2023Activity reportProjectTeamODYSSEY
RNSR: 202224252V Research center Inria Centre at Rennes University
 In partnership with:Université de Bretagne Occidentale, Ecole Nationale Supérieure MinesTélécom Atlantique Bretagne Pays de la Loire, Institut Français de Recherche pour l'Exploitation de la Mer, CNRS, Université de Rennes
 Team name: Ocean DYnamicS obSErvation analYsis
 In collaboration with:Institut de recherche mathématique de Rennes (IRMAR), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance, Laboratoire d'océanographie physique et spatiale
 Domain:Digital Health, Biology and Earth
 Theme:Earth, Environmental and Energy Sciences
Keywords
Computer Science and Digital Science
 A3.1. Data
 A3.1.1. Modeling, representation
 A3.2.3. Inference
 A3.4. Machine learning and statistics
 A3.4.5. Bayesian methods
 A3.4.6. Neural networks
 A3.4.7. Kernel methods
 A3.4.8. Deep learning
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.2. Stochastic Modeling
 A6.1.4. Multiscale modeling
 A6.2. Scientific computing, Numerical Analysis & Optimization
 A6.2.1. Numerical analysis of PDE and ODE
 A6.2.3. Probabilistic methods
 A6.2.4. Statistical methods
 A6.3. Computationdata interaction
 A6.3.1. Inverse problems
 A6.3.2. Data assimilation
 A6.3.3. Data processing
 A6.3.4. Model reduction
 A6.3.5. Uncertainty Quantification
 A6.4.1. Deterministic control
 A6.4.2. Stochastic control
 A6.5.2. Fluid mechanics
 A6.5.3. Transport
 A6.5.4. Waves
 A9.3. Signal analysis
Other Research Topics and Application Domains
 B3.2. Climate and meteorology
 B3.3.2. Water: sea & ocean, lake & river
 B3.3.3. Nearshore
 B3.3.4. Atmosphere
1 Team members, visitors, external collaborators
Research Scientists
 Etienne Memin [Team leader, INRIA, Senior Researcher, HDR]
 Bertrand Chapron [IFREMER, Researcher]
 Clement De Boyer Montégut [IFREMER, Researcher]
 Jocelyne Erhel [INRIA, Emeritus, HDR]
 Quentin Jamet [INRIA, Starting Research Position]
 Noe Lahaye [INRIA, Researcher, from Feb 2023]
 Long Li [INRIA, Starting Research Position]
 Claire Menesguen [IFREMER, Researcher]
 Alexis Mouche [IFREMER, Researcher]
 Frederic Nouguier [IFREMER, Researcher]
 JeanFrancois Piolle [IFREMER, Researcher]
 Aurelien Ponte [IFREMER, Researcher]
 Nicolas Reul [IFREMER, Researcher]
 Florian Sevellec [CNRS, Researcher, from Apr 2023]
 Gilles Tissot [INRIA, Researcher]
Faculty Members
 Xavier Carton [UBO, Professor, HDR]
 Lucas Drumetz [IMT ATLANTIQUE, Associate Professor]
 Ronan Fablet [IMT ATLANTIQUE, Professor, HDR]
 Carlos Granero Belinchon [IMT ATLANTIQUE, Associate Professor]
 Jonathan Gula [UBO, Associate Professor, HDR]
 Roger Lewandowski [UNIV RENNES, Professor, HDR]
 Guillaume Roullet [UBO, Professor, from Feb 2023, HDR]
 Pierre Tandeo [IMT ATLANTIQUE, Associate Professor, HDR]
PostDoctoral Fellows
 PierreMarie Boulvard [INRIA]
 Louis Thiry [INRIA, until Aug 2023]
PhD Students
 Adrien Bella [INRIA]
 Benjamin Dufee [INRIA, until Aug 2023]
 Mael Jaouen [INRIA, from Jun 2023]
 François Legeais [UNIV RENNES I]
 Igor Maingonnat [INRIA]
 Antoine Moneyron [INRIA, from Mar 2023]
 Francesco Tucciarone [INRIA]
Interns and Apprentices
 Zoe CasparCohen [INRIA, until Feb 2023]
 Olivier Larroque [INRIA, Intern, from Mar 2023 until Jul 2023]
Administrative Assistant
 Caroline Tanguy [Inria]
2 Overall objectives
Covering more than 70% of the Earth's surface, the oceans play key roles on the Earth climate regulation as well as for human societies. Yet, from wave breaking events to the movement of weather systems, the predictive capabilities of models notoriously quickly diminish with increasing lead times, even with the assistance of the world's largest supercomputers. Despite everincreasing developments to simulate and observe the coupled oceanatmosphere system, our ability to understand, reconstruct and forecast the ocean dynamics remains fairly limited for numerous applications.
Our motivations are to help break this apparent logjam, and more specifically to bridge model driven and observationdriven paradigms to develop and learn novel stochastic representations of the coupled oceanatmosphere dynamics. To address these challenges, Odyssey gathers a unique transdisciplinary expertise in Numerical Methods, Applied Statistics, Data Science, Satellite and Physical Oceanography. Methodological developments are primarily implemented and demonstrated through three main objectives: (i) the analysis of mesoscale/submesoscale processes and internal waves, (ii) the monitoring of extremes oceanatmosphere events and routes to rapid intensifications; (iii) the derivation of forefront deeplearning stochastic data assimilation techniques. The name Odyssey is a shortcut that stands for “Ocean DYnamicS obSErvation analYsis' – the keyword “Analysis” has to be understood in terms of physical understanding, mathematical analysis and data analysis.
The objectives and research actions of the team can be separated in four methodological axes:

Ocean observations analysis
This axis aims at exploiting novel multimodal highresolution of the ocean – mostly at the surface – through new methods of mathematical analysis, numerical simulations, stochastic analysis and machine learning to create new capabilities. The main scientific target, besides the upper ocean variability, addresses the airsea exchanges and the rapid intensification of extreme events.

Development and analysis of numerical and mathematical models of geophysical flows
The context of this research axis is the modelling and analysis issues of geophysical fluid dynamics. A major research effort concerns the development of stochastic modelling and its implementation in numerical models in order to address uncertainty quantification. More generally, the analysis of mathematical models on the one hand, and of data from highresolution numerical models, on the other hand; together with the improvement of numerical schemes and the development of parameterizations (of unresolved processes) for numerical models forms the corpus of objectives in this axis.

Data/Models interactions and reduced order modelling
Several data assimilation models are being developed with a wide range of applications, from near surface highfrequency submesoscale motions estimation to extreme event hindcast and up to basinscale dynamics reconstruction. At the base of this work is the design and validation of simplified models based on physics and datadriven reduced order models that allows for an optimal coupling with observations. At the same time, new uncertaintyhandling data assimilation strategies are being developed.

AI models and methods for ocean data analysis
We aim to bridge the physical paradigm underlying ocean and atmosphere science and AI paradigms with a view to developing and identifying physically relevant representations of geophysical dynamics accounting for the specificities and complexities of the processes involved. To this end, we propose to jointly explore three main complementary datadriven frameworks (including their possible couplings): analog schemes, kernel approaches (especially RKHS – Reproducing kernel Hilbert space) and deep neural network (NN) representations.
3 Research program
A primary focus of the team intends to better characterize poorly known mechanisms of energy redistribution operating at different scales, through the interactions of different physical mechanisms such as hydrodynamical instabilities, internal or wind waves, turbulence and ocean atmosphere feedback exchanges. Our first credo is that an improved physical understanding cannot be achieved uniquely on the basis of sparseintime observations alone or from intrinsically imperfect models: data without models are uninformative and models built without data are useless, as models are generally too far from realworld situations of interest. Today, data and models shall thus be combined to tackle uncertainty quantification and probabilistic ensemble forecasting issues, as advanced datadriven representation of ocean dynamics requires; to that end we need to drift from a purely deterministic physics toward stochastic representations. This is the second credo. Many aspects of the models or of the datamodel coupling functional still need to be specified or parameterized through dynamicallyadapted basis functions, evolving parameters or covariance matrices. Our third credo is that the improved physical understanding of the multiscale interactions encoded in such parametrizations can be learned or estimated from data.
The research objectives of our group naturally distribute in several challenges, exploring multimodal (differing spacetime resolutions, differing passive and active microwave instruments, ...) observations, airsea exchanges and upper ocean dynamics, bottom boundary turbulent processes, stochastic flow representations, data assimilation and machine learning procedures. All these challenges take place or rely on principles and/or tools of the four methodological contexts introduced above.
3.1 Ocean observations analysis: upperocean dynamics, oceanatmosphere interaction, waves and extreme events.
Global Earth Observation (GEO) systems, in situ and satellite platforms, have significantly improved our understanding and capability to manage the Earth's environment. Key products today include, among others, merged global ocean surface topography using the different available altimeter missions, global and daily highresolution sea surface temperature and ocean colour using multisensor and platform measurements. One may also cite the mapping of high sea winds from combined radiometer/scatterometer, including veryhigh resolution synthetic aperture radar observations, and more recently, the fusion of sea state data (largely improved with the recently launched CFOSAT mission, combined with Copernicus Sentinel1 and 2 measurements). Pushing to higher spatial resolution (about 10 m to 1 km), signatures of tracer variations from imaging instruments can further provide quantitative information, especially for characterizing internal and surface waves in interactions with the ambient underlying upper ocean flow. Note, modern satellite sensor capabilities, sustained under the Copernicus programme, will soon include the new wideswath Surface Water & Ocean Topography (SWOT) altimeter, to more precisely characterize ocean sea surface height variability. An essential goal is thus to incorporate and combine these high resolution global observations of airsea exchanges and upper ocean dynamics into our applications of new methods of mathematical analysis, numerical simulations, stochastic analysis and machine learning to create new capabilities. We aim to combine multisensor data algorithm developments with advances in mining and learning from multimodal observations, i.e. satellite and insitu measurements, including numerical outputs. The scientific targets of this axis are to fully unveil (1) upper ocean mesoscale variability and its associated lateral exchange processes, known as “eddy fluxes”, (2) submesoscale variability and associated upperocean vertical exchange processes, known as “vertical exchange”, and finally (3) internal gravity wave variability (induced by winds, tides, and interactions of lowfrequency currents with topography). Another central scientific objective is to explore and develop datamodeldriven techniques in the context of extreme marineatmosphere events, to provide new insights for airsea exchanges processes and adapted parameterization under extreme conditions.
3.2 Development and analysis of numerical and mathematical models of geophysical flows
The core of this theme of research addresses modelling and analysis issues in geophysical fluid dynamics. Within this context, we mainly focus on the study of the dynamics of the upper oceanic circulation. One overall objective is to devise random models representing the effects of the computationally unresolvable scales of fluid motion on the resolved scales. Such models are used for ensemble forecasting, uncertainty quantification and data assimilation. The representation of the finescale effects on the coarser scales of motion depends on the level of geophysical fluid approximation pertinent to the data resolution and to the scale of the other physical processes involved. An important research effort of the team in this context is to pursue the development of a recently established class of models of stochastic transport in fluid dynamics at the most fundamental level. This class of models, referred to as model under Location Uncertainty (LU), has the advantage to be derived from physical conservation laws expressed through the stochastic transport of fluid parcels. As such, they are easily extendable to classical approximations of geophysical dynamics. and the stochastic partial differential equations have nearly the same shape as the corresponding deterministic ones. As for the ocean models, a known hierarchy of approximate stochastic models can be built from the NavierStokes equations almost exactly in the same way as in the deterministic setting. One of their strong assets is to lead to proper energy conservation and provide new approaches to subgrid parameterization, expressed both in terms of fluctuation distributions, and spatial/temporal correlations.
Research activities in the ODYSSEY team on this subject are manifold. First, the mathematical properties of the involved stochastic partial differential equations are poorly known and need to be explored. The overall objective of the challenge is to explore to what extent the known properties of deterministic flow dynamics models are conserved in the stochastic framework. This concerns for instance local wellposedness of the Navier Stokes equation or of its oceanic representatives. Another issue concerns the physical analysis of such systems. Do the stochastic systems with general noise models still admit some wave solutions (Rossby wave, Gravity waves, internal waves, etc.)? The characterization of the statistical moments associated with those wave solutions are of primal interest from a physical perspective but also to define proper shape functions for the random terms involved. All these issues are currently being studied within the STUOD project. Finally, the ODYSSEY team also addresses the development and validation of new numerical scheme for both deterministic and stochastic models of geophysical flows. In the stochastic case, the numerical approximation of the SPDEs requires the discretization of both the space and time domains. For the spatial discretization classical schemes can be used, however special care must be taken for the temporal schemes. The consistency of several splitting schemes is studied and numerically implemented.
3.3 Data/Models interactions and reduced order modelling
A first research effort in this theme is dedicated to the development of ensemble data assimilation techniques for geophysical problems (in this context, models and observations from e.g. satellites), addressing the issue of linearity and gaussianity hypotheses, which are major limitations of these approaches. Following recent results on the application of particle filters to address these issues on highdimension problems, we further develop new schemes relying on multiscale dynamical paradigms. Particle filters comprise a class of numerical methods that produce asymptotically consistent approximations of posterior distributions of partially observed systems. We study hierarchical ensemble data assimilation filters, able to handle multiscale interaction in a nested hierarchy of models (from coarse to fine scale). This multiscale capability (not available today even in a simple coarse form) is expected to provide an important analysis tool to study ocean/atmosphere interactions at different scales. The hierarchy of ocean dynamics models rely on the nested capability provided by the stochastic derivation framework described in the second methodological context.
A second axis of work is more dedicated more directly to the development, the implementation and the validation of simplified models of th ocean dynamics, with the main target to couple these models to the observation via data assimilation techniques. These models aims at covering a wide range of motions in the ocean. The mesoscale eddying dynamics (with typical horizontal scales greater than 100 km), such as multilayer QG models with the inclusion of active temperature tracer (Thermal QG or coupled Surface QG / QG models) and/or surface mixed layer, allowing to couple the dynamics to sea surface temperature data. Higher frequency motions, such as internal waves and internal tides, are addressed using a hierarchy of models based on the rotating shallow water equations (possibly with some linearization). The development of these models mirrors the evolving nature and growing quantity of data available, with recent and new missions such as SWOT or CFOSAT.
3.4 AI models and methods for ocean data analysis
This research axis is focused on the exploration and development of datadriven and learningbased schemes and their interactions with modelbased approaches, which constitute the stateoftheart in ocean and atmosphere science. The general goal is to improve the understanding, modeling, forecasting and reconstruction of airsea exchanges and upper ocean dynamics, as well as bottom turbulent processes, from the indepth exploration of the existing observation and simulation data. We jointly explore three main complementary datadriven frameworks, including their possible couplings: analog schemes, kernel approaches, especially RKHS (Reproducing kernel Hilbert space), and deep neural network (NN) representations. RKHS and NN naturally arise as they may directly link to modeldriven representations (e.g., NN regarded as discrete numerical solvers for ODE/PDE). Analog methods provide simple yet efficient sampling schemes for complex dynamics. Our recent contributions emphasize the relevance of these datadriven frameworks for the modelling, forecasting and assimilation of upper ocean dynamics on toy models. Ongoing studies aim at extending such methodologies for the learning of subgrid processes in full models. Besides, our recent developments illustrated on simplified systems, including for instance the identification of Neural ODE representations for partiallyobserved systems as well as the identification of stochastic latent dynamics, provide the methodological and numerical basis for the considered challenges.
This research axis specifically investigate the following issues: (i) embedding explicit or implicit physicsinformed priors (e.g., stability, conservation laws, stochasticity, chaos...) into datadriven and hybrid representations, (ii) learning latent representations for oceanic flows and airsea exchanges accounting for flow stochasticity, including extremes (iii) learning schemes when dealing with partiallyobserved, irregularlysampled and noisy dynamics, (iv) the joint learning of datadriven representation and associated data assimilation schemes, possibly directly from observation data.
4 Application domains
The application domain is mainly geophysical environmental flows, related to ocean dynamics. By designing new approaches for observation analysis, datamodel coupling and stochastic representation of fluid flows, the Odyssey group contributes to several application domains of great interest for the community and in which the analysis of complex turbulent flow is key.
5 Social and environmental responsibility
Ocean circulations play a major role in the climate and in the biodiversity of ecosystems. These aspects are crucial for the sustainability of the resources of human societies. Understanding and providing tools to predict ocean dynamics is a brick to apprehend our environment and to help making decisions.
6 Highlights of the year
The team has nothing special to report. We had quite a few new project funded, and pursued our efforts in the context of previouslylaunched projects. The newgeneration wideswath altimeter mission SWOT has been succesfully launched in December 2022, and provided a first round data that overperform the expectations, opening very exciting and promising perspectives for the team.
7 New software, platforms, open data
 Ronan Fablet : most softwares are available under freelicense (licence CeccilC) on the Oceanix GIT repository
 Pierre Tandeo : Python library for Kalman filtering and smoothing with augmented state for estimating latent variables in dynamical systems.
8 New results
8.1 Ocean observations analysis: upperocean dynamics, oceanatmosphere interaction, waves and extreme events.
Tropical cyclone characterization from observations
Participants: Alexis Mouche, Nicolas Reul, Frédéric Nouguier, Bertrand Chapron.
Recalling that our current paradigm is that process understanding derived from measurements shall foster improved models (theoretical, numerical) for improved both shortterm predictions and longterm projections, important efforts have been dedicated on targeting marineatmosphere extreme events. Indeed, NWP reanalysis (e.g. ERA5) generally poorly resolve extreme marineatmosphere events and their surrounding environment. Such spatiotemporal inconsistencies and unreliability of global historical reanalyses can thus hamper more accurate simulation and the projection of future changes in the main characteristics (size, intensity, locations, translation speed) of extreme events. In particular for intense vortex systems (tropical cyclones, polar lows), nearcore surface wind structural properties are today still not precisely recorded and reanalyzed. Presentday available modeldata cubes must thus be more systematically combined with direct observations (satellite, in situ). In particular, some theoretical and observational evidences have been accumulated and tested to monitor the integrated kinetic energy. Two characteristic scales have been identified and uniquely estimated using highresolution ocean surface winds from allweather spaceborne synthetic aperture radar: the radius of significant upward motions in the inflow layer, controlled by the surface wind decay, and the radius of vanishing azimuthal velocity in the outflow layer, associated with the maximum surface winds. By juxtaposing the highresolution measurements with besttrack intensity and size time derivative estimates, the instantaneous knowledge of the two characteristic scales has then been shown to inform on the steadiness of integrated kinetic energy. The resulting criterion of steadiness depends on a multiplicative constant characterizing the system's thermodynamics. Part of this investigation is in the context of Arthur Avenas PhD work.
Building databases of marineatmosphere extreme event
Participants: Alexis Mouche, Nicolas Reul, JeanFrançois Piollé.
Within the MarineAtmosphere eXtreme Sensor Synergy (MAXSS) project, the team builds an advanced and unique workbench to more precisely study these oceanatmosphere extreme events, from their generation to their impacts. Specifically, efforts have been dedicated to generate new 10yearlong databases:
 Intercalibrated satellite surface winds in extreme conditions
 A global 10year multimission surface wind (MMW) derived from the merging of these intercalibrated sensor wind estimates
 A storm atlas of allavailable Earth Observation (EO) data collected around tropical cyclones (TCs), extratropical storms (ETC), and polar lows (PLs)
 An atlas of prestorm upper ocean conditions, atmospheric forcing during the storms, and induced poststorm upper ocean impacts in the storm wakes
 A new database of high resolution TC vortex, inner and outer core wind structural distribution
 A new database of ocean swell characteristics (energy, wavelength, direction) generated by different all available sensors (satellite, in situ) and model outputs
Multiscale and Anisotropic Characterization of Images Based on Complexity
Participants: Carlos Granero Belinchon.
We present multiscale, nonlinear and directional statistical characterizations of images based on high order statistics and information theory. These characterizations allow us to characterize the multiscale properties directionally and to explore their anisotropy. We use this framework to study different turbulent flows from homogeneous and isotropic to inhomogeneous and anisotropic flows.
Characterization of oceanic high frequency variability from altimeter and surface drifting buoys
Participants: Zoé CasparCohen, Noé Lahaye, Aurélien Ponte.
We first address several challenges that are expected to arise when analyzing future SWOT data: the separation of wave and eddy dynamics, and spatiotemporal sampling issues. In particular, we aim to quantify the contribution of complementary data sources (drifting buoys, satellite temperature or optical imagery) to resolving these various challenges. To this end, we have so far concentrated our efforts on the analysis of idealized, highresolution global numerical simulations (LLC4320, eNATL60). This year, we have pursued our analysis and valorization efforts following Zoé CasparCohen's PhD thesis. A final article is in preparation (CasparCohen et al. "Combining surface drifters and high resolution global simulations enables the mapping of internal tide surface energy" ). More recently, analyses of altimetry and in situ observations (drifting buoys) were carried out as part of Margot Demol's thesis. This work is the subject of a first manuscript. We actively contributed to the success of the CSWOT experimental campaign (April 2023). Analysis of the corresponding SWOT data is in progress. New activities have been initiated around SWOT data analysis (physics of short internal tidal wave measurements).
Towards a stochastic generalized Ekman model with application to uncertainty quantification
Participants: Long Li, Étienne Mémin, Bertrand Chapron.
We introduce a stochastic approach to model the ocean surface Ekman boundary layer. This model incorporates wind, surface waves, and turbulent mixing effects. A steady version as well as a time dependent version of this generalized Ekman model has been developed. They both consider the vertical mixing effect of Stokes drift in addition to traditional EkmanStokes terms. The stochastic approach aligns with traditional parameterizations through random parameter definitions. Numerical simulations are used to assess uncertainties in the Ekman layer, focusing on statistical moment responses and sensitivity analyses of random parameters.
Estimation of Koopman eigenvalues from time series autocovariance matrix
Participants: Bertrand Chapron, Étienne Mémin.
To infer eigenvalues of the infinitedimensional Koopman operator, we study the leading eigenvalues of the autocovariance matrix associated with a given observable of a dynamical system. For any observable for which all the timedelayed autocovariance exist, we construct a related Hilbert space and a Koopmanlike operator that acts on it. We prove that the leading eigenvalues of the autocovariance matrix has onetoone correspondence with the energy of that observable; the associated eigenvectors correspond to the eigenvectors of the Koopman operator. The proof is associated to several representation theorems of isometric operators on a Hilbert space, and the weakmixing property of the observables represented by the continuous spectrum.
Impact of oceanic meso and submesoscale eddies in the ocean
Participants: Xavier Carton, Jonathan Gula.
In the context of mesoscale/submesoscale variability of the surface and shallow subsurface ocean, two geographical sites have been more particularly studied: the region north of Brazil and the Straits of Gibraltar. Both have been sampled experimentally, but have also been the loci of process studies. 1) In the former (article by Subirade et al), we have characterized the number, structure, trajectory, and lifetime of NBC rings using satellite altimetry and the insitu measurements of the EUREC4A experiment. We have shown that altimetry in the preSWOT era yields weaker currents than sampled in situ. Also, it appeared that 4 to 5 NBC rings were spawn each year. These rings interact with the Amazon plume, and form fronts, with a seasonal variability, as shown by Marin Menard's M.Sc. work. Below the NBC rings, submesoscale vortices are generated in the Demerara Bay and later interact vertically with the NBC rings. The vertical interaction of eddies has been studied more theoretically in the paper by Reinaud and Carton. We have also conducted a study on the definition of the boundaries of an oceanic eddy. Using both theory and in situ data, we have shown that it is characterized by a maximum of horizontal to vertical components of Ertel PV (paper by Barabinot et al., 2024). Several criteria have been derived for the value of this ratio, in particular the limitation of existence of a stable boundary by symmetric instability, or the observation of an inflexion point of the isopycnals at this place. 2) In the latter, at very fine scale (article by Roustan et al.), we have shown that the barotropic tide coupled with the Atlantic inflow/Med outflow exchange, leads to hydraulic jumps on Camarinal Sill and to the formation of internal bores. These bores degenerate into internal waves and particularly into solitary waves (ISW), which propagate eastward and to a lesser degree, westward, southward and northward (by reflection on the Moroccan shelf). Bore and wave breaking lead to an intense diapycnal mixing which is well characterized at the interface between the inflow and the outflow. Vertical recirculation and strong turbulent mixing is observed in the bottom (frictional) layer. The dynamics of ISWs and the quantification of mixing are the subject of forthcoming papers (PhD thesis by Jean Baptiste Roustan). Finally, as a whole, the PhD thesis by Ashwita Chouksey has covered the whole Atlantic Ocean with a focus on Mediterranean water eddies.. She has statistically characterized subsurface, submesoscale eddies (including meddies). She has discovered new deep eddies and she has described their interactions. Finally, she has shown that bottom eddies west of the Mid Atlantic Ridge were shielded and achieved very slow motion and interactions.
Toward a Stochastic Parameterization for Oceanic Deep Convection
Participants: Quentin Jamet, Étienne Mémin.
Current climate models are known to systematically overestimate the rate of deep water formation at high latitudes in response to too deep and too frequent deep convection events. We propose in this study to investigate a misrepresentation of deep convection in Hydrostatic Primitive Equation (HPE) ocean and climate models due to the lack of constraints on vertical dynamics. We discuss the potential of the Location Uncertainty (LU) stochastic representation of geophysical flow dynamics to help in the process of reintroducing some degree of nonhydrostatic physics in HPE models through a pressure correction method. We then test our ideas with idealized Large Eddy Simulations (LES) of buoyancy driven free convection with the CROCO modeling platform. Preliminary results are encouraging, and support future efforts in the direction of enriching coarse resolution, hydrostatic ocean and climate models with a stochastic representation of nonhydrostatic physics.
Climate scale and regional scale climate variability
Participants: Florian Sévellec.
We have focused on understanding the role of climate variability in observation of climate changes. This was first with Antoine Hochet (Hochet et al., 2023a) done is estimating if the length of satellite records (30 years) is long enough to detect the effect of anthropogenically forced climate change on wave height trends? Using a statistical model to derive Hs from sea level pressure field and exploiting ERA5 reanalysis data as well as 80 members of the Community Earth System Model v2 large ensemble, we show that, over the North Atlantic (NA), altimetrybased trends are mostly caused by internal variability. This suggests that changes computed over the satellite era are not yet controlled by anthropogenic climate change. Starting from 1993, the date of emergence, defined as the date when the forced signal becomes dominant over the internal variability, is later than 2050 for H s in the NA Then we have focused with Antoine Hochet (Hochet et al., 2023b) on understanding the mechanisms of regional steric sea level variability in the context of regional sea level variability. We have developed a novel method based on steric sea level variance budget that allows to detect the sources and sinks of the variability. Using ECCO state estimate, we show that interannual steric sea level variability is mainly sustained by interannual fluctuating winds via Ekman transport almost everywhere. The damping of the variability is made by both the interannual fluctuating net heat flux from the atmosphere, that largely dominates the atmospheric freshwater fluxes, and the parametrized effect of eddies. It is also found that the parametrized effect of diffusion on the variability is weak in most regions and that, although globally weak, the fluctuations of atmospheric freshwater fluxes are a source of variance close to the Equator in the Pacific Ocean.
Characterization of internal tide dynamics in highresolution realistic simulations
Participants: Adrien Bella, Noé Lahaye, Aurélien Ponte, Gilles Tissot.
Using outputs from the realistic highresolution ($dx\sim 2$ km) numerical simulation of the North Atlantic Ocean “eNATL60”, we are analyzing the lifecycle of the internal tide field based on a vertical mode decomposition of the dynamics. We analyse and quantify the impact of several processes affecting the propagation of internal tides, such as topographic scattering and interaction with the mesoscale dynamics, and show that their implications is very contrasted depending of the region considered. Overall, all these mechanisms seems to participate to a transfer of energy towards smaller scale, hence ultimately favouring the dissipation of energy. A paper has been published in the 2022 STUOD proceedings, and another one has been submitted to JGR: Oceans.
In parallel, we focus on the surface signature of the internal tide and the incoherence (lack of regularity in time). We show that the typical time of decorrelation varies between 1 month and 1 day, with shorter time associated with regions of strong mesoscale activity and internal tide with the shortest horizontal scale (i.e., high vertical mode number). A paper is about to be submitted to GRL.
Equatorial ocean coherent vortices with temperature anomalies
Participants: Noé Lahaye, Olivier Larroque.
In the context of the M2 internship of Olivier Larroque (cosupervized by Vladimir Zeitlin, LMD, IPSL), we investigated the properties of exact dipolar solution that can propagate along the equator while carrying a temperature (density) anomaly. These structures are exact solutions of an asymptotic, weakly nondivergent, system of equation describing the equatorial dynamics, and where tested in a parent model of greater complexity, the thermal rotating shallow water model on the equatorial betaplane, by means of numerical simulations. A paper is currently under revision in the Journal of Fluid Mechanics.
Nearsurface ocean dynamics
Participants: Claire Ménesguen.
We address the dynamics of the nearsurface. A collaboration with Hereon has launched us on the analysis of a dataset from two campaigns in the Agulhas Current region, where the Diurnal Warm Layer signal is predominant, and in which microstructure measurements have been made. Analysis of nearsurface mixing processes is currently underway and will be the subject of an article and a chapter in Mariana Lage's thesis.
8.2 Development and analysis of numerical and mathematical models of geophysical flows
Geometrypreserving Lie group integrators for differential equations on the manifold of symmetric positive definite matrices
Participants: Lucas Drumetz.
We have developed new methods – Geometrypreserving lie group integrators –, for numerical integration of differential equations, that rely on covariance matrices, [Drumetz et al 2023, International Conference on Geometric Science of Information]. In addition, in the context of C. Bonnet PhD thesis (UBS), we have constructed efficient methods for probability distributions based on covariant matrices and optimal transport (published in International Conference on Machine Learning). Finally, in the context of G. Morel postdoc, we improved generative AI models using optimal transport and variational penalization of Euler equations in large dimension (published in Transactions on Machine Learning Research).
Mathematical models for the interface of two coupled fluids and surface boundary layers
Participants: Francois Legeais, Roger Lewandowski.
In a first paper ("Continuous boundary condition at the interface for two coupled fluids"), we consider two laminar incompressible flows coupled by the continuous law at a fixed interface ${\Gamma}_{I}$. We approach the system by one that satisfies a friction Navier law at ${\Gamma}_{I}$, and we show that when the friction coefficient goes to $\infty $, the solutions converges to a solution of the initial system. We then write a numerical Schwarzlike coupling algorithm and run 2Dsimulations, that yields same convergence result. In a second paper, (“Surface boundary layers through a scalar equation with an eddy viscosity vanishing at the ground”), we introduce a scalar elliptic equation defined on a boundary layer given by ${\Pi}_{2}\times [0,{z}_{top}]$, where ${\Pi}_{2}$ is a two dimensional torus, with an eddy vertical eddy viscosity of order ${z}^{\alpha}$, $\alpha \in [0,1]$, an homogeneous boundary condition at $z=0$, and a Robin condition at $z={z}_{top}$. We show the existence of weak solutions to this boundary problem, distinguishing the cases $0\le \alpha <1$ and $\alpha =1$. Then we carry out several numerical simulations, showing the ability of our model to accurately reproduce profiles close to those predicted by the MoninOboukhov theory, by calculating stabilizing functions.
In a possible forthcoming paper, we consider the same framework as in the first paper, i.e two incompressible fluids, but this time coupled with a nonlinear interface law and driving conditions at the top and at the bottom. Moreover a transport term has been added. We show the existence of weak solutions and the convergence of numerical simulations obtained using the same kind of Scharz algorithms. The evolution case is being processed from a theoretical and a numerical point of view as well
Veryhigh numerical simulations of the ocean dynamics
Participants: Jonathan Gula, Claire Ménesguen, Xavier Carton, Guillaume Roullet.
Over the past year we have continued to analyse our numerical solutions GIGATL Gula et al. 2021, which are simulations of the Atlantic Ocean using the CROCO model at meso and submesoscale resolutions (6 km, 3 km and 1 km) with realistic topography, highfrequency surface forcing and tidal forcing. An example animation showing the surface dynamics (eddies and waves) and the richness of the deep circulation, in particular the coherent eddies, is shown here.
One of the recently published results using these simulations concerns the kinetic energy cascade at the ocean surface and the ability to estimate it from observations [Schubert et al., 2023]. We have shown that the total geostrophic inverse scale kinetic energy flux is linearly related to quantities that can be computed from alongtrack altimetry, and have presented for the first time its regional distribution and seasonal cycle on scales of 40 to 150 km for large parts of the global ocean based on observations.
Finally, we have also proposed a new form of potential vorticity (PV), rescaled using the rearranged Lorenz density profile, the novelty being that we consider its time evolution. We argue that this rescaled PV is more representative of the dynamics, in particular for assessing the respective effects of mixing and friction on the generation of the geostrophic circulation. The effect of mixing at the global scale, which only modifies the global stratification at rest, is taken into account in the evolution equation of this "objective" definition of PV, in the sense that it scales the PV changes with respect to their effect on the circulation [Morel et al, 2023].
Geophysical flows modelling under location uncertainty
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Participants: Noé Lahaye, Long Li, Étienne Mémin, Gilles Tissot, Francesco Tucciarone.
In this research axis we have devised a principle to derive representation of flow dynamics under location uncertainty. Such an uncertainty is formalized through the introduction of a random term that enables taking into account largescale approximations or truncation effects performed within the dynamics analytical constitution steps. Rigorously derived from a stochastic version of the Reynolds transport theorem, this framework, referred to as modeling under location uncertainty (LU), encompasses several meaningful mechanisms for turbulence modeling. It indeed introduces without any supplementary assumption the following pertinent mechanisms: (i) a dissipative operator related to the mixing effect of the largescale components by the smallscale velocity;(ii) a multiplicative noise representing smallscale energy backscattering; and (iii) a modified advection term related to the socalled turbophoresis phenomena, attached to the migration of inertial particles in regions of lower turbulent diffusivity. In a succession of works we have shown how the LU modelling can be applied to provide stochastic representations of a variety of classical geophysical flows dynamics. Numerical simulations and uncertainty quantification have been performed on Quasi Geostrophic approximation (QG) of oceanic models. It has been shown that LU leads to remarkable estimation of the unresolved errors opposite to classical eddy viscosity based models. The noise brings also an additional degree of freedom in the modeling step and pertinent diagnostic relations and variations of the model can be obtained with different scaling assumptions of the turbulent kinetic energy (i.e. of the noise amplitude). For a wind forced QG model in a square box, which is an idealized model of northAtlantic circulation, we have shown that for different versions of the noise the QG LU model leads to improve longterms statistics when compared to classical largeeddies simulation strategies. For a QG model we have demonstrated that the LU model allows conserving the global energy. We have also shown numerically that Rossby waves were conserved and that inhomogeneity of the random component triggers secondary circulations. This feature enabled us to draw a formal bridge between a classical system describing the interactions between the mean current and the surface waves and the LU model in which the turbophoresis advection term plays the role of the classical Stokes drift. A study of a stochastic version of the primitive equations model is currently investigated within the PhD of Francesco Tucciarone. Preliminary results have been published in the STUOD proceedings.
In another study we explored the calibration of the noise term through dynamic mode decomposition (DMD). This technique is performed on highresolution data to learn a basis of the unresolved velocity field, on which the stochastic transport velocity is expressed. Timeharmonic property of DMD modes allowed us to perform a clean separation between timedifferentiable and timedecorrelated components. Such random scheme is assessed on a quasigeostrophic (QG) model and has been published in the STUOD proceedings.
Analysis of stochastic representation of NavierStokes equations.
Participants: Arnaud Debussche, Berenger Hug, Étienne Mémin.
In this study we analyze the theoretical properties of a stochastic representation of the incompressible NavierStokes equations defined in the framework of the modeling under location uncertainty (LU). We demonstrate, through classical arguments, the existence of martingale solutions for the stochastic NavierStokes equations in LU form. We show they are pathwise and unique for 2D flows. We then prove that if the noise intensity goes to zero, these solutions converge, up to a subsequence in dimension 3, to a solution of the deterministic NavierStokes equation. similarly to the grid convergence property of wellestablished largeeddies simulation strategies, this result brings some guarantee on the interpretation of the LU NavierStokes equations as a consistent largescale model of the deterministic NavierStokes equation.
Analysis of stochastic representation of the primitive equations.
Participants: Arnaud Debussche, Étienne Mémin, Antoine Moneyron.
We investigate how weakening the classical hydrostatic balance hypothesis impacts theoretical properties of the LU primitive equation, such as its wellposedness. The models we consider are intermediate between the incompressible 3D LU NavierStokes equations and the LU primitive equations with standard hydrostatic balance. Also, they are expected to be numerically tractable, while accounting well for nonhydrostatic phenomena. Our main result is the wellposedness of a certain stochastic interpretation of the LU primitive equations: we proposed a weak filtered hydrostatic hypothesis, meaning the system we consider accounts for the influence of the transport noise of the vertical velocity component, of which higher frequencies are cut off. This wellposedness result holds with rigidlid type boundary conditions, and when the horizontal component of noise is independent of depth. However, the vertical component of the noise can remain general. In fact, this assumption can be related to the physical validity domain of the primitive equations. Moreover, we present and study two nonfiltered models, in which the transport noise of the vertical component is regularised using eddy(hyper)viscosity terms.
Analytical Properties for a Stochastic Rotating Shallow Water Model under Location Uncertainty
Participants: Étienne Mémin.
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class of rotating shallow water models which are stochastically perturbed in order to incorporate model uncertainty into the underlying system. The stochasticity is chosen in a judicious way, by following the principles of location uncertainty. We prove that the resulting equation is part of a class of stochastic partial differential equations that have unique maximal strong solutions. The methodology is based on the construction of an approximating sequence of models taking value in an appropriately chosen finitedimensional LittlewoodPaley space. Finally, we show that a distinguished element of this class of stochastic partial differential equations has a global weak solution. This work in collaboration with Dan Crisan and Oana Lang has been published in the journal of Mathematical Fluid Mechanics.
Wave solution of stochastic geophysical models
Participants: Bertrand Chapron, Noé Lahaye, Long Li, Étienne Mémin.
In this work we investigated the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind or coming as the feedback of the ocean on the atmosphere and leading in a very fast way to the selection of some wavelength. This interwoven, yet simple, mechanism explains the emergence of typical wavelength associated to near inertial waves. Waves that are not in phase with the random forcing are damped at a rate that depends on the random forcing variance. Geostrophic adjustment is also interpreted as a statistical homogeneization process in which, in order to conserve potential vorticity, the smallscale component tends to align to the velocity fields to form a statistically homogeneous random field. We are pursuing this study to devise a stochastic model of wavecurrent interaction.
Parameterization for coarseresolution ocean modeling
Participants: Louis Thiry, Long Li, Étienne Mémin, Guillaume Roullet.
We work on simple parameterization for coarseresolution oceanic models to replace computationally expensive highresolution ocean models. We focus on the eddypermitting scale (grid step Rossby radius) and computationally cheap parameterization. We are currently investigating the modification of the diffusion (friction) operator to reproduce the mean velocity observed via measurements or a highresolution reference solution. To test this new parameterization on a doublegyre quasigeostrophic model, we are implementing a fast and portable python implementation of the multilayer quasigeostrophic model. This study has been published in the STUOD proceedings. In another study we have explored a new discretization of the multilayer quasigeostrophic (QG) model that models implicitly the subgridscale effects. This new discrete scheme is based on several numerical choices that first ensure an exact material conservation of the potential vorticity. The advection is performed with a weighted essentially nonoscillatory interpolation whose implicit dissipation replaces the usual explicit (bi)harmonic dissipation. We finally proposed a new method for solving the elliptic equation that warrants reversibility which on a staggered discretization. The method has the advantage to not requiring the tuning of any additional parameter, e.g. additional hyperviscosity. This work has been recently submitted and we released a very short, concise, and efficient PyTorch implementation of our method to facilitate future data assimilation or machinelearning developments upon this new discretization.
We also have developed a unified QG and the RSW models, exploring the effect of higher order numerics, exploring the potential of WENO interpolation, developing alternative way of describing interfacial stress (bottom, surface, lateral), diagnosing the numerical implicit dissipation, using discrete differential geometry as a framework for discretization, testing Pytorch and Julia as alternatives languages to Fortran, inventing new code architectures. This work is under review in Geoscientific Model Development (EGU journals).
Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discretetime schemes
Participants: PierreMarie Boulvard, Étienne Mémin.
In this paper we characterize numerically through two criteria the Lévy area related to unresolved fluctuation velocities associated to a stochas tic coarsescale representation of geophysical fluid flow dynamics. We study in particular whether or not the process associated to the random unresolved velocity components exhibits a Lévy area corresponding to a Wiener process, and if the law of this process can reasonably be approached by a centered Dirac measure. This exploration enables us to answer positively to a conjecture made for the constitution of highorder discrete time evolution schemes for stochastic representation defined from stochastic transport.
Discrete numerical schemes for stochastic shallow water models under location uncertainty
Participants: PierreMarie Boulvard, Étienne Mémin, Jacques Sainte Marie.
In this work we focus on the derivation of efficient discrete schemes, for a stochastic version of the shallow water model derived and analyzed in previous works of the team. We in particular pay attention to the devise of ”second order” like methods. This scheme that takes the form of an iterated double advection of the noise allow us to have an implicit, implementation of the noise associated diffusion, bringing a natural equilibrium, at the discrete level between the energy dissipation by the noise and its energy intake. The corresponding scheme corresponding to an extension of entropy conserving schemes proposed in the discrete setting by the Ange Inria team is fully justified in this study.
Stochastic compressible fluid dynamics
Participants: Étienne Mémin, Gilles Tissot.
The aim of this study is to provide a stochastic version under location uncertainty of the compressible NavierStokes equations. The modelling under location uncertainty setting is used here to derive a physically consistent stochastic dynamical system for compressible flows. It relies on an extended stochastic version of the Reynolds transport theorem involving stochastic source terms. In a similar way as in the deterministic case, this conservation theorem is applied to density, momentum and total energy in order to obtain a transport equation of the primitive variables, i.e. density, velocity and temperature. For the modelling of ocean dynamics, the transport of mass fraction of species, such as salinity, is also considered. We show that performing low Mach and Boussinesq approximations to this more general set of equations allows us to recover previous versions of incompressible stochastic NavierStokes equations and the stochastic Boussinesq equations, respectively. Finally, we provide some research directions on the use of this general set of equations in the perspective of relaxing the Boussinesq and hydrostatic approximation for ocean modelling.
Stochastic hydrodynamic stability under location uncertainty
Participants: Étienne Mémin, Gilles Tissot.
Stochastic linear modeling proposed in Tissot, Mémin, and Cavalieri [J. Fluid Mech. 912, A51 (2021)] is based on classical conservation laws subject to a stochastic transport. Once linearized around the mean flow and expressed in the Fourier domain, the model has proven its efficiency to predict the structure of the streaks of streamwise velocity in turbulent channel flows. It has been in particular demonstrated that the stochastic transport by unresolved incoherent turbulence allows us to better reproduce the streaks through liftup mechanism. In the present work, we focus on the study of streamwiseelongated structures, energetic in the buffer and logarithmic layers. In the buffer layer, elongated streamwise vortices, named rolls, are seen to result from coherent wavewave nonlinear interactions, which have been neglected in the stochastic linear framework. We propose a way to account for the effect of these interactions in the stochastic model by introducing a stochastic forcing, which replace the missing non linear terms. In addition, we propose an iterative strategy in order to ensure that the stochastic noise is decorrelated from the solution, as prescribed by the modelling hypotheses. This study has been published in the journal Physical Review Fluids. This work is in collaboration with André Cavalieri (Instituto Tecnologico de Aeronautica, SP, Brésil).
Surface wave modelling
Participants: Bertrand Chapron.
Not only for extreme events, ocean surface waves have been demonstrated to be an important component of coupled earth system models. They affect atmosphereocean momentum transfer, break ice floes, alter CO2 fluxes, and impact mixedlayer depth through Langmuir turbulence. In contrast to the goals of thirdgeneration spectral models, the wave information needed for mixing, airsea, and waveicecoupling is much less than a full directional wave spectrum. All present parameterizations – for waveinduced mixing, surface drag, floe fracture, or sea spray – use primarily the wave spectrum's dominant frequency, direction, and energy or quantities that can be estimated from these such as Stokes drift and bending moments. Modest errors in sea state do not strongly affect the impacts of these parameterizations. This minimal data and accuracy need starkly contrasts with the computational costs of spectral wave models as a component of nextgeneration Earth System Models (ESM). In that context, an alternative, costefficient wave modeling framework for airsea interaction to enable the routine use of sea statedependent airsea flux parameterization in ESMs. In contrast to spectral models, the ParticleinCell for Efficient Swell Wave Model (PiCLES) is under developments targeting coupled atmosphereoceansea ice modeling. Combining Lagrangian wave growth solutions with the ParticleInCell method leads to a periodically meshing wave model on an arbitrary grid that scales in an embarrassingly parallel manner. The set of equations solves for the growth and propagation of a parametric wave spectrum's peak wavenumber and total wave energy, which reduces the state vector size by a factor of 50200 compared to spectral models. Ideally, PiCLES will only require a fraction of the cost of established wave models with sufficient accuracy for ESMs–rivaling that of spectral models in the open ocean. We will evaluate PiCLES against WaveWatchIII in efficiency and accuracy and discuss planned extensions of its capability. This work is in collaboration with M. Hell, B. FoxKemper and T. Protin (PhD)
8.3 Data/Models interactions and reduced order modelling
Datadriven methods for partially observed systems
Participants: Pierre Tandeo, Florian Sévellec.
In collaboration with Pierre Ailliot [Tandeo et al, 2023] and within a datadriven context, we have demonstrated our ability to obtain accurate and reliable predictions of a partially observed Lorenz63 system, where only the second and third components are observed and access to the equations is not allowed. This was done by a combination of machine learning and data assimilation techniques. The key aspects were the following: the introduction of latent variables, a linear approximation of the dynamics and a database that is updated iteratively, maximizing the likelihood. Interestingly, we found that the latent variables inferred by the procedure are related to the successive derivatives of the observed components of the dynamical system. The method is also able to reconstruct accurately the local dynamics of the partially observed system. Overall, the proposed methodology is simple, is easy to code and gives promising results, even in the case of small numbers of observations.
The state of the atmosphere, or of the ocean, cannot be exhaustively observed. Crucial parts might remain out of reach of proper monitoring. Also, defining the exact set of equations driving the atmosphere and ocean is virtually impossible because of their complexity. The goal of this study is to obtain predictions of a partially observed dynamical system without knowing the model equations. In this datadriven context, we focus on the Lorenz63 system, where only the second and third components are observed and access to the equations is not allowed. To account for those strong constraints, a combination of machine learning and data assimilation techniques is proposed. The key aspects are the following: the introduction of latent variables, a linear approximation of the dynamics and a database that is updated iteratively, maximizing the likelihood. We find that the latent variables inferred by the procedure are related to the successive derivatives of the observed components of the dynamical system. The method is also able to reconstruct accurately the local dynamics of the partially observed system. Overall, the proposed methodology is simple, is easy to code and gives promising results, even in the case of small numbers of observations.
Ensemble data assimilation of largescale dynamics with uncertainty
Participants: Benjamin Dufé, Étienne Mémin.
We investigated the application of a physically relevant stochastic dynamical model in ensemble Kalman filter methods. Ensemble Kalman filters are very popular in data assimilation because of their ability to handle the filtering of highdimensional systems with reasonably small ensembles (especially when they are accompanied with so called localization techniques). The stochastic framework used in this study relies on Location Uncertainty (LU) principles which model the effects of the model errors on the largescale flow components. The experiments carried out on the Surface Quasi Geostrophic (SQG) model with the localized square root filter demonstrate two significant improvements compared to the deterministic framework. Firstly, as the uncertainty is a priori built into the model through the stochastic parametrization, there is no need for adhoc variance inflation or perturbation of the initial condition. Secondly, it yields better MSE results than the deterministic ones. This work has been published in QJRMS.
In another study, we investigated the calibration of the stochastic noise in order to guide the realizations towards the observational data used for the assimilation. This is done in the context of the stochastic parametrization under Location Uncertainty (LU) and data assimilation. The new methodology is rigorously justified by the use of the Girsanov theorem, and yields significant improvements in the experiments carried out on the Surface Quasi Geostrophic (SQG) model, when applied to Ensemble Kalman filters. The particular test case studied here shows improvements of the peak MSE from 85% to 93%.
Reduced Order Modelling for internal waves
Participants: Noé Lahaye, Igor Maingonnat, Gilles Tissot.
Using an idealized configuration in a 1layer rotating shallow water model, we study the evolution of an inertiagravity wave interacting with a turbulent mesoscale jet. The resulting incoherent inertiagravity wave field is then analyzed using several methods: spectral POD, extended spectral POD and resolvent analysis. The goal of this study is twofold: 1) better understand and characterize the lossof coherence of the inertiagravity wave when interacting with the turbulent background flow and 2) extract the relevant modes of variability to formulate a reduced order model that is able to capture and predict the inertiagravity wave, given some knowledge of the mesoscale flow contribution. The latter is oriented towards the devise of dataassimilation models for incoherent internal wave fields in the ocean. A paper summarizing the results as been published in the STUOD proceedings (2022), and another one is in preparation.
8.4 AI models and methods for ocean data analysis
Neural network based generation of 1dimensional stochastic fields with turbulent velocity statistics
Participants: Carlos Granero Belinchon.
We define generative neural network architectures to model stochastic 1dimensional fields with turbulent velocity statistics. The main ideas are 1) to use architectures mimicking the structure of classical stochastic models such as random wavelet cascades and 2) to introduce Kolmogorov and Obukhov laws in both the training and validation of the models. Two approaches are used: an unsupervised one which does not require turbulent data and only needs the desired statistics to be imposed, and one based on GANs which requires turbulent data.
Learningbased prediction of the particles catchment area of deep ocean sediment traps
Participants: Jonathan Gula, Ronan Fablet.
We have studied how finescale ocean dynamics affect carbon export and its fate in the water column. The mesoscale and submesoscale currents play an important role, not only creating very strong heterogeneity in particle production at the surface, but also driving horizontal and vertical velocities that affect the exchange between the surface layer and the interior of the ocean. We have used numerical Lagrangian experiments and a realistic highresolution ocean model to train a neural network to predict the surface origin of particles trapped in a deep sediment trap, with success and suggesting an application to satellite data. The results have been submitted to the EGU Journal Ocean Science.
Ensemble forecasts in reproducing kernel Hilbert space family
Participants: Benjamin Dufé, Berenger Hug, Maël Jaouen, Étienne Mémin, Gilles Tissot.
A methodological framework for ensemblebased estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a family of reproducing kernel Hilbert spaces (RKHS) with kernel functions driven by the dynamics. In the RKHS family, the Koopman and Perron–Frobenius operators are unitary and uniformly continuous. This property warrants they can be expressed in exponential series of diagonalizable bounded evolution operators defined from their infinitesimal generators. Access to Lyapunov exponents and to exact ensemble based expressions of the tangent linear dynamics are directly available as well. The RKHS family enables us the devise of strikingly simple ensemble data assimilation methods for trajectory reconstructions in terms of constantintime linear combinations of trajectory samples. Such an embarrassingly simple strategy is made possible through a fully justified superposition principle ensuing from several fundamental theorems. This study has been published in the journal Physica D: nonlinear phenomena. Duting the PhD of Mael Jaouen we extend the numerical experimentation to a windforced threelayers QG model.
Learning of representations for geophysical dynamics
Participants: Maxime Beauchamp, Lucas Drumetz, Ronan Fablet, Said Ouala.
We focused our efforts on learning closure terms for the representation of subgridscale processes, and more broadly on learning corrections to a reference model in simulations of geophysical flows.We have applied an “aposteriori” learning method introduced in (Frezat et al., 2022) to nondifferentiable direct simulation codes. Our contributions explore both emulatorbased methods (Frezat et al., 2023) and Eulertype approximations for computing the gradient of the a posteriori learning cost (Ouala et al., 2023).
Datadriven methods and Endtoend learning for data assimilation
Participants: Bertrand Chapron, Lucas Drumetz, Ronan Fablet, Etienne Mémin, Pierre Tandeo.
We developed several datadriven variational data assimilation methods, addressing various methodological challenges tackled, namely:
 learning from partial data (incomplete in space and time, in collaboration with A. Frion)
 parameterization of generative/stochastic models enabling the prediction of time series and the resolution of inverse problems with uncertainties (A. Frion, N. El Bekri).
This work applies to several topics, and in particular the short and midterm prediction of sea level anomaly from real data (in the Gulf Stream area – H. Goeogenthum PhD thesis) and the prediction of multispectral image reflectance dynamics (A.Frion PhD thesis). We also proposed a CNN model with "attention mechanism" for the prediction of chlorophyll concentration from atmospheric and oceanic physical drivers, for the long term reconstruction of past chlorophyll time series at global scale (J. Rousillon PhD thesis). Finally, in the context of P. Aimé PhD work and in collaboration with S. Sharma (postdoc), we studied different evaluation metrics as well as various AI methods for merging multispectral and panchromatic data.
We are also developing original endtoend approaches for learning neural data assimilation methods based on both variational formulations (Fablet et al., 2021) and Kalman filtering methods (Ouala et al., 2022). Our contributions over the past year concern in particular the quantification of uncertainties in the 4DVarNet scheme, for example by exploiting Bayesian variational inferencetype formulations (Lafon et al., 2023) and stochastic PDEtype representations of the underlying dynamics. We are developing various simulated and real case studies to demonstrate these approaches (e.g. surface currents, turbidity, sea surface height) (Febvre et al., 2023; Fablet et al., 2023). This line of work is in the context of the PhD thesis (at IMT) of Quentin Febvre, Hugo Georgenthum and Simon Bennaïchouche, and in collaboration with Said Ouala (postdoc IMT) and Maxime Beauchamp (postdoc IMT).
Machine learning for trajectory data
Participants: Carlos Graneo Belinchon, Ronan Fablet.
Simulation and analysis of trajectometric data are specific issues for ocean observation (e.g., ocean surface drift, ship trajectories, marine animal movements...). We are exploring learning methods for the simulation and analysis of these different types of trajectory data. This includes both new GAN methods for the simulation of bird trajectories [Roy et al., 2022], conditional simulation of drift trajectories [Botvinko et al., 2022], shortterm prediction of ship trajectories [Nguyen et al., 2024] or the exploitation of ship trajectory data for the estimation of marine currents [Benaichouche et al., 2022].
9 Bilateral contracts and grants with industry
9.1 Bilateral Grants with Industry
Participants: Carlos Granero Belinchon, Ronan Fablet, Pierre Tandeo.
 ADIOS project with SHOM.
 M. Zambra PhD thesis with NavalGroup
 CMEMS project 4DVarNETOFDA with CLS, OceanDataLab (P. Tripathi PhD thesis)
 Eodyn (S. Benaïchouche PhD thesis)
 H2020 project EditoModelLab with MercatorOceanIntl (D. Botvinko PhD thesis)
10 Partnerships and cooperations
10.1 International initiatives
 EUREC4AOA: Improving the representation of smallscale nonlinear oceanatmosphere interactions in Climate Models by innovative joint observing and modelling approaches. JPlOcean project, 20202024. Jonathan Gula : LOPS coordinator and Xavier Carton .
 STUWA: Impacts of submesoscale turbulence and internal waves on the energetics of the Atlantic Ocean. ONR project, 2022  2023. Jonathan Gula : participant
 ARCHANGE: MOGBPA chair on climate change in Arctic (PI: A.V. Fedorov – Yale University & LOCEANIPSL). 20202024. Florian Sévellec : contributor.
10.2 International research visitors
10.2.1 Visits to international teams
Jonathan Gula

Visited institution:
University of California, Los Angeles

Country:
USA

Dates:
mid2022 – mid2023

Context of the visit:
collaboration in the group of James C. McWilliams

Mobility program/type of mobility:
sabbatical
Etienne Mémin

Visited institution:
Imperial College, London

Country:
UK

Dates:
January – February 2023

Context of the visit:
collaboration with D. Crisan and D. Holm

Mobility program/type of mobility:
CNRS/Imperial Fellowship UMI Abraham De Moivre, Visiting professor
Aurélien Ponte

Visited institution:
University of Western Australia

Country:
Australia

Dates:
June – September 2023

Context of the visit:
collaboration with Nicole Jones and Matthew Rayson in the context of the experimental campaign carried out below the SWOT pass on the edge of the North Australian Plateau.

Mobility program/type of mobility:
Gledden visiting fellowship (UWA)
Florian Sévellec

Visited institution:
University of Southampton

Country:
UK

Context of the visit:
visiting scientist
Pierre Tandeo

Visited institution:
Univ. Buenos Aires (Argentine)

Country
: Argentina

dates
: February 27th – March 10th

Context of the visit:
teaching: doctoral course in machine learning for geophysics
Pierre Tandeo

Visited institution:
Univ. Grenada

Country
: Spain

dates
: December 11th – 19th

Context of the visit:
teaching: doctoral course in turbulence
10.3 European initiatives
10.3.1 Horizon Europe
 Florian Sévellec : EERIE – European Eddy Rich Earth System Models, PIs: Thomas Jung (Alfred Wegner Intitute, Université de Bremen, Allemagne) and Malcolm Roberts (MetOffice, UK). F. Sévellec is coinvestigator.
10.3.2 H2020 projects
 Jonathan Gula , Guillaume Roullet : iAtlantic  Integrated Assessment of Atlantic Marine Ecosystems in Space and Time, participants, 2019 – 2023
 Ronan Fablet : EditoModelLab, Eurosea
10.3.3 Other european programs/initiatives
 Jonathan Gula : COSSMoSS Capturing Oceanic Submesoscales, Stirring and Mixing with Sound and Simulations. ERC Consolidator Grant, participant, 20232028
10.4 National initiatives
PPR "Océan et climat" CLIMARCTIC
Participants: Pierre Tandeo, Ronan Fablet, Lucas Drumetz.
The CLIMARCTIC project aims at improving our understanding of climate change in the arctic, both at regional and global scales. Pierre Tandeo is coPI and R. Fablet and L. Drumetz participate to WP1.
PPR MEDIATION
Participants: Etienne Mémin, Carlos Granero Belinchon, Pierre Tandeo.
The MEDIATION project aims at improving and developping better numerical code of the ocean dynamics. E. Mémin is coPI of WP2 “parametrisation stochastique et quantification d'incertitude” and participate to WP3 “Modèles sous maille”. P. Tandeo and C. Granero Belinchon participate to WP4 “IA pour les codes océaniques”.
PPR CLIMArcTIC
Participants: Florian Sévellec.
“From regional to global impacts of climate change in the Arctic : an interdisciplinary perspective” (procjet “Océan 2030”, PI: C. Lique, LOPS Ifremer). F. Sévellec is in charge of WP1.
ANR Chair: OceaniX
Participants: Ronan Fablet, Florian Sévellec.
“ PhysicsInformed AI for Observation driven Ocean AnalytiX” (PI: R. Fablet)
ANR Melody
Participants: Ronan Fablet.
“Bridging geophysics and MachinE Learning for the modeling, simulation and reconstruction of Ocean DYnamics”. (PI: R. Fablet)
ANR JCJC ModITO
Participants: Noé Lahaye.
"Modelling the Internal Tide in the Ocean" project aims at developing a data assimilation model for the ocean internal tide field, in the context of the SWOT mission. (PI: N. Lahaye)
ANR JCJC SCALES
Participants: Carlos Granero Belinchon.
“ Statistical ChAracterization of multiscaLE complex Systems with information theory ” (PI: C. Granero Belinchon)
ANR JCJC DEEPER
Participants: Jonathan Gula.
“Impacts of DEep submEsoscale Processes on the ocEan ciRculation” (PI: J. Gula), 2020 – 2025. The goals of the DEEPER project are to quantify the impacts of deep submesoscale processes and internal waves on mixing and water mass transformations. In addition, the DEEPER project will explore ways of parameterizing these impacts using the latest advances in machine learning.
LEFEIMAGO: ARVOR
Participants: Florian Sévellec.
“Assessing the Role of forced and internal Variability for the Ocean and climate Response in a changing climate” (PI: F. Sévellec), 2022–2024.
LEFEGMMC: OASIS
Participants: Florian Sévellec.
“Ocean state Analog inSItu analyses System (PI: N. Kolodziejczyk – CNAP, LOPS), 2022–2024
ALESE
Participants: Carlos Granero Belinchon.
ALESE is a MITI CNRS project
TOSCA CNES projects

DIEGO
(SWOT science team). Participants: A. Ponte (PI), J. Gula, N. Lahaye, P. Tandeo, R. Fablet, C. Menesguen

THEIA
PI: C. Granero Belinchon

IMHOTEP
PI: T. Penduff (IGE, CNRS) & W. Llovel (CNRS, LOPS). Participants: F. Sévellec
InraeInria Funding
Participants: Etienne Mémin.
PhD thesis of Merveille Talla, on the development of diffusion generative models applied to turbulent flows. Collaboration with Dominique Heitz and Valentin Resseguier (ACTA Inrae Rennes team).
Action exploratoire “KoopduMonde”
Participants: Gilles Tissot, Étienne Mémin.
This project (“Koopman operator modelling of nonlinear dynamical systems for ensemble methods”) consists in expressing the Koopman operator associated with a highdimensional geophysical dynamical system in a family of reproducing kernel Hilbert spaces. The interest is to learn the nonlinear dynamics, locally in the phase space, in order to solve efficiently ensemble data assimilation problems. Multilayer quasigeostrophic models representative of the Gulf stream area is considered in this work.
10.5 Regional initiatives
ARED AMMSDO
Participants: Étienne Mémin, Antoine Moneyron.
The Britany ARED project " Analyse Mathématique de Modèles Stochastiques réalistes de la Dynamique Océanique" in collaboration with Arnaud Debussche (ENS/MINGUS) funds 50 percent of the PhD thesis of Antoine Moneyron.
SAD AMIGAS
Participants: Pierre Tandeo, Florian Sévellec.
“Analog Methods to Identify Global Atmospheric Simulations” (PI: P. Tandeo).
11 Dissemination
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
Member of the organizing committees
 Lucas Drumetz : Organization of a special session at GRETSI 2023, “Signal processing and AI for environmental data”
 Carlos Granero Belinchon : Organiszation of Brest workshop on Environmental Physics and Signal Processing – June 19th–21st 2023.
 Florian Sévellec : Organization of the AI4OAC workshop (Artificial Intelligence for Ocean, Atmosphere, and Climate) as part of GDR “Défis théoriques pour les sciences du climat” and ANR chair OceaniX, spring 2023, Brest, France.
11.1.2 Scientific events: selection
Member of the conference program committees
 Jocelyne Erhel : Reviewing for the JEMP workshop (Journées d'Etude des Milieux Poreux)
11.1.3 Journal
Member of the editorial boards
 Pierre Tandeo : Member of the editorial board in Nonlinear Processes in Geophysics (EGU journal).
 Jocelyne Erhel : Member of the editorial board in Interstices, and review activity in this journal (10 reviews in 2022); Member of the editorial board in ETNA; Member of the editorial board in ESAIM Proceedings and Surveys.
 Jonathan Gula : Member of the editorial board in Ocean Modelling
 Ronan Fablet : Associate editor in Frontier in Marine Science (special issue on AI & Ocean Remote Sensing); Associated editor in Remote Sensing
 Pierre Tandeo : assocate editor in "Nonlinear Processes in Geophysics" (EGU).
Reviewer  reviewing activities
 Clément de Boyer Montégut is a reviewer for Deep sea research and GRL.
 Lucas Drumetz is a reviewer for ICML, NeurIPS, IEEE ICASSP, GRETSI, IEEE TGRS .
 Carlos Granero Belinchon has reviewed for Physica A, Physical Review E, Nature and Remote Sensing (MDPI).
 Jonathan Gula is reviewer for JAMES, JPO, Nature Communication
 Noé Lahaye has reviewed for has reviewer for J. Phys. Oceanogr., Geophysical Research Letter, Ocean Science, Ocean Modeling
 Roger Lewandowski has reviewed for Physica D, Nonlinear Analysis, M2AN
 Etienne Mémin is reviewer for J. Fluid Mech., Ocean Modelling, J. Comp. Phys., Siam Review, Comp. and Fluids, Dutch Research Council NWO.
 Claire Ménesguen has reviewed for J. Phys. Oceanogr..
 Aurélien Ponte has reviewed for J. Phys. Oceanogr..
 Gilles Tissot has reviewed for AIAA Journal; Theoretical and Computational Fluid Dynamics, European Journal of Mechanics / B Fluids, Physica Scripta
 Guillaume Roullet is a reviewer for JAMES and Ocean Modelling
 Xavier Carton has reviewed for Physics of Fluids, Journal of Physical Oceanography, Journal of Fluid Mechanics.
 Florian Sévellec : reviewer for Journal of Climate, Fluids, Communications Earth & Environment
11.1.4 Invited talks
 Gilles Tissot : Institut Pprime (Poitiers, 27/04/2023), LAUM (Le Mans, 07/02/2023)
 Jonathan Gula : “Turbulence in the wake of seamounts”, Invited Seminar, Stanford University, USA, Feb. 28 2023.

Ronan Fablet
 “Océans et Jumeaux Numériques: Quels enjeux derrière ces termes ?”, GdR Omer, Paris, Jan. 2023.
 “Endtoend and physicsinformed learning for ocean dynamics”, Int. Liege Colloqium on Ocean Dynamics, Liege, May 2023.
 “Leveraging Deep learning for ocean reanalyses. Why? How? When?”, CMEMS Ocean Reanalyses workshop, Oct. 2023.
 “IA et Jumeaux numériques de l’Océan: Quels enjeux et défis?”, Techno Conférence “Numérique & Maritime”, Oct. 2023.
11.1.5 Scientific expertise
 Claire Menesguen is member of CT1 for GENCI, CS LEFE CLIMAGO and member of the board of the GdR "Theoretical challenges for climate sciences".
 Florian Sévellec : member of panels of funding agencies DFG (Germany), Lefe GMMC et CLIMAGO (France)
 Ronan Fablet : member of CS LEFEMANU, CS FOF, CST SHOM and science Board Mercator Ocean Intl.
11.1.6 Research administration
 Roger Lewandowski : member of IRMAR head commity, CA of Rennes University, Rennes University commitee for ecological transition of l'Université de Rennes, council of the department of mathematics
 Jonathan Gula is a member of the panel of IRGA projets (UGA)
 Ronan Fablet is a member of the ANR committee for AAP ASTRID
11.2 Teaching  Supervision  Juries
11.2.1 Teaching
 Clément De Boyer Montégut : UE interdisciplinaire en sciences de la mer et du littoral : présentation générale des aspects physique du système O/A, puis focus sur la thématique de la vulnérabilité des socioécosystèmes face au changement climatique (19h, M1 UBO).
 Carlos Granero Belinchon : Analysis, signal processing, numerical calculus, probability and statistics (L3, IMT Atlantique); Introduction to machine learning, Dynamical systems modelling, Big data and cloud computing for climate (M1 & M2, IMT Atlantique).
 Lucas Drumetz : Master “Sciences des données océaniques” (UBOIMT AtlantiqueENSTA Bretagne), in charge of course: “Data Science 1 ; statistiques descriptives, problèmes inverses, régression, interpolation optimale, analyse en composantes principales, applications à des données océanographiques”
 Jonathan Gula : Numerical modelling (M2 Marine Sciences, UBO) and Ocean Turbulence (M2 Marine Sciences, UBO).
 Roger Lewandowski : Finite elements (M2 Mathematics, UR1).
 Pierre Tandeo : Summer school on the Atlantic salmon (27th June to 1st July).
 Gilles Tissot : Numerical methods for acoustics and vibration (M2 acoustics and mechanics université du Mans).
 Xavier Carton : dynamique des fluides geophysiques M2 physique ocean climat, dynamique de meso echelle oceanique M2 physique ocean climat
 Florian Sévellec : Advanced Methods in Physical Oceanography, M1 (Université de Bretagne Occidentale, France). Master Sciences des données océaniques (UBOIMT AtlantiqueENSTA Bretagne), responsabilité du cours “Data Science 1” ; statistiques descriptives, problèmes inverses, régression, interpolation optimale, analyse en composantes principales, applications à des données océanographiques.
11.2.2 Supervision
 Phd in progress: Margot Demol, supervised by Aurélien Ponte (started Sept. 2022).
 PhD in progress: Adrien Bella, Understanding interactions between internal tides a nd currents in the ocean using highfidelity numerical simulations, started October 2021, supervised by Noé Lahaye, Gilles Tissot, Étienne Mémin.
 PhD in progress: Igor Maingonnat, Understanding and modelling nonlinear mechanisms in the ocean: internal waves / background flow interactions. Started November 2021, supervised by Noé Lahaye, Gilles Tissot, Étienne Mémin.
 PhD in progress: Manolis Perrot (Inria AirSea), student at U. Grenoble Alpes, Consistent modelling of subgrid scale for ocean climate models. Started October 2021, supervised by Eric Blayo, Florian Lemarié, Étienne Mémin.
 PhD in progress : Berenger Hug, analysis of stochastic models under location uncertainty, started November 2020, supervisors: Étienne Mémin, Arnaud Debussche.
 PhD defended: Benjamin Dufée, Particle filters in high dimentional spaces, defense in Sept. 2023. Supervisors: Dan Crisan, Étienne Mémin.
 PhD in progress: Francesco Tucciarone, Stochastic models for high resolution oceanic models, started November 2020, supervisors: Long Li, Étienne Mémin.
 PhD in progress: Antoine Moneyron, Mathematical analysis of stochastic ocean dynamics models, started May 2023, supervisors: Arnaud Debussche, Étienne Mémin.
 PhD in progress: Mael Jaouen, Learning of ocean dynamics models through Koopman operator and Kernel methods, started June 2023, supervisors: Étienne Mémin, Gilles Tissot.
 PhD in progress: Merveille Talla, Generative diffusion methods for turbulent flows, started october 2023, supervisors: Dominique Heitz, Étienne Mémin, Valentin Resseguier.
 PhD in progress: Margot Demol (Ifremer), 2022  2024. "Estimating the Ocean Circulation in the SWOT era », supervisors: Aurélien ponte, Pierre Gareau
 PhD in progress: Mathis Grangeon (DGA/Region Bretagne), 2021  2023: "Acoustic geolocation and smallscale ocean variability", supervisors: Aurélien Ponte, FrançoisXavier Socheleau, Florent Le Courtois
 PhD in progress: Mariana Lage (HelmhotzZentrum Hereon  Germany), 20212024, « Smallscale variability of turbulence and stratification in the Surface Mixed Layer », Supervisors: Claire Menesguen, Jeff Carpenter
 PhD in progress: Yao Meng (Exeter), 20212024. « Investigating Submesoscale Ocean Dynamics in the Mozambique Channel with Seismic and Simulation Datasets », supervisors: K. Sheen, K. Gunn, C. Menesguen, I. Ashton
 PhD in progress: R. Ravasse, 2023  2026. Structure and dynamics of submesoscale coherent vortices in the ocean. Supervisors: Xavier Carton , Jonathan Gula .
 PhD in progress: Théo Picard, “Data‐driven MOdeling and sampling to MOnitor PARticle origins in deep sediment traps”, 2021  2024. Supervisors: J. Gula, L. Memery (LEMAR), R. Fablet.
 PhD in progress: N. Schifano, “Tracer transport and mixing in the bottom mixedlayer”, 2021  2024. Supervisors: J. Gula, C. Vic.
 PhD in progress: C. Lemaréchal, “Deep Hydrodynamic Processes near Hydrothermal vents”, 2020  2023 (defense planned May 2024). Supervisors: J. Gula, G. Roullet
 PhD in progress; L. Wang, Impact of the meso and submesoscale dynamics on the fate of exported particles in the deep ocean. Supervisors: J. Gula (50%) and L. Mémery.
 PhD in progress: Armand Vic, The dynamics of oceanic Vortices Coupled with the Atm osphere at the Mesoscale and submesoscale, started 2020 (defense planned March 2024). Supervisors: J. Gula and X. Carton.
 PhD finished of A. Chouksey, Submesoscale coherent vortices in the Atlantic and their impact on the large scale circulation. Supervisors: J. Gula and X. Carton. Defended Dec. 2023.
 PhD in progress: François Legeais, Couplage et turbulence à l'interface océan/atmo sphère, started in 2021. Supervisor: R. Lewandowski.
 PhD in progress: Pierre Le Bras, since 2020, “Méthodes analogues pour l’identification de simulations océanographiques globales, Université de Bretagne Occidentale. Bourse AREDISblue (région Bretagne) et UBO. Supervisors: F. Sévellec; cosupervisors: P. Tandeo et J. Riuz.
 PhD in progress: Perrine Bauchot, since 2021, “Intelligence artificielle pour l’observation de l’environnement marin”, ENSTA Bretagne. Bourse ANR Chair OceaniX. Cosupervisors: F. Sévellec, R. Fablet
 PhD in progress: Erwan Oulhen, thèse, since 2021, “Ocean state Analog inSItu analyzes System”, UBO. Bourse ARED (région Bretagne) and UBO. Supervisors: B. Blanke , N. Kolodziejczyk, P. Tandeo, F. Sévellec.
 PhD in progress: Soumaïa Tajouri, since 2021, “Impact of freshwater flux interannual variability on regional ocean circulation and sea level changes over the altimetric period 19932020”. Bourse CNES and UBO. supervisor: F. Sévellec and cosupervisor