue) and GS C RT (black). The current feedback, by reducing F m K mg , weakens the mean circulation The integrated KE is reduced by 27%.

Figure

  Figure from Renault et al. (2016c).

Figure 2 . 4 :

 24 Figure 2.4:

Figure 2 . 5 :

 25 Figure 2.5: Top panel: Mean surface Eddy Kinetic Energy (EKE, cm 2 s -2 ) from US_NOCRT (EXP1), US_CRTF (EXP2), and US_CRT (EXP3). Bottom panel: Temporal evolution of the EKE averaged over the whole domain. The difference percentages between the uncoupled experiments and the coupled experiment are indicated. There is a reduction of the EKE when using the current to estimate the surface stress. The atmospheric response dampens the EKE reduction.

Fig. 2 .

 2 6 shows the spatial distribution of only F e K e , P e K e , and K m K e from US_NOCRT (top panel) and from US_CRT (bottom panel), and Figure 2.7 is the cross-shore profile for each term averaged between 30 • N and 45 • N from US_NOCRT, US_NOCRTF, and US_CRT. As in Marchesiello et al.

Figure 2 . 6 :

 26 Figure 2.6: Depth-integrated EKE-budget components (cm 3 s -3 ) from US N OCRT (EXP1, top) and US C RT (EXP3, bottom): from left to right: the eddy wind work (F e K e ), the baroclinic conversion (P e K e ), and the barotropic conversion (K m K e ). F e K e and P e K e are the main energy source terms. The reduction of the EKE in Fig. 2.5 is explained by the reduction of F e K e by the current feedback. Figure from Renault et al. (2016d).

Figure 2 . 7 :

 27 Figure 2.7: (a) F e K e cross-shore profiles (cm 3 s -3 ) averaged between 30 • N and 45 • N from US N OCRT (EXP1, blue), US C RTF (black, EXP2), and US C RT (red, EXP3). (b) Differences between US N OCRT and US C RTF (black), and US N OCRT and US C RT (red). (c) same as (a) except for F e K eg . (d) Same as (b) except for the geostrophic eddy wind work F e K eg . The total integrated differences over the box [30 • N and 45 • N x d=500 km] between US N OCRT and the other experiments are indicated in the legend. Two regions can be distinguished: the coastal region (cross-shore distance d < 80 km), and the offshore region (d > 80 km). In the coastal region there is a reduction of F e K e mainly through its geostrophic component; in the offshore region there is an actual sink of F e K e again, through its geostrophic component (F e K eg ). The wind response to the current dampens the F e K e reduction. Figure from Renault et al. (2016d).

Figure 2 . 8 :

 28 Figure 2.8: Geostrophic eddy wind work (F e K eg ) from (a) US N OCRT (EXP1) and (b) US C RT (EXP3). The reduction of F e K e is mainly explained by a coastal reduction of F e K eg , and an offshore sink of energy through F e K eg . Figure from Renault et al. (2016d).

Figure 2 . 9 :

 29 Figure 2.9: Schematic representation of the current feedback effects over an anticyclonic eddy, considering a uniform southward wind. The green, black, and blue arrows represent the wind, surface stress, and surface current, respectively. The red (blue) shade indicates a positive (negative) F e K e . The black (green) +/-signs indicate the current-induced stress (wind) curl. (a) A simulation without current feedback (e.g., US N OCRT). (b) A simulation that takes into account the current feedback in the estimation of the surface stress but neglects the atmospheric response (e.g.,

Figure 2 . 10 :

 210 Figure 2.10: Schematic representation of the current feedback considering a uniform southward wind blowing along the coast. (a) A simulation without current feedback (e.g., US N OCRT). (b)

Figure 2 . 11 :

 211 Figure 2.11:

Figure 2 .

 2 Figure 2.12: (a) Mean eddy wind work (F e K e ) estimated using a temporal filter (91 days). (b) Predicted F e K ep = 2 ρ o s τ EKE using the seasonal values of s τ and EKE. A negative F e K e indicates a transfer of energy from the oceanic eddies to the atmosphere. It induces a damping of the eddies.

Figure

  Figure from Renault et al. (2017a).

  is implemented over the U.S. West Coast and is coupled with the Weather Research Forecast (WRF Skamarock et al. 2008) model using an horizontal spatial resolution of 500 m for the ocean and of

Figure 2 .

 2 Figure 2.13: Ocean (OCE) and Atmosphere (ATM) models configuration illustrated by snapshots of surface vorticity from the CTRL500 simulation.

  2.14a).The spectral KE density integrated over the submesoscale range is reduced by 14%, which is close to the first SKE reduction estimate. The SMCs are associated with large vertical velocity (w), horizontal vorticity (ζ = ∂ x v -∂ y u), and horizontal buoyancy gradient at the surface(Capet et al., 2008d; Srinivasan et al., 2017). To confirm the impact of the CFB on SMCs, the variance of w (from the surface to 100m depth) and b are computed for NOCRT500 and CTRL500 (Fig.2.14b,c). When including the CFB, both w and b variance are reduced in the submesoscale range, indicating a weakening of the submesoscale frontal intensity. The reduction of the SMCs can also be highlighted by Probability Density Functions (PDFs) for w and ζ. Basically the CFB reduces the vertical velocities. The PDF of w has a higher standard deviation without CFB. The occurrence of |w| > 10 m day -1 is reduced by16.5% (Fig. 2.14d). A similar result is found for ζ. Finally, the weakening of the SMCs in CTRL500 is corroborated by a reduction of the variances of w from 2.14 × 10 -8 m 2 s -2 to 1.76 × 10 -8 m 2 s -2 (i.e., by 18%) and of ζ from 2.29 × 10 -9

Figure 2 .

 2 Figure 2.14: a) Horizontal Surface KE spectrum. b) Vertical velocity w averaged between surface and 100 m depth spectrum. c) Surface buoyancy b spectrum. d) Probability Density function of w over all the domain between surface and 100 m depth, but excluding the upwelling region (first 50 km offshore). NOCFB stands for NOCRT500 and CFB stands for CFB500. Figure adapted from Renault et al. (2018b).

  (2012) define a thermal coupling coefficient based on the surface stress magnitude and SST anomalies. Such a coefficient at submesoscale has a value of ≈ 1.3 × 10 -2 N m -2 in both simulations, which is similar to the values found by O'Neill et al. (2012) at the mesoscale.

Figure 2 .

 2 Figure 2.16b,c shows F s K s estimated from NOCRT500 and CTRL500. Consistent with the positive s τ , NOCRT500 has a positive F s K s , i.e., a slight energization of the SMCs by the atmosphere induced by the TFB. At the mesoscale this TFB energization is not present. At the submesoscale the wind has not previously been identified as a significant source (or sink) of energy because of the smoothness of the stress product used to force the oceanic model(Capet et al., 2008c). When taking into account the CFB in CTRL500, because of a negative s τ , F s K s becomes negative, indicating a sink of energy at the SMCs that represents a source of atmospheric energy. At the submesoscale the CFB overwhelms the TFB effect on F s K s . The domain averaged F s K s magnitude is indeed 3.5 times larger in CTRL500 than in NOCRT500. It should, thus, induce a dampening of the submesoscale activity and explain the enhanced V in the KE balance(Figure 2.15). Those results are confirmed by analyzing the wind-work (FK = ø • u) wavenumber spectrum. In NOCRT500, the wind-work causes a slight energization of the ocean at the submesoscale while, consistent with the previous results, the wind-work spectrum is always negative in CTRL500, indicating a sink of energy. The magnitude of the power spectrum is between 2 to 7 times larger in CTRL500 than in NOCRT500, confirming the primary effect of the CFB on the wind-work. Finally, the difference in wind-work spectrum between NOCRT500 and

Figure 2 .

 2 Figure 2.15: a) Spectra of Kinetic Energy (KE) tendency terms [m 3 s -3 ] (submesoscale range) for injection of energy by baroclinic conversion (C), 3D pressure work (P), wind and vertical mixing work (V), 3D Advection (A), the horizontal mixing (H), and the tendency term (T). (see Chapter 1 for more details.) The solid (dashed) lines represent CTRL500 (NOCRT500)). All terms have been averaged over the summer period and between the surface and 100 m depth. b) Kinetic Energy Balance averaged over the upper 100 m depth for a period of 3 months. The spectra of KE tendency terms have been integrated over the submesoscale range (0.0822 -0.999 cycle km -1 ).

Figure 2 .

 2 Figure 2.16: The CFB induces a sink of energy from SMCs to the atmosphere but also an additional injection of energy by baroclinic conversion that partly counteracts the sink of energy. a) Binned scatter-plot of the full time series of 1-day running means of surface stress curl and surface current vorticity over the 500 m CROCO simulations domain. The bars indicate plus and minus one the standard deviation from the average value (stars). The linear regression is indicated by a line, and the slope s τ is indicated in the legend (10 -2 N s m -3 ). NOCRT500 and CTRL500 are represented in blue and orange, respectively. NOCRT500 has a slight positive slope that may be due to the TFB to the atmosphere, but the CFB overwhelms it in CTRL500, causing a negative slope. The CFB induces submesoscale surface stress structures. b) Mean submesoscale wind-work (F s K s ) from NOCRT500 and (c) CTRL500. The CFB induces a sink of energy from the SMCs to the atmosphere, which in turn dampens the SMCs. d) Two-dimensional wind work (FK = ø • u ) spectrum from NOCRT500 (blue) and CTRL500 (orange). e) Twodimensional co-spectrum of Ekman pumping induced by the stress (w τ ) and b averaged over 100 m depth for NOCRT500 (blue) and CTRL500 (orange).

  The sink of energy by wind-work is in fact partially counteracted by a second effect of the induced Ekman pumping: the induced vertical velocities cause an additional injection of kinetic energy into SMCs by enhanced baroclinic conversion. This injection by Ekman pumping dominates over the reduction of the mesoscale APE source and partly re-energizes the SMCs relative to their wind-work depletion.

  sink of energy by wind-work is partially counteracted by a second effect of the induced Ekman pumping: the induced vertical velocities cause an additional injection of kinetic energy into SMCs by additional baroclinic conversion. This injection by Ekman pumping dominates over the reduction of the mesoscale APE source and partly re-energizes the SMCs relative to their wind-work depletion.The current feedback to the atmosphere should have an influence on the SMCs everywhere in the world ocean; however, the SMCs could have different local responses.For the U. S. West Coast, the main drivers that explain the alteration of the SMCs variability are the mixed-layer baroclinic conversion and the negative submesoscale windwork. However, in other regions, the dampening of the SMCs could cause a reduction in the density restratification process caused by the submesoscale[START_REF] Fox-Kemper | Parameterization of mixed layer eddies. Part I: Theory and diagnosis[END_REF], thus further induce a deepening of the mixed layer; this might counteract the reduction of the mesoscale APE by the weakening of the mesoscale buoyancy horizontal gradients.

Contents 3 . 1

 31 The Case of the Gulf Stream . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Case of the Agulhas Current . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Agulhas Retroflection . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Reduction of the Eddy-Mean Flow Interactions . . . . . . . . . . . . . . . 3.4 Conclusion of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . Western Boundary Currents (WBCs) -Gulf Stream (GS), Kuroshio,Agulhas Current (AC), East Australia, Somalia Current and Brazil Currents -are the strongest oceanic currents on Earth and major features of the global ocean circulation that largely controls the Earth's climate. Understanding their equilibrium, variability and trend is critical to oceanic and climate research.

  Understanding and modeling its mean path and variability is of uttermost importance for climate modeling. Upstream of Cape Hatteras the mean path is constrained by the topography[START_REF] Gula | Gulf Stream dynamics along the southeastern US seaboard[END_REF] and is generally well understood and resolved by numerical models. However, at separation -at Cape Hatteras and downstream -most models are characterized by large biases and too meandering a GS.Recent advances in numerical ocean modeling have shown the importance of resolving the eddy scale while simulating the GS path and separation[START_REF] Bryan | Resolution convergence and sensitivity studies with North Atlantic circulation models. Part I: The western boundary current system[END_REF][START_REF] Chassignet | Gulf Stream separation in numerical ocean models[END_REF][START_REF] Talandier | Improvements of simulated Western North Atlantic current system and impacts on the AMOC[END_REF]. Recently,[START_REF] Schoonover | North Atlantic Barotropic Vorticity Balances in Numerical Models*[END_REF] confirmed the difficulties of numerical models to represent the mean GS separation and the post-separation stability using state of the art numerical simulations (across model platforms and resolutions). In particular, the vicinity of Cape Hatteras is erroneously marked by the presence of a standing eddy, making the GS separation convex. The reason for this sensitivity is not yet clear, although a strong link between GS separation and the strength and depth of the southward flowing deep western boundary current has been

Figure 3 . 1 :

 31 Figure 3.1: Eddy Kinetic Energy (EKE) for the period 2000-2004 from AVISO, GS_NOCRT (UNCOUPLED) , and GS_CRT (COUPLED) for the North Atlantic (a, b, c), and around the Gulf Stream (GS) separation (d, e, f). The black contours in (d, e, f) depict the mean EKE from AVISO (one contour each 1000cm 2 s -2 ). The current feedback causes a drastic reduction of the EKE by 30%. In particular, it limits the propagation of the eddies far from the mean GS path.

Figure

  Figure fromRenault et al. (2016c).

Figure 3 . 2 :

 32 Figure 3.2: Eddy killing improves the Gulf-Stream simulation. The color field presents a snapshot of surface currents relative vorticity from (a) a coupled simulation without current feedback to the wind (NOCFB, GS_NOCRT) and (b) a coupled simulation with current feedback (CFB, GS_CRT). The black contour lines represent the simulated long-term mean GS path and the gray contour line the observed GS path (contour of 0.6 m s -1 ). c) Probability Density Function of SLA around the diamond box [indicated in (a)] from AVISO (blue); NOCFB (green); and CFB (red). The eddy-resolving coupled model rectifies a long-standing bias of bimodal and unsteady separation in numerical models. Figure adapted from Renault et al. (2016c).

Figure 3 .

 3 Figure 3.3 depicts the mean SSH from AVISO and from the experiments. AGH_NOCRT is c characterized by the presence of two too persistent standing eddies nearby Port Elizabeth (around 36 • S -32 • E), and over the AC retroflection. The eastern standing eddy is induced by the Natal Pulses that propagate from the Natal Bight and eventually merge with the AC near Port Elizabeth around 36 • S -32 • E (e.g., Rouault and Penven 2011) but also from eddies from the ARC, which detach and propagate westward (McWilliams,

Figure 3 . 3 :

 33 Figure 3.3: The figure colors show the mean geostrophic Eddy Kinetic Energy (EKE) for the period 2000-2004 from (a) AVISO, (b) AGH_NOCRT (NOCURR), and (c) AGH_CRT (CURR). Contours show 20-cm delineations of mean sea surface height for this period. AGH_NOCRT is characterized by a too large EKE, and by the presence of a standing eddy around the east of the Agulhas Basin that has a strong influence on the retroflection (see Fig. 3.4). (d) Mean EKE over the whole domain, the Mozambique Channel, the AC retroflection, the ARC, and the Benguela (black boxes on (a)). The current feedback in CURR induces a drastic reduction of the EKE by 25% over the whole domain. It limits the presence of the standing eddies, improving the realism of the mean circulation and of the Agulhas Current retroflection. Figure from Renault et al. (2017b).

Figure 3 . 4 :

 34 Figure 3.4: (a) Zonal Probability Density Function (PDF) of the retroflection location for the period 2000-2004 from (a) AVISO, (b) AGH_NOCRT (NOCURR), and (c) AGH_CRT (CURR).The black lines represent the PDF values and their standard deviations obtained using a bootstrap method (see text). The red lines represent the Gaussian fits applied on the significant PDF peaks.The blue circles highlight the center of each regimes (i.e., the peaks of the PDF), and the blue lines represent the spatial extension of each regime as estimated from the standard deviation of the Gaussian fits. The % of occurrences of each regime is indicated in blue (see text for more details). The current feedback to the atmosphere improves the representation of the Agulhas Current retroflection. In particular, by weakening the mesoscale activity, it strongly reduces the importance of the eastern retroflections, shifting the distribution of the retroflection location. (d) Illustration of an Agulhas Current eastern Retroflection from AVISO as estimated by the detection method (See Renault et al. (2017b)). The colors represent the Sea Surface Height (SSH) from AVISO; the thick black contour represents the detected Agulhas current and the red dot its retroflection longitude and latitude. e) Mean Eddy Kinetic Energy during the eastern Retroflections. The black box is used in Fig. 3.5. The solid line represents the shipping line ("Good-Hope Line") section, whereas the dotted lines represents the control sections used to estimate the Agulhas Current leakage using Lagrangian particles. Figure from Renault et al. (2017b).

Figure 3 . 5 :

 35 Figure 3.5: Relationship between the Eddy Kinetic Energy (EKE), the eddy windwork (F e K eg ), and the leakage from AGH_CRT (CURR). The EKE and F e K eg have been spatially average over the box indicated in Fig. 3.4e. The resulting timeseries and the leakage timeserie have been lowpass filtered ( f c = 180 days -1 ) and are shown on (a). The lag-correlation between EKE and leakage is plotted on (b). A large EKE near Port Elizabeth induces a large deflection of energy from the ocean to the atmosphere but also a short-cut of the Agulhas Current and, then, a weakening of the Agulhas Current leakage. Figure from Renault et al. (2017b).

Figure 3 .

 3 4e depicts the mean EKE averaged over the eastern regime mode periods. The very large anomalies of EKE near Port Elizabeth (more than twice the long-term mean values) likely induce a short-cut of the AC and, thus, an eastern AC retroflection. This relationship between EKE and AC is in good agreement with Backeberg et al. (2012) and[START_REF] Beal | Broadening not strengthening of the Agulhas Current since the early 1990s[END_REF]. Finally, to discard an eventual effect of the atmospheric forcing in our simulation (WRF) on the representation of the third category (eastern retroflection), an additional uncoupled simulation has been carried out using climatological forcing (e.g., QuikSCAT stress) as in e.g.,Capet et al. (2008a), with the same spatial resolution as NOAGH_CRT and AGH_CRT. That simulation has similar characteristics to NOAGH_CRT in terms of EKE and AC retroflection and, in particular, has an overestimation of the standing eddies.

Figure 3 . 6 :

 36 Figure 3.6: Spectral flux π KE (k) of surface oceanic geostrophic kinetic energy in (a) the Gulf Stream and (b) the Agulhas Current (see Chapter 1), for coupled simulations with current feedback (GS_CRT and blue). The shaded curves represent the associated error as estimated using a bootstrap method (see 1). Eddy Killing induces a large reduction of the inverse energy cascade, responsible for GS stabilization and for the observed Agulhas retroflection position.

Figure 3 . 7 :

 37 Figure 3.7: Spectral flux π KE (k) of surface ocean geostrophic kinetic energy over the Agulhas Current (same box as Fig. 3.6) from AVISO (green), and filtered coupled simulations with current feedback (AGH_CRT: CFB, red) and without current feedback (AGH_NOCRT: NOCFB, blue) (see text for more details). The shaded curves represent the associated error as estimated using a bootstrap method (see 1). Fully coupled simulations (CFB) have a more realistic energy flux π KE (k) with respect to AVISO.

Figure 4 .

 4 Figure 4.1 shows the resulting scatterplots. A coupling correlation coefficient s τ[N s m -3 ] (or s st inRenault et al. (2016d)) is defined as the slope of the linear regression in this scatter-plot. Because US_NOCRT does not consider the surface currents in its surface stress estimate, its wind stress curl does not show any significant dependence on the oceanic vorticity. US_CRTF and US C RT show a clear negative linear relationship between the surface currents vorticity and the surface stress curl, with s st < 0. The negative sign is consistent with the F e K eg sink and Fig.2.9, i.e., the current feedback induces an opposite sign surface stress curl. From US_CRTF to US C RT the magnitude of s st decreases significantly. The difference is due to the atmospheric response of an intensification of the surface wind that attenuates the current feedback effect on the surface stress. Simulations that neglect the wind adjustment to the current feedback (e.g., US_CRTF and the North Atlantic simulations of[START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF]) overestimate the reduction of the surface stress by the oceanic surface currents, missing the partial re-energization of both the atmosphere and ocean through full coupling.To quantify the effect of the mesoscale surface current on the surface stress at a global scale, the coupling coefficient s τ ([N s m -3 ]) is defined as the slope of the linear regression at each grid point between monthly average and spatially filtered (see Chapter 1 for more details) geostrophic surface vorticity (from AVISO) and surface stress curl (from a QuikSCAT product[START_REF] Bentamy | Compatibility of C-and Ku-band scatterometer winds: ERS-2 and QuikSCAT[END_REF]) over the whole altimeter-scatterometer overlap period(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) and also by seasons (not shown). The resulting global map is slightly

Figure 4 . 1 :

 41 Figure 4.1: Binned scatterplot of the full time series of 1-month running means of surface stress curl and surface current vorticity over the domain 30 • N -45 • N and (150 km < d < 500km). The bars indicate plus and minus one the standard deviation about the average drawn by stars.The linear regression is indicated by a black line, and the slope s st is indicated in the title (10 -2 N s m -3 ). From the left to the right: US_NOCRT (EXP1), US_CRTF (EXP2), and US_CRT (EXP3). US_NOCRT does not have a significant slope because it does not have the current feedback to the atmosphere, nor the surface stress. US_CRTF and US_CRT presents a clear negative linear relationship between currents and stress curl. The current feedback induces fine scale wind stress structure. Consistent with the previous results, the atmospheric response reduces the current feedback effect on the stress. Figure fromRenault et al. (2016d).

Figure 4 . 2 :

 42 Figure 4.2: The current feedback to the atmosphere linearly induces persistent surface stress anomalies, causing a sink of energy from geostrophic currents. (a) Coupling coefficient s τ between surface geostrophic current and surface stress. (b) Binned scatterplot of the full time series of 10mwind magnitude and s τ over the World Ocean. The bars indicate plus and minus one standard deviation about the mean marked by stars. The linear regression is indicated by a black line, and the slope is indicated in the title. (c) Predicted s τ = (-2.5 10 -3 |U a | + 0.013 m s -1 ) N s 2 m -4 (see text). The Figures has been realized using the data from QuikSCAT and AVISO. Figure from Renault et al. (2017a).

Figure 4 . 3 :

 43 Figure 4.3: (a) Mean eddy wind work (F e K e ) estimated using a temporal filter (91 days). (b) Predicted F e K ep = 2 ρ o s τ EKE using the seasonal values of s τ and EKE. A negative F e K e indicates a transfer of energy from the oceanic eddies to the atmosphere. It induces a damping of the eddies. The Figures has been realized using data from QuikSCAT and AVISO. Figure from Renault et al. (2017a).

Figure 4 . 4 :

 44 Figure 4.4: Cross-shore profile of the Turbulent Kinetic Energy (TKE) of the surface wind averaged between 30 • N and 45 • N from US_NOCRT (EXP1, cyan) and US_CRT (EXP3, red). The

Figure 4 . 5 :

 45 Figure 4.5: (a) Same as Fig. 4.1 but for the wind curl and the surface current vorticity in US_CRT (EXP3). There is a positive linear relationship between the current vorticity and the wind curl, i.e., the current feedback on the atmosphere induces fine scale structures in the wind field that counteract the current-induced stress structure (Fig. 4.1). This explains the dampening of the current feedback effect on the EKE. The linear regression is indicated by a black line and the dimensionless slope s w is indicated in the title. (b) Vertical attenuation of s w with respect to the surface s w . Figure from Renault et al. (2016d).

  warms up to 1.5 • . This warms up the atmosphere and alters the mean precipitation from AGH_NOCRT to AGH_CRT. The change in mean precipitation over the period 2000-2004 is defined as C rain = rain AGH_CRT -rain AGH_NOCRT ×100 rain AGH_NOCRT . A positive C rain indicates an increase of the precipitation from AGH_NOCRT to AGH_CRT. Only significant C rain (σ > 0.95 using a t-test) are shown in Fig. 4.7. Over the AC retroflection and the southern Benguela, from AGH_NOCRT to AGH_CRT the current feedback increases the precipitation rate by 50% (from 1.5 mm days -1 to 2.2 mm days -1 , see Fig. 4.7). This may be caused by the warmer SST and associated larger SST gradients over the Agulhas retroflection in AGH_CRT. Further investigation is needed to clarify the impact of air-sea interactions on the precipitation (similar as e.g., Kilpatrick et al. 2016). The other regions of the domain are not significantly impacted by the current feedback. The mean precipitation rate is fairly reproduced by the atmospheric model in both AGH_CRT and AGH_NOCRT (Figure 4.7c). Over the ocean, the main spatial gradients are well reproduced with very weak precipitation over the southern Benguela region (< 1mm day -1 ) and larger precipitation over the western part of the Agulhas Current System and, in particular, over the Agulhas Current, near Port Elizabeth (> 3mm day -1 ). Over the land, the agreement between the satellite observations and the model is remarkable. Such a good agreement is confirmed by the high resolution observations dataset from e.g., Harris et al. (2014); Lynch (2004). For instance, the precipitation caused by convective cells over the Highveld plateau is well reproduced (confirming the realism of the scheme used in the atmospheric model) as well as the arid region of the Northern Province and the local minimum of the Klein Karoo and north-east of Cederberg regions. Other variables such as mean cloud cover or mean Marine Boundary Layer Height are only marginally impacted by the SST changes from AGH_CRT to AGH_NOCRT (less than 5%, not shown). Note both simulations represent the SST feedback and, therefore, have SST large scale and mesoscale feedbacks to the atmosphere.

Figure 4 . 6 :

 46 Figure 4.6: a) The colors represent the current-wind coupling coefficient s w from AGH_CRT at each grid point and smoothed over 100 km. b) Vertical attenuation of s w with respect to the surface s w over the Agulhas Return Current box (similar results are found for other regions). c) Binned scatterplot of the mean Marine Boundary Layer Height and s w over the whole domain. The bars indicate plus and minus one the standard deviation about the average drawn by stars. The linear regression is indicated by a black line, and the slope is indicated in the title (10 -3 m -1 ). s w is

Figure 4 . 7 :

 47 Figure 4.7: Precipitation rate response to the current feedback a) Mean precipitation rate from AGH_CRT (CURR) over the period 2000-2004. b) Relative difference C rain (see text) between AGH_NOCRT and AGH_CRT. Only the significant values (σ > 95% using a t-test) are shown. c) Mean precipitation rate from the Tropical Rainfall Measuring Mission (Satellite data). The mean precipitation rate is realistically reproduced by AGH_CRT. The warmer Sea Surface Temperature and associated larger SST gradients in AGH_CRT over the Agulhas Basin and the Benguela likely induce larger precipitation in AGH_CRT with respect to AGH_NOCRT. Figure from Renault et al. (2017b).

;

  [START_REF] Eden | Effects of mesoscale eddy/wind interactions on biological new production and eddy kinetic energy[END_REF]; McClean et al. (2011); Hutchinson et al. (2010); Anderson et al. (2011); Renault et al. (2016d, 2017a); Oerder et al. (

  QuikSCAT have been largely used to characterize the wind/stress responses to the mesoscale TFB and CFB. Scatterometers represent an unique measurement technique that allowed the scientific community to improve its understanding of the air-sea interactions. In particular they have been used to demonstrate the global ubiquity and the seasonality of both TFB and CFB effects on surface winds at oceanic mesoscale (see e.g.,[START_REF] Kelly | Ocean currents evident in satellite wind data[END_REF];[START_REF] Cornillon | Warm core ring velocities inferred from NSCAT[END_REF];[START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]; Chelton and Xie (2010); O'Neill et al. (2010); ONeill et al. (2012); Renault et al. (2017a)). They have also motivated models development and analysis, like the study presented here. As detailed in Sec. ??, within a scatterometers framework, an important point to clarify is the definition of the 10m-wind. Hereinafter, the 10-m wind U a is defined as the absolute wind at the first vertical level of the atmospheric model (which has been defined at ≈ 10m), whereas the relative wind U r is defined as the difference between U a and the surface oceanic currents. Satellite scatterometers (such as QuikSCAT) provide a 10m-wind that does not correspond to U a . It is reported as the so-called Equivalent Neutral stability Wind (U ENW ,

First, it strives

  to assess to what extent the various coupling coefficients allow disentangling the TFB from the CFB. Second, it aims to determine whether scatterometers can adequately monitor the wind and stress responses to mesoscale air-sea coupling. The chapter is organized as follows: In Sec. 5.1, the current feedback coupling coefficients are assessed. Sec. 5.2 aims to address the thermal feedback coupling coefficients. The results are discussed in Sec. 5.3

Figure 5 . 1 :

 51 Figure 5.1: The current feedback to the atmosphere induces persistent surface stress anomalies that can be expressed using a linear relationship. The coupling coefficients between the surface geostrophic current vorticity and the surface stress curl (s τ ) is able to efficiently isolate the current feedback from the thermal feedback. (a) s τ as estimated from the observations. (b) s τ as estimated from PULS_CTRL (CTRL). (c) s τ as estimated from PULS_NOCRT (NOCRT).

Figure 5 . 2 :

 52 Figure 5.2: The current feedback to the atmosphere induces persistent surface 10-m wind anomalies that can also be expressed using a linear relationship. As s τ , the coupling coefficients between the surface geostrophic current vorticity and the 10-m wind curl (s w ) is able to efficiently isolate the current feedback from the thermal feedback. Scatterometers such as QuikSCAT are not able to characterize the wind response to the current feedback. (a) s w as estimated from the observations. (b) s w as estimated from PULS_CTRL (CTRL) using the relative ENW wind. (c) s w as estimated from PULS_CTRL (CTRL) using the 10m-wind.

Figure 5 . 3 :

 53 Figure 5.3: The surface current vorticity can partially drive the mesoscale wind curl variability. Scatterometers wind can not monitor it. a) Temporal correlations between the surface stress and the relative ENW from PULS_CTRL (CTRL). b) Temporal correlations between the surface stress and the 10-m absolute wind from PULS_CTRL (CTRL). c) Temporal correlations between the surface stress and the 10-m absolute wind from PULS_SMTH (SMTH). The larger correlations (in red) indicate regions where the mesoscale wind determines the stress (top-down effect). Negative correlations highlight regions where the current forces the mesoscale wind (bottom-up effect).

Figure 5 . 4 :

 54 Figure 5.4: The coupling coefficient between the surface stress curl and the cross-wind SST (s Cstr ) does not properly isolate the thermal feedback from the current feedback: the current feedback can cause surface stress mesoscale features that are correlated with the cross-wind SST. Similar results are found for s Cu . a) s Cstr as estimated from the observations for the summer period. b) s Cstr as estimated from PULS_CTRL (CTRL) for the summer period. c) s Cstr as estimated from PULS_NOCRT (NOCRT) for the summer period. d) s Cstr as estimated from PULS_SMTH (SMTH) for the summer period (note the different colorscale). Similar results are found when considering all the seasons.

  that ignores the CFB(Figure 5.4c). Surprisingly, from PULS_CTRL to PULS_NOCRT, the positive values of s Cstr diminish by ≈ 30% (Figure5.5a), likely indicating the CFB has a non-negligible influence on s Cstr , especially in the most eddying regions, e.g., the Agulhas Current signature almost disappears. As pointed out by[START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific[END_REF], geostrophic currents tend to follow isotherms, therefore their impact on the stress curl contaminates the correlation and the coupling coefficient between surface stress curl and crosswind SST gradient. The contamination of s Cstr by the CFB is furthermore confirmed by estimating s Cstr from PULS_SMTH (Figure5.4d). In such a simulation, the absence of mesoscale TFB should be reflected by weak values of s Cstr . However, s Cstr has large values in particular over the WBCs and the Indian Ocean, reflecting the influence of the current on s Cstr . s Cstr in PULS_SMTH represents on average 36% of s Cstr and can be even larger over the most eddying regions such as the WBCs (Figure5.5b). However, as explained in Chapter 1, some of the mesoscale stress signal presents in PULS_SMTH could still be due to residual SST signal. To estimate which part of s Cstr in PULS_SMTH is effectively due to the CFB, s Cstr is estimated from PULS_SMTH_NOCRT (not shown).

Figure 5 . 5 :

 55 Figure 5.5: The current feedback can cause surface stress mesoscale features that are correlated with the cross-wind SST, contaminating the coupling coefficient sC str . a) Probability Density Function of the ratio between s Cstr as estimated from PULS_NOCRT (NOCRT) and s Cstr as estimated from PULS_CTRL (CTRL). Low-level and High-level EKE regions are considered. Only positive values of s Cstr are considered as negative values do not stand for a TFB effect. The 2 • S -2 • N band is masked as the summer of each hemisphere is considered. b) Same as (a) but between PULS_SMTH (SMTH) and PULS_CTRL (CTRL). Similar results are found for s Cu and when considering all the seasons.

Figure 5 . 6 :

 56 Figure 5.6: The coupling coefficient between the mesoscale surface stress and SST anomalies (s str ) properly isolates the thermal feedback from the current feedback. Similar results are found for s u . a) s str as estimated from the observations. b) s str as estimated from PULS_CTRL (CTRL). c) s str as estimated from PULS_NOCRT (NOCRT).

Figure 5 . 7 :

 57 Figure 5.7: Probability Density Function of the ratio between s str as estimated from NOCRT and s str as estimated from CTRL. Low-level and High-level EKE regions are considered. Only positive values of s Cstr are considered as negative values do not stand for a TFB effect. Confirming Fig. 5.6, the current feedback does not influence the coupling coefficients based on stress or wind magnitude.

  ;[START_REF] Gaube | Satellite observations of mesoscale eddy-induced Ekman pumping[END_REF];[START_REF] Seo | Eddy-wind interaction in the California Current System: dynamics and impacts[END_REF];Renault et al. (2016d);[START_REF] Oerder | Impacts of the Mesoscale Ocean-Atmosphere Coupling on the Peru-Chile Ocean Dynamics: The Current-Induced Wind Stress Modulation[END_REF]). For both TFB and CFB, it may alter the biogeochemical production by tampering the concentration of nutrients or iron in the euphotic zone. Understanding and characterizing those feedbacks is therefore crucial to represent the mean and mesoscale ocean circulation, but also the ocean production, ventilation, and carbon uptake. Finally, those results also raise up the question how to force an ocean model.Consistent with[START_REF] Duhaut | Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation[END_REF];[START_REF] Chelton | Summertime coupling between sea surface temperature and wind stress in the California Current System[END_REF], we show the use of scatterometers as a forcing can be the source of various biases mainly because they represent relative ENW wind and also because the surface stress already incorporates the mesoscale anomalies induced by the real eddies (that are not coherent with simulated eddies by an ocean model without data assimilation). Simple parameterizations based on coupling coefficients could be used to mimic the air-sea interactions. However to do so, the coupling coefficients used should allow disentangling the TFB and CFB effects on the wind (or stress). Future satellite missions (such as e.g.,SKIM, Ardhuin et al. (2017) and WaCM[START_REF] Bourassa | Winds and currents mission: Ability to observe mesoscale AIR/SEA coupling[END_REF];[START_REF] Rodríguez | Estimating Ocean Vector Winds and Currents Using a Ka-Band Pencil-Beam Doppler Scatterometer[END_REF]) would likely allow measuring the surface stress and the surface currents in a consistent way and, thus, would help to better understand and characterize the ENW and surface stress responses to both TFB and CFB.

  nault et al. (2016d) to the Renault et al. (2016d) experiments. As in Renault et al. (2016d),

  USW4 has slightly less EKE than US_CRT (by 5%). This difference might partly be due to the different open boundary conditions used (Mercator vs. Simple Ocean Data Assimilation (SODA, Carton and Giese 2008) in Renault et al. 2016d), which may induce slightly different mesoscale behaviors, but it also probably reflects some bias related to the simple parameterization of the wind response to the current feedback (discussed in the next paragraph).

Figure 6 . 1 :

 61 Figure 6.1: a) Temporal evolution of the Eddy Kinetic Energy (EKE) averaged over the whole domain. US_NOCRT (EXP1), US_CRTF (EXP2), and US_CRT (EXP3) are the SST-coupled, uncoupled with current feedback, and fully coupled experiments from Renault et al. (2016d), respectively. b) Binned scatter-plot of the time series of 1-month running means of surface stress curl and surface current vorticity over the domain 30 • N -45 • N and an offshore strip (150 km < d < 500 km, where the orography and coastline meandering effects are insignificant). from US_NOCRT, US_CRTF, US_CRT, and USW4. The bars indicate plus and minus one the standard deviation about the average drawn by stars. The linear regression is indicated by a black line, and the associated slope s st [10 -2 N s m -3 ] is indicated in the title. The slope error is estimatedas the standard deviation of the slopes time series estimated using the full time series of 1-month running means of surface stress curl and surface current vorticity. The parameterization of the wind response to the current feedback allows USW4 to have similar levels of EKE than the fully coupled experiment (US_CRT); USW4 has a clear negative linear relationship between current vorticity and stress curl. s st from USW4 is slightly larger than s st from US_CRT, but it is within the range of the associated estimation error.

Figure 6 . 2 :

 62 Figure 6.2: Mean geostrophic EKE estimated from (a) AVISO and (b) USW4 over the period 1995-2013. The EKE of USW4 is computed using low-pass filtered geostrophic velocities (Gaussian spatial filter with 36-km-half-width) as an approximate match to the AVISO resolution. The current feedback to the atmosphere dampens the eddies and, thus, allows the simulation to have a realistic EKE level, albeit with not quite the same spatial pattern.

Figure 6 . 3 :

 63 Figure 6.3: Depth-integrated kinetic energy budget components [cm 3 s -3 ] from USW4 over the period 1995-2013 (see Renault et al. 2016d for definitions): (a)(c) geostrophic eddy wind work (F e K eg ), baroclinic conversion (P e K e ), and barotropic conversion from the mean flow (K m K e ). (d) Cross-shore bins of the energy budget components averaged over 50-km intervals and between 30 • N and 45 • N. The geostrophic eddy wind work (F e K eg ) is estimated from USW4 (red) and from observations (QuikSCAT and AVISO; grey). For the first 50 km off the coast the observations estimate is not shown because of the QuikSCAT and AVISO coastal issues. The baroclinic conversion

  lation, the current feedback to the atmosphere dampens the mesoscale activity, but the wind response partly re-energizes it. Long-term comparisons with satellite observations show a realistic simulation results for the EKE and the energy transfer between the ocean and atmosphere. Oceanic models, if uncoupled, should take into account the current feedback and should include a parameterization of the wind response for a realistic representation of the transfer of energy between the atmosphere and the ocean, and thus of the mesoscale and mean oceanic circulations.As explained in Chapters 2 and 3, the current feedback can also slow down the mean circulation at a basin scale by reducing the mean input of energy from the atmosphere to the ocean (e.g.,[START_REF] Luo | Reducing climatology bias in an ocean-atmosphere CGCM with improved coupling physics[END_REF]; Eden and Dietze 2009 and control major western boundary currents. The parameterizations tested here (based on s w ) and the other one suggested inRenault et al. (2017a) (see alsoChapter 4) should be test at global scale and over other regions. This is something I'm currently doing by using the quasi-global ocean configuration (PULSATION, e.g., PULS_CTRL). The results presented in this manuscript also raise the questions of how to interpret the surface stress and wind from observational or atmospheric simulation products and how to force an uncoupled oceanic simulation.

6 . 3 . 1

 631 My on-going research also aim to assess to what extent the mesoscale air-sea interactions control the precipitation. I'm collaborating on that topic since a couple of years with Agostino Meroni during his PhD (See Chapter 8), Fabien Desbiolles (PostDoc at University of Cape Town, see Chapter 8), and, more recently with a Master II student (R. Ngomo, Benin, see Chapter 8). I summarize in the following the two main papers derived from those collaborations. Role of the Mesoscale Sea Surface Temperature in Determining the Precipitation Mesoscale Sea Surface Temperature (SST) variability plays an important role in shaping local atmospheric boundary layers through thermodynamic processes. This study focuses on the upscaling effects of mesoscale SST gradients in sensitive areas on the southern Africa regional atmospheric circulation. Using regional atmospheric model sensitivity experiments which differ only in the mesoscale SST forcing characteristics (either the full spectrum of SST variability or only its large-scale components are included), we

6. 4 A

 4 Missing Piece of the Puzzle: the Wave Feedbacks to the Atmosphere and the Ocean In this manuscript, I focused on the Current Feedback to the Atmosphere and (briefly)

Figure 6 . 4 :

 64 Figure 6.4: Example of the Significant Wave Height (m.) as simulated by the NOAA WW3 global model.

Figure 6 . 5 :

 65 Figure 6.5: Cartoon of the main Wave feedbacks to the Ocean and the Atmosphere in the presence of a Western Boundary Current and mesoscale activity.

8. 1

 1 Implication in Research Project I have a solid experience in writing and managing research projects. Through those projects, I have developed my research line and I've had the opportunity to supervise students and post-docs. In the following, I will synthesize the main projects I managed or co-managed. main project I have managed in my career and I realize now it has been a great opportunity. It has re-enforced and complemented my knowledge on the Earth System Interactions since, as described in the next paragraph, this project shifts my area of research from the U.S. West Coast to other regions (mainly Eastern Boundary Upwelling System (EBUS)). Overall, it has strenghtened my main research line on air-sea coupling, and has given me a better understanding of the associated biogeochemical response. As stated before, this project dealt with the EBUS, but it also gave me the chance to extend my air-sea coupling research to Western Boundary Currents (as the mean dynamic is much stronger and also because the Agulhas Current has a strong influence on the Benguela Upwelling System) and also to a tropical channel (45 • S 45 • N) simulation (with S. Masson through his ANR PULSATION project). Within the framework of this project, I was able to fund my former position at UCLA as well as small team of postdocs, and to write several papers (See Chapter 9). I transcribe in the following the abstract of the project in the following.

  led by J.C. McWilliams. I mainly participated on the physical side and co-supervized a post-doc hired through this project. The primary tasks of this project are the following: (1) Develop a coast-wide OHA model of the CCS (Baja California to British Columbia) based on the Regional Oceanic Modeling System (ROMS), comprised of circulation, biogeochemical cycles, lower-trophic ecosystem, a rudimentary food web for higher-trophic animals, with regional down-scaling into coastal sub-regions with finer spatial resolution in the simulation. The model will be used for validation against measurements in an historical reanalysis, for demonstration of the consequences of local pollution inputs, and for a forecast of the likely future trends in OHA. (2) Collect and analyze laboratory and field data on ecologically important pteropod species to derive empirically-based sensitivities of biological rates to OHA and temperature, and then incorporate them into the model as new ecosystem parameterizations. (3) Use the model to understand relative contributions of the various drivers of OHA in the CCS. (4) Transmit these findings to coastal zone managers and help them explore the implications for marine resource management and pollution control. This project was led by C. Dong (UCLA). The overall objective of this project was to improve the understanding of multiscale (interannual, seasonal , and intra-seasonal scales) variations of physical processes (wind, current, and wave) in an extended southern California coast. Specific objectives are as follows: (1) Extend the existing12-years (1996 - 2007) hindcast product in the South Cafifornia Bight (SCB) to a broader geographic region including Morro Bay and north of Point Conception , and tomodern 10 years (2004-2013).

  Master I, Miguel Saavedra, 2007-2008. Miguel was a Peruvian student I trained during 2 years during my PhD on the atmospheric model WRF. We developed and validated a regional configuration carried out over the Peruvian Upwelling.Miguel obtained his Master I and has now a permanent position at the Senamhi, i.e., the Peruvian Met-Office.-Master II, Fabien Desbiolles, 2012. Fabien was doing his Master II in Marseilles, France. I supervised him during my experience in Spain for 5 months. His internship aimed (1) to validate regional oceanic and atmospheric simulations carried out over the Western Mediterranean Sea, and (2) to assess the role of the atmospheric forcing in determining the oceanic mesoscale activity. Fabien also contributed to develop a toolbox used in an operational model in Spain (see Outreach section).After hisMaster II, Fabien did a PhD in Brest and has now a post-doctoral position in South Africa (University of Cape Town). As stated in Chapter 6, we are now collaborating on the role of the mesoscale air-sea coupling on the determination of the precipitation (see Desbiolles et al. 2018) -Postdoc, Melanie Juza, 2013-2014. Melanie joined the modeling team I was managing in SOCIB, in Spain. Under my supervision, she assessed the water masses in

8. 3 4 38 2. 5 2 . 8 2 . 9

 343852829 Referring activities and outreach I have been referee for several scientific journals such as JGR Ocean and Atmosphere, Ocean modeling, Journal of Progress in Oceanography, Journal of Physical Oceanography, Geophysical Research Letter, Natural Hazard, Progress in Oceanography, Nature Geoscience. I also evaluated several projects from the USGC internal reviews, IRD (1 project), and US NSF (3 Projects), FONDECYT (Chile, 1 project). As an outreach, I was contacted by newspapers after Renault et al. (2011) e.g., (The links are available in the pdf file): al. (2011), I participated in the creation of an animation on Meteotsunamis: Youtube Video During my experience in Spain, I developed two operational models: -Forecast of the Meteotsunamis: Rissaga -Forecast of the ocean currents, temperature, and salinity: WMOP 2.Mean sea surface geostrophic currents from (a) AVISO, (b) AGH_NOCRT (NOCURR), and (c) AGH_CRT (CURR) for the period 2000-2004. (d) Total depth-integrated Kinetic Energy (KE) over the whole domain, the Mozambique Channel and the Agulhas Basin region (black boxes, Fig. 2.1a). In AGH_CRT, the weakening of the mean windwork (F m K mg ) induces a global slow down of the circulation. However, due to a less present eastern retroflection of the Agulhas Current, the Agulhas Current over the Agulhas Basin has a larger mean flow in AGH_CRT with respect to AGH_NOCRT. The Agulhas retroflection is more realistic in AGH_CRT than in AGH_CRT. Figure from Renault et al. (2017b) . . . . . . . . . . . . . . . . . Top panel: Mean surface Eddy Kinetic Energy (EKE, cm 2 s -2 ) from US_NOCRT (EXP1), US_CRTF (EXP2), and US_CRT (EXP3). Bottom panel: Temporal evolution of the EKE averaged over the whole domain. The difference percentages between the uncoupled experiments and the coupled experiment are indicated. There is a reduction of the EKE when using the current to estimate the surface stress.The atmospheric response dampens the EKE reduction. From US_NOCRT to US_CRTF, the EKE is reduced by 55%, whereas from US_NOCRT to US_CRT, the EKE is reduced by 40%. Figure from Renault et al. (2016d) . . . . . . . . . . 39 2.6 Depth-integrated EKE-budget components (cm 3 s -3 ) from US N OCRT (EXP1, top) and US C RT (EXP3, bottom): from left to right: the eddy wind work (F e K e ), the baroclinic conversion (P e K e ), and the barotropic conversion (K m K e ). F e K e and P e K e are the main energy source terms. The reduction of the EKE in Fig. 2.5 is explained by the reduction of F e K e by the current feedback. Figure from Renault et al. (2016d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.7 (a) F e K e cross-shore profiles (cm 3 s -3 ) averaged between 30 • N and 45 • N from US N OCRT (EXP1, blue), US C RTF (black, EXP2), and US C RT (red, EXP3). (b) Differences between US N OCRT and US C RTF (black), and US N OCRT and US C RT (red). (c) same as (a) except for F e K eg . (d) Same as (b) except for the geostrophic eddy wind work F e K eg . The total integrated differences over the box [30 • N and 45 • N x d=500 km] between US N OCRT and the other experiments are indicated in the legend. Two regions can be distinguished: the coastal region (cross-shore distance d < 80 km), and the offshore region (d > 80 km). In the coastal region there is a reduction of F e K e mainly through its geostrophic component; in the offshore region there is an actual sink of F e K e again, through its geostrophic component (F e K eg ). The wind response to the current dampens the F e K e reduction. Figure from Renault et al. (2016d). . . . . . . . . . . . . . . . . 43 Geostrophic eddy wind work (F e K eg ) from (a) US N OCRT (EXP1) and (b) US C RT (EXP3). The reduction of F e K e is mainly explained by a coastal reduction of F e K eg , and an offshore sink of energy through F e K eg . Figure from Renault et al. (2016d). . Schematic representation of the current feedback effects over an anticyclonic eddy, considering a uniform southward wind. The green, black, and blue arrows represent the wind, surface stress, and surface current, respectively. The red (blue) shade indicates a positive (negative) F e K e . The black (green) +/-signs indicate the current-induced stress (wind) curl. (a) A simulation without current feedback (e.g., US N OCRT). (b) A simulation that takes into account the current feedback in the estimation of the surface stress but neglects the atmospheric response (e.g., US C RTF). And (c) a fully coupled simulation, ı, that has the current feedback in the surface stress estimate and the atmospheric response (e.g., US C RT). In US N OCRT (i.e., simulations without current feedback), the net F e K e is equal to zero. In US C RTF (i.e., simulations with current feedback to the surface stress), over an eddy, the amount of positive wind work (F e K e ) is reduced, and the amount of negative F e K e becomes more negative. As a result, the net F e K e becomes negative, deflecting energy out of the eddy into the atmosphere. In a fully coupled model (US C RT), the atmospheric response dampens the sink of F e K e by increasing the positive F e K e and decreasing the negative F e K e ; the net F e K e remains negative. The current feedback induces a positive (negative) stress curl (wind curl) in the eddy's center. Figure from Renault et al. (2016d). . . . . . . . . . . . . . . . . . . 2.10 Schematic representation of the current feedback considering a uniform southward wind blowing along the coast. (a) A simulation without current feedback (e.g., US N OCRT). (b) A simulation that takes into account the current feedback in the estimation of the surface stress but neglects the atmospheric response (e.g., US C RTF). And (c) A fully coupled simulation, i.e., that has the current feedback into the stress estimate and the atmospheric response (e.g., US C RT). The green, black, and blue arrows represent the wind, surface stress, and oceanic surface current, respectively. The red shade represents the induced F e K e (positive in all cases).The wind induces an oceanic coastal geostrophic jet that is partially in the same as direction the wind, inducing a positive F e K e . From US N OCRT to US C RTF, the reduction of the stress induces, in turn, a weakening of F e K e . From US C RTF to US C RT, the wind accelerates, increasing the surface stress and hence F e K e and the oceanic coastal geostrophic jet. Figure fromRenault et al. (2016d). . . . . . . . 2.11 Mean geostrophic eddy wind work (F e K eg ) from (a) the observations, (b) AGH_NOCRT (NOCURR), and (c) AGH_CRT (CURR) for the period 2000-2004. The observations and AGH_CRT are characterized by the presence of a pathway of energy from the ocean to the atmosphere all over the Agulhas Current, which is not present in AGH_NOCRT. The negative F e K eg is partly responsible for the dampening of the Eddy Kinetic Energy (EKE) in Fig. 2.5. Figure from Renault et al. (2017b). . . 2.12 (a) Mean eddy wind work (F e K e ) estimated using a temporal filter (91 days). (b) Predicted F e K ep = 2 ρ o s τ EKE using the seasonal values of s τ and EKE. A negative F e K e indicates a transfer of energy from the oceanic eddies to the atmosphere. It induces a damping of the eddies. Figure from Renault et al. (2017a). . . . . . . . . 2.13 Ocean (OCE) and Atmosphere (ATM) models configuration illustrated by snapshots of surface vorticity from the CTRL500 simulation. . . . . . . . . . 2.14 a) Horizontal Surface KE spectrum. b) Vertical velocity w averaged between surface and 100 m depth spectrum. c) Surface buoyancy b spectrum. d) Probability Density function of w over all the domain between surface and 100 m depth, but excluding the upwelling region (first 50 km offshore). NOCFB stands for NOCRT500 and CFB stands for CFB500. Figure adapted from Renault et al. (2018b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.15 a) Spectra of Kinetic Energy (KE) tendency terms [m 3 s -3 ] (submesoscale range) for injection of energy by baroclinic conversion (C), 3D pressure work (P), wind and vertical mixing work (V), 3D Advection (A), the horizontal mixing (H), and the tendency term (T). (see Chapter 1 for more details.) The solid (dashed) lines represent CTRL500 (NOCRT500)). All terms have been averaged over the summer period and between the surface and 100 m depth. b) Kinetic Energy Balance averaged over the upper 100 m depth for a period of 3 months. The spectra of KE tendency terms have been integrated over the submesoscale range (0.0822 -0.999 cycle km -1 ). .

2. 16 3 . 2

 1632 The CFB induces a sink of energy from SMCs to the atmosphere but also an additional injection of energy by baroclinic conversion that partly counteracts the sink of energy. a) Binned scatter-plot of the full time series of 1day running means of surface stress curl and surface current vorticity over the 500 m CROCO simulations domain. The bars indicate plus and minus one the standard deviation from the average value (stars). The linear regression is indicated by a line, and the slope s τ is indicated in the legend (10 -2 N s m -3 ). NOCRT500 and CTRL500 are represented in blue and orange, respectively. NOCRT500 has a slight positive slope that may be due to the TFB to the atmosphere, but the CFB overwhelms it in CTRL500, causing a negative slope. The CFB induces submesoscale surface stress structures. b) Mean submesoscale wind-work (F s K s ) from NOCRT500 and (c) CTRL500. The CFB induces a sink of energy from the SMCs to the atmosphere, which in turn dampens the SMCs. d) Two-dimensional wind work (FK = ø • u ) spectrum from NOCRT500 (blue) and CTRL500 (orange). e) Two-dimensional co-spectrum of Ekman pumping induced by the stress (w τ ) and b averaged over 100 m depth for NOCRT500 (blue) and CTRL500 (orange). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Eddy Kinetic Energy (EKE) for the period 2000-2004 from AVISO, GS_NOCRT (UNCOUPLED) , and GS_CRT (COUPLED) for the North Atlantic (a, b, c), and around the Gulf Stream (GS) separation (d, e, f). The black contours in (d, e, f) depict the mean EKE from AVISO (one contour each 1000cm 2 s -2 ). The current feedback causes a drastic reduction of the EKE by 30%. In particular, it limits the propagation of the eddies far from the mean GS path. Figure from Renault et al. (2016c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eddy killing improves the Gulf-Stream simulation. The color field presents a snapshot of surface currents relative vorticity from (a) a coupled simulation without current feedback to the wind (NOCFB, GS_NOCRT) and (b) a coupled simulation with current feedback (CFB, GS_CRT). The black contour lines represent the simulated long-term mean GS path and the gray contour line the observed GS path (contour of 0.6 m s -1 ). c) Probability Density Function of SLA around the diamond box [indicated in (a)] from AVISO (blue); NOCFB (green); and CFB (red). The eddy-resolving coupled model rectifies a long-standing bias of bimodal and unsteady separation in numerical models. Figure adapted from Renault et al. (2016c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3. 3 6 . 2

 362 The figure colors show the mean geostrophic Eddy Kinetic Energy (EKE) for the period 2000-2004 from (a) AVISO, (b) AGH_NOCRT (NOCURR), and (c) AGH_CRT (CURR). Contours show 20-cm delineations of mean sea surface height for this period. AGH_NOCRT is characterized by a too large EKE, and by the presence of a standing eddy around the east of the Agulhas Basin that has a strong influence on the retroflection (see Fig. 3.4). (d) Mean EKE over the whole domain, the Mozambique Channel, the AC retroflection, the ARC, and the Benguela (black boxes on (a)). The current feedback in CURR induces a drastic reduction of the EKE by 25% over the whole domain. It limits the presence of the standing eddies, improving the realism of the mean circulation and of the Agulhas Current retroflection. Figure from Renault et al. (2017b). . . . . . . . . . . . . . . . . . . 67 3.4 (a) Zonal Probability Density Function (PDF) of the retroflection location for the period 2000-2004 from (a) AVISO, (b) AGH_NOCRT (NOCURR), and (c) AGH_CRT (CURR). The black lines represent the PDF values and their standard deviations obtained using a bootstrap method (see text). The red lines represent the Gaussian fits applied on the significant PDF peaks. The blue circles highlight the center of each regimes (i.e., the peaks of the PDF), and the blue lines represent the spatial extension of each regime as estimated from the standard deviation of the Gaussian fits. The % of occurrences of each regime is indicated in blue (see text for more details). The current feedback to the atmosphere improves the representation of the Agulhas Current retroflection. In particular, by weakening the mesoscale activity, it strongly reduces the importance of the eastern retroflections, shifting the distribution of the retroflection location. (d) Illustration of an Agulhas Current eastern Retroflection from AVISO as estimated by the detection method (See Renault et al. (2017b)). The colors represent the Sea Surface Height (SSH) from AVISO; the thick black contour represents the detected Agulhas current and the red dot its retroflection longitude and latitude. e) Mean Eddy Kinetic Energy during the eastern Retroflections. The black box is used in Fig. 3.5. The solid line represents the shipping line ("Good-Hope Line") section, whereas the dotted lines represents the control sections used to estimate the Agulhas Current leakage using Lagrangian particles. Figure from Renault et al. (2017b). . . . . . . . . . . . . . 69 3.5 Relationship between the Eddy Kinetic Energy (EKE), the eddy windwork (F e K eg ), and the leakage from AGH_CRT (CURR). The EKE and F e K eg have been spatially average over the box indicated in Fig. 3.4e. The resulting timeseries and the leakage timeserie have been low-pass filtered ( f c = 180 days -1 ) and are shown on (a). The lag-correlation between EKE and leakage is plotted on (b). A large EKE near Port Elizabeth induces a large deflection of energy from the ocean to the atmosphere but also a short-cut of the Agulhas Current and, then, a weakening of the Agulhas Current leakage. Figure from Renault et al. (2017b). . . . . . . . . . 3.6 Spectral flux π KE (k) of surface oceanic geostrophic kinetic energy in (a) the Gulf Stream and (b) the Agulhas Current (see Chapter 1), for coupled simulations with current feedback (GS_CRT and blue). The shaded curves represent the associated error as estimated using a bootstrap method (see 1). Eddy Killing induces a large reduction of the inverse energy cascade, responsible for GS stabilization and for the observed Agulhas retroflection position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Spectral flux π KE (k) of surface ocean geostrophic kinetic energy over the Agulhas Current (same box as Fig. 3.6) from AVISO (green), and filtered coupled simulations with current feedback (AGH_CRT: CFB, red) and without current feedback (AGH_NOCRT: NOCFB, blue) (see text for more details). The shaded curves represent the associated error as estimated using a bootstrap method (see 1). Fully coupled simulations (CFB) have a more realistic energy flux π KE (k) with respect to AVISO. . . . . . . . . . . . 4.1 Binned scatterplot of the full time series of 1-month running means of surface stress curl and surface current vorticity over the domain 30 • N -45 • N and (150 km < d < 500km). The bars indicate plus and minus one the standard deviation about the average drawn by stars. The linear regression is indicated by a black line, and the slope s st is indicated in the title (10 -2 N s m -3 ). From the left to the right: US_NOCRT (EXP1), US_CRTF (EXP2), and US_CRT (EXP3). US_NOCRT does not have a significant slope because it does not have the current feedback to the atmosphere, nor the surface stress. US_CRTF and US_CRT presents a clear negative linear relationship between currents and stress curl. The current feedback induces fine scale wind stress structure. Consistent with the previous results, the atmospheric response reduces the current feedback effect on the stress. Figure from Renault et al. (2016d). . . . . . . . . . . . . . . . . . . . . . 4.2 The current feedback to the atmosphere linearly induces persistent surface stress anomalies, causing a sink of energy from geostrophic currents. (a) Coupling coefficient s τ between surface geostrophic current and surface stress. (b) Binned scatterplot of the full time series of 10m-wind magnitude and s τ over the World Ocean. The bars indicate plus and minus one standard deviation about the mean marked by stars. The linear regression is indicated by a black line, and the slope is indicated in the title. (c) Predicted s τ = (-2.5 10 -3 |U a | + 0.013 m s -1 ) N s 2 m -4 (see text). The Figures has been realized using the data from QuikSCAT and AVISO. Figure from Renault et al. (2017a). . . . . . . . . . . . . . . . . . . . . . 4.3 (a) Mean eddy wind work (F e K e ) estimated using a temporal filter (91 days). (b) Predicted F e K ep = 2 ρ o s τ EKE using the seasonal values of s τ and EKE. A negative F e K e indicates a transfer of energy from the oceanic eddies to the atmosphere. It induces a damping of the eddies. The Figures has been realized using data from QuikSCAT and AVISO. Figure from Renault et al. (2017a). . . . . . . . . . . . . 4.4 Cross-shore profile of the Turbulent Kinetic Energy (TKE) of the surface wind averaged between 30 • N and 45 • N from US_NOCRT (EXP1, cyan) and US_CRT (EXP3, red). The F e K e sink from the ocean to the atmosphere results in a slightly larger TKE in US_CRT compared to US_NOCRT. In the near-shore region there is a larger wind enhancement that is likely partly explained by the presence of the steady oceanic geostrophic jet that flows in the same direction as the wind. Figure from Renault et al. (2016d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 (a) Same as Fig. 4.1 but for the wind curl and the surface current vorticity in US_CRT (EXP3). There is a positive linear relationship between the current vorticity and the wind curl, i.e., the current feedback on the atmosphere induces fine scale structures in the wind field that counteract the current-induced stress structure (Fig. 4.1). This explains the dampening of the current feedback effect on the EKE. The linear regression is indicated by a black line and the dimensionless slope s w is indicated in the title. (b) Vertical attenuation of s w with respect to the surface s w . Figure from Renault et al. (2016d). . . . . . . . . . . . . . . . . . . . . . . . 4.6 a) The colors represent the current-wind coupling coefficient s w from AGH_CRT at each grid point and smoothed over 100 km. b) Vertical attenuation of s w with respect to the surface s w over the Agulhas Return Current box (similar results are found for other regions). c) Binned scatterplot of the mean Marine Boundary Layer Height and s w over the whole domain. The bars indicate plus and minus one the standard deviation about the average drawn by stars. The linear regression is indicated by a black line, and the slope is indicated in the title (10 -3 m -1 ). s w is characterized by a complex spatial pattern that depends on the Marine Boundary Layer Height. The deeper is the Marine Boundary Layer, the weaker is s w . The current feedback to the atmosphere mainly acts on the surface wind. Figure from Renault et al. (2017b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Precipitation rate response to the current feedback a) Mean precipitation rate from AGH_CRT (CURR) over the period 2000-2004. b) Relative difference C rain (see text) between AGH_NOCRT and AGH_CRT. Only the significant values (σ > 95% using a t-test) are shown. c) Mean precipitation rate from the Tropical Rainfall Measuring Mission (Satellite data). The mean precipitation rate is realistically reproduced by AGH_CRT. The warmer Sea Surface Temperature and associated larger SST gradients in AGH_CRT over the Agulhas Basin and the Benguela likely induce larger precipitation in AGH_CRT with respect to AGH_NOCRT. Figure from Renault et al. (2017b). . . . . . . . . . . . . . . . . 5.1 The current feedback to the atmosphere induces persistent surface stress anomalies that can be expressed using a linear relationship. The coupling coefficients between the surface geostrophic current vorticity and the surface stress curl (s τ ) is able to efficiently isolate the current feedback from the thermal feedback. (a) s τ as estimated from the observations. (b) s τ as estimated from PULS_CTRL (CTRL). (c) s τ as estimated from PULS_NOCRT (NOCRT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The current feedback to the atmosphere induces persistent surface 10-m wind anomalies that can also be expressed using a linear relationship. As s τ , the coupling coefficients between the surface geostrophic current vorticity and the 10-m wind curl (s w ) is able to efficiently isolate the current feedback from the thermal feedback. Scatterometers such as QuikSCAT are not able to characterize the wind response to the current feedback. (a) s w as estimated from the observations. (b) s w as estimated from PULS_CTRL (CTRL) using the relative ENW wind. (c) s w as estimated from PULS_CTRL (CTRL) using the 10m-wind. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 The surface current vorticity can partially drive the mesoscale wind curl variability. Scatterometers wind can not monitor it. a) Temporal correlations between the surface stress and the relative ENW from PULS_CTRL (CTRL). b) Temporal correlations between the surface stress and the 10m absolute wind from PULS_CTRL (CTRL). c) Temporal correlations between the surface stress and the 10-m absolute wind from PULS_SMTH (SMTH). The larger correlations (in red) indicate regions where the mesoscale wind determines the stress (top-down effect). Negative correlations highlight regions where the current forces the mesoscale wind (bottom-up effect). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 The coupling coefficient between the surface stress curl and the cross-wind SST (s Cstr ) does not properly isolate the thermal feedback from the current feedback: the current feedback can cause surface stress mesoscale features that are correlated with the cross-wind SST. Similar results are found for s Cu . a) s Cstr as estimated from the observations for the summer period. b) s Cstr as estimated from PULS_CTRL (CTRL) for the summer period. c) s Cstr as estimated from PULS_NOCRT (NOCRT) for the summer period. d) s Cstr as estimated from PULS_SMTH (SMTH) for the summer period (note the different colorscale). Similar results are found when considering all the seasons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 The current feedback can cause surface stress mesoscale features that are correlated with the cross-wind SST, contaminating the coupling coefficient sC str . a) Probability Density Function of the ratio between s Cstr as estimated from PULS_NOCRT (NOCRT) and s Cstr as estimated from PULS_CTRL (CTRL). Low-level and High-level EKE regions are considered. Only positive values of s Cstr are considered as negative values do not stand for a TFB effect. The 2 • S -2 • N band is masked as the summer of each hemisphere is considered. b) Same as (a) but between PULS_SMTH (SMTH) and PULS_CTRL (CTRL). Similar results are found for s Cu and when considering all the seasons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 The coupling coefficient between the mesoscale surface stress and SST anomalies (s str ) properly isolates the thermal feedback from the current feedback. Similar results are found for s u . a) s str as estimated from the observations. b) s str as estimated from PULS_CTRL (CTRL). c) s str as estimated from PULS_NOCRT (NOCRT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Probability Density Function of the ratio between s str as estimated from NOCRT and s str as estimated from CTRL. Low-level and High-level EKE regions are considered. Only positive values of s Cstr are considered as negative values do not stand for a TFB effect. Confirming Fig. 5.6, the current feedback does not influence the coupling coefficients based on stress or wind magnitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 a) Temporal evolution of the Eddy Kinetic Energy (EKE) averaged over the whole domain. US_NOCRT (EXP1), US_CRTF (EXP2), and US_CRT (EXP3) are the SST-coupled, uncoupled with current feedback, and fully coupled experiments from Renault et al. (2016d), respectively. b) Binned scatter-plot of the time series of 1-month running means of surface stress curl and surface current vorticity over the domain 30 • N -45 • N and an offshore strip (150 km < d < 500 km, where the orography and coastline meandering effects are insignificant). from US_NOCRT, US_CRTF, US_CRT, and USW4. The bars indicate plus and minus one the standard deviation about the average drawn by stars. The linear regression is indicated by a black line, and the associated slope s st [10 -2 N s m -3 ] is indicated in the title. The slope error is estimated as the standard deviation of the slopes time series estimated using the full time series of 1-month running means of surface stress curl and surface current vorticity. The parameterization of the wind response to the current feedback allows USW4 to have similar levels of EKE than the fully coupled experiment (US_CRT); USW4 has a clear negative linear relationship between current vorticity and stress curl. s st from USW4 is slightly larger than s st from US_CRT, but it is within the range of the associated estimation error. . . . . Mean geostrophic EKE estimated from (a) AVISO and (b) USW4 over the period 1995-2013. The EKE of USW4 is computed using low-pass filtered geostrophic velocities (Gaussian spatial filter with 36-km-half-width) as an approximate match to the AVISO resolution. The current feedback to the atmosphere dampens the eddies and, thus, allows the simulation to have a realistic EKE level, albeit with not quite the same spatial pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Depth-integrated kinetic energy budget components [cm 3 s -3 ] from USW4 over the period 1995-2013 (see Renault et al. 2016d for definitions): (a)(c) geostrophic eddy wind work (F e K eg ), baroclinic conversion (P e K e ), and barotropic conversion from the mean flow (K m K e ). (d) Cross-shore bins of the energy budget components averaged over 50-km intervals and between 30 • N and 45 • N. The geostrophic eddy wind work (F e K eg ) is estimated from USW4 (red) and from observations (QuikSCAT and AVISO; grey). For the first 50 km off the coast the observations estimate is not shown because of the QuikSCAT and AVISO coastal issues. The baroclinic conversion is the main energy conversion term. F e K eg is positive nearshore and deflects energy from the ocean to the atmosphere offshore while damping the mesoscale activity. . . . . . . . . . . . . . . . . . . . . . . . . . . .

  • W to 21.7 • W and from 0.4 • N to 73.2 • N, and is 1152 x 1059 points with a resolution of 6 -

	7 km.

As the US West coast configuration, bathymetry is constructed from the Shuttle Radar Topography Mission (SRTM30 plus) dataset based on the 1-min Sandwell and Smith

Table 1 . 1 :

 11 Numerical Experiments. (Period does not account for the spin up)

	SST Feedback Current feedback Region OCN dx ATM dx Period Models	Yes No California 4km 6km 1995-1999 CROCO-WRF	No Yes, forced California 4km 6km 1995-1999 CROCO-WRF	Yes Yes California 4km 6km 1995-1999 CROCO-WRF	Yes No California 0.5km 2km 3-months CROCO-WRF	Yes Yes California 0.5km 2km 3-months CROCO-WRF	Yes No NATL 5-6km 18km 2000-2005 CROCO-WRF	Yes Yes NATL 5-6km 18km 2000-2005 CROCO-WRF	Yes No Greater Agulhas 5-6km 18km 2000-2005 CROCO-WRF	Yes Yes Greater Agulhas 5-6km 18km 2000-2005 CROCO-WRF	Yes Yes 45 • S 45 • N 1/12 • 1/4 • 1989-1993 NEMO-WRF	Yes No 45 • S 45 • N 1/12 • 1/4 • 1989-1993 NEMO-WRF	Smoothed Yes 45 • S 45 • N 1/12 • 1/4 • 1989-1993 NEMO-WRF	Smoothed No 45 • S 45 • N 1/12 • 1/4 • 1989-1993 NEMO-WRF
	Experiments	US_NOCRT	US_CRTF	US_CRT	CTRL500	NOCRT500	GS_NOCRT	GS_CRT	AGH_NOCRT	AGH_CRT	PULS_CTRL	PULS_NOCRT	PULS_SMTH	PULS_SMTH_NOCRT

Table 1 .

 1

	2: Coupling Coefficients.

wind magnitude 1.7.2 Thermal Feedback Coupling Coefficients based on Derivatives

	Consistent with Chelton et al. (2007) and Wang and Castelao (2016), the following cou-
	pling coefficients have been estimated for the summer period of each hemisphere 10-m
	(or ENW): wind curl and cross-wind SST gradient (s Cu ); 10-m (or ENW) wind divergence
	and down-wind SST gradient (s Du ); wind stress curl and cross-stress SST gradient (s Cstr );

1.7.3 Thermal Feedback Coupling Coefficients based on Mesoscale Anomalies

	The coupling coefficients defined by ONeill et al. (2012) have been computed. They
	are based on mesoscale SST and the magnitude of wind (s u ) or surface stress (s str ). As in
	O'Neill et al. (2017), the influence of the storm have been damped out by removing large
	wind speed or surface stress magnitude with values greater than two standard deviations
	σ from the time mean at each grid point. This procedure allows removing potential biases
	in the TFB response estimate that can be induced by the storm (atmospheric forcing vs.

Chapter 2 A Direct Control of the Oceanic Circulation, from the Large Scale to the Submesoscale Contents 2.1 A Large Scale Effect: A Slow Down of the Gyre . . . . . . . . . . . . . . . 2.2 At the Mesoscale: An "Eddy Killer" . . . . . . . . . . . . . . . . . . . . . .

  • x 6 • ) in our case. The cutoff of this filter is about 250 km. Land points are treated as missing data and the weights of windows including land points are renormalized over the remaining oceanic points.

	field. Note the use of a larger filter cut-off would lead to similar results as this filter is
	applied on both SMTH and to the coupling coefficients described hereafter. Note the
	choice of the filter characteristics can also affect the strength of the coupling coefficient (in
	particular the one based on the mesoscale wind speed anomalies), however, it would not
	change the conclusion of this study.
	2.2.1 A Dampening of the Mesoscale Activity . . . . . . . . . . . . . . . .
	2.2.2 Energy Conversion and Large Scale Sink of Energy . . . . . . . . .
	the smoothed

Mesoscale anomalies of a field φ are then defined as φ = φ -[φ], with

[φ]

2.3 At the Submesoscale: A Catalizer but Still a Killer, the case of the Cali- fornia Current System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	2.3.1 Dampening of the Submesoscale Activity . . . . . . . . . . . . . . .
	2.3.2 A Submesoscale Sink of Energy . . . . . . . . . . . . . . . . . . . . .
	2.3.3 A Catalizer of Submesoscale Baroclinic Instability . . . . . . . . . .
	2.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	2

.4 Conclusion of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . .

	The objectives of this Chapter are to assess how the current feedback direct effects on
	the ocean dynamic. In my recent research, I focused on 3 main direct effects: on the large
	scale, on the mesoscale, and on the submesoscale. The chapter is organized as follows:
	In Sec. 2.1 the direct effect of the current feedback on the mean circulation is assessed.
	I will use two examples: the North Atlantic Basin and the Greater Agulhas System. In
	Sec. 2.2, I will show how the current feedback plays a crucial role in determining the
	mesoscale activity. Finally, the submesoscale response will be addressed by focusing on
	the California Upwelling System in Sec. 2.3. The results are discussed and summarized
	in Sec. 2.4.
	2.1

A Large Scale Effect: A Slow Down of the Gyre

	To illustrate the influence of the current feedback on the large scale circulation, I will
	consider in this section two different regions: the North Atlantic Basin, and the Greater
	Agulhas region (it encompasses the Mozambique channel, The Agulhas Current, and the
	Benguela Upwelling System). Both regions are characterized by an intense mean dynamic
	and by the presence of a Western Boundary Current: the Gulf Stream and the Agulhas
	Current, respectively. The results presented in this section have been published in the
	Journal of Physical Oceanography (JPO) (Renault et al. 2016c and Renault et al. 2017b).
	The observed mean surface stress from the SCOW product (Scatterometer Climatol-
	ogy of Ocean Wind, Risien and Chelton 2008), is illustrated in Fig. 2.1a for the North
	Atlantic Basin. The surface stress is driven by the mean atmospheric circulation that is
	characterized by the presence of westerly and easterly winds in the north and south of
	the North Atlantic Basin, respectively. GS_CRT and GS_NOCRT have a good general
	representation of the mean surface stress, however, they both have a bias in the surface
	stress direction in the northwestern part of the domain, with a northward component
	overestimated with respect to the SCOW product (Fig. 2.1b). Because the mean cur-
	rents are moving in the same direction as the wind, from GS_CRT to GS_NOCRT, the
	current feedback reduces the mean surface stress up to 0.3 N m -2 , where the currents
	are the strongest (τ

  , but is more than the U.S. West Coast (no significant changes). The mean wind work is reduced by the current feedback only if the mean currents are strong enough, which is not the case of the U.S. West Coast (mean currents of less than 0.2 ms -1 ). Consistently, the weakening of the mean wind work slows down

the mean circulation by 15% (against 27% for the north Atlantic). This furthermore locally reduces the barotropic conversion of energy from mean to eddy by 15%, weakening the EKE generation over Madagascar Channel, and the Agulhas Basin region. As shown by e.g.,

Renault et al. (2016d)

, the current feedback induces a surface stress curl opposite

  The added dissipation helps, but appears is an ad hoc fix for processes that are not represented in the model, such as eddy killing. The challenge here is to justify a forward route to dis-

	sipation when geostrophic turbulence is characterized by an inverse cascade. Looking
	into it with a submesoscale resolving model (200m resolution), Gula et al. (2016) recently

[START_REF] Chassignet | Impact of horizontal resolution (1/12 to 1/50) on gulf stream separation, penetration, and variability[END_REF]

, reflecting excessive meandering similar to our NOCFB simulation.

  5.1a). s τ is characterized by a large-scale variability.The high-latitude regions have the largest s τ . Eddies in those regions should therefore be strongly damped by the current feedback. Eastern boundary currents have medium range values of s τ around 1 N s m -3 , slightly weaker than the value found byRenault et al. (2016d) for the U.S. West Coast using numerical coupled model. While no doubt part of the discrepancy may be due to model bias, it could also be explained by uncertainties in the observations as discussed in the last section. There are a few regions where s τ appears positive, although it could be due to uncertainties in the observations, this could also indicate regions where wind variations force weak eddy variability.

Table 6 .

 6 1: F e K eg from the experiments integrated between 30 • N and 45 • N and over the coastal or offshore region, and averaged during 1995-2000 [m 5 s -3 ].

	Region	US_NOCRT US_CRTF US_CRT USW4
	Coastal (0 km < d < 300 km)	7.82e5	5.61e5	6.08e5	6.18e5
	Offshore (300 km < d < 500 km) 0.05e5	-0.85e5	-1.31e5	-1.35e5
	Finally, as in Renault et al. (2016d), the current-surface stress coupling coefficient s st
	[N s m

  If the simulation does not have enough energy, one should first understand why, maybe use less dissipative advection scheme or simply increase its spatial resolution (this has a cost, but it is another issue). The second reason simply relies on the results of[START_REF] Pacanowski | Effect of equatorial currents on surface stress[END_REF] and[START_REF] Luo | Reducing climatology bias in an ocean-atmosphere CGCM with improved coupling physics[END_REF] (I confirmed these results for the North Atlantic Gyre inRenault et al. 2016c). The current feedback also have a large scale effect, i.e., a slow-down of the mean currents. Ignoring this effect would induce an overestimation of the mean input of energy from the atmosphere to the ocean, and too strong a mean circulation. As presented in Chapter 6, how to best force an ocean model is one of my on-going research topics. Parameterizing the atmospheric response to the current feedback is one possibility. Maybe Atmospheric Boundary Layer models that are currently under development, could lead to a better way to force an ocean model. They show the increase of the resolution allows a better representation of the Gulf Stream dynamic, of its barotropization, and of the mesoscale activity. However, in this study, the current feedback is ignored and diffusive advection scheme is used to dampen the excessive mesoscale energy. Future studies should aim to revisit this kind of study and to assess at to what extent and what scales the mesoscale actvivity simulated in numerical models present a convergence with the increase of the spatial resolution. and regions of interest. The risk it to get lost in diversity, however, it works well for me because it gives me a lot of scientific stimulation. Furthermore, it helps me to have a larger picture of all the processes I am interested in, such as (sub)mesoscale processes, air-sea interactions, and their link with the biogeochemical variability and the precipitations. When I first tried to write this manuscript, I had doubts about how to present my career. I first thought to present it by regions of interests. Then I changed my mind and decided to focus on processes (e.g., wind drop-off, mesoscale, submesoscale, current feedback). But finally, I choose to focus on the part of my research that has inspired me the most, which is the air-sea interactions, and, in particular, the current feedback. I think it makes my HDR manuscript more interesting and useful.To conclude, I have been working abroad for 8 years in Spain and USA and recently integrated the IRD. Retrospectively, I am very happy about those abroad experiences. It was not easy everyday: moving and restarting a new life in a new country with a new language can be tough sometimes. However, the social and scientific benefits I got are

	The finding presented in this manuscript also raised the question on the convergence
	of the models. Chassignet and Xu (2017) assess the impact of horizontal resolution ( 1 12
	• to 1 50
	More generally, the HDR exercise has allowed me to revisit my (short) research career
	and my entire experience. From my PhD to my on-going research, I always tried to focus
	on the air-sea interactions. However, because of my natural curiosity, I have been in-
	terested in many topics (including mesoscale, submesoscale, biogeochemical variability,

• ) on Gulf Stream separation, penetration, and variability. deoxygenation and acidification) and by different regions, among them, obviously the Eastern Boundary Upwelling Systems and the Western Boundary Currents, but I have also worked for 4 years on the Western Mediterranean Sea. I always liked to focus on various topics at the same time, which also explained why my career has such a diversity of topics priceless. It allowed me to meet different kind of people from various nationalities, to improve my language skills, and also, from a scientific point of view, to develop my independent research line. Through those experiences I have developed an international network, which gives me the possibility to expend collaborations and the outreach of my work.

  own students at a PhD level. The HDR has given me the opportunity to think about the role of a PhD advisor. As in her/his own research, I think a PhD advisor should have a strong implication in the student's work. She/he should help the student to be up-to-date of the state of the art of her/his research topic (both in literature and technical tools). It is important to me to collaborate and help the student, but it is also vitale to give her/him enough freedom to develop her/his own research line. She/he should be encouraged to collaborate with other researchers. This could help her/him to develop her/his network and to be open-minded about other researchers and research lines. So far, I always

km for the atmosphere (Fig.2.13a and Chapter 1); the coarser atmospheric resolution

ing of the consequences of climate change and its interplay with decadal variability over the coming decades for all four EBUS regions. Members of a cross-disciplinary team consisting of a climate scientist, two oceanographers, a marine biogeochemist and a software engineer will train two graduate students. The project will lay essential groundwork for further study of climate impacts on upper trophic levels and prediction of fish populations in EBUS regions. Moreover, the earth system model development work will lay the groundwork for the scientific community to study higher-trophic-level response of marine ecosystems to climate variability and change. Marine ecosystem variability has profound implications for natural resource management, and it is anticipated that this project will be of great interest to stakeholders and the general public.

This project is focused on the future evolution of the four Eastern Boundary Upwelling Systems (EBUS). Three interconnected research themes will be pursued:

1. Air-sea-land interaction at the regional scale, 2. Climate change signals in EBUS regions,

Climate controls on marine ecosystems.

A suite of high-resolution regional earth system model simulations will be undertaken. They involve:

-Historical reconstructions of the variations of the recent past in all four EBUS regions. These reanalysis-driven simulations will be used to validate the regional model against available observations and characterize the substantial variability of the regions' physical and ecosystem states. All sets of experiments will be performed for the U.S. West Coast and Humboldt EBUS regions first, and then the lessons learned will be leveraged to perform the same series of experiments for the two other major upwelling systems.

-Mid-century future climate simulations for all EBUS regions. These simulations, driven by global climate model (GCM) output, will be used to quantify and understand physical and ecosystem changes due to anthropogenic forcing. They will also be analyzed together with the historical reconstructions to quantify the importance of anthropogenic signals relative to the regions' natural variability, and detect anthropogenic signals in the recent past. To maximize relevance to decadal prediction, the future climate experiments will emphasize the mid-21st-century time frame. However, we will also undertake one experiment focused on end-ofcentury to have a more extreme climate change signal to analyze.

-Process evaluation simulations in select EBUS regions. These are also reanalysisdriven, but with key processes disabled. These experiments will allow for a quan--Master II, Roland Ngomo, on-going. Roland is doing a Master II in Benin (cobadging with University Paul Sabatier, Toulouse). The aim of the project is to assess the role of the air-sea coupling (both thermal and mechanical) on the determination of the cold tongue of the Atlantic Ocean.

-PhD, Romain Escudier (2011Escudier ( -2014)). Romain did his PhD in Spain with A. Pascual and myself. His PhD aimed (1) to develop a regional configuration of the oceanic model ROMS over the Western Mediterranean Sea, ( 2 -PhD, Juan Manuel Sayol, 2013-2014. I did not directly supervise Juan Manuel but I closely worked with him on the modeling aspect of his PhD. One of the aims of his work was to determine the mesoscale variability of the Western Mediterranean Sea using a Lagrangian approach. We published two papers together based on his PhD work (Sayol et al. (2013(Sayol et al. ( , 2014))).

-PhD, Meroni Agostino, 2015. Agostino was doing his PhD in Italy but came to visit me at UCLA to be trained in the ocean and atmosphere coupling. His aim was to assess the role of the mesoscale air-sea coupling on the determination of severe rain events over the Ligurian Sea. We developed a regional high-resolution (2km) coupled configuration and analyzed the results. See Meroni et al. (2018).

-PhD and Postdoc, Alexandre Jousse, 2014-2016. Alex did his PhD at UCLA. I started working with him in 2014. He obtained his PhD in 2015. After his PhD, I hired him as a postdoctoral for 1 year (through my NSF grant). Alex was working on the development and validation of a regional configuration of the atmospheric model WRF over the U.S. West Coast. His main research interest was to understand the processes that drive the stratocumulus clouds formation. Alex developed a full budget of the humidity and temperature variability. He's about to submit two papers: (1) on the role of the aerosols in determining the cloud cover and the shortwave radiation (Jousse et al., 2018a); ( 2) on the impact of the on-going climate change on the cloud cover over the US West coast [START_REF] Jousse | On the Climate Change Impact on the Stratocumulus clouds off Central California[END_REF].

Alex is also participating in a study I'm about to submit on the US West coast oceanic variability (Renault et al., 2018a). His development will be also used by F.

Desbiolles (South Africa, see above).

List of Figures

List of Tables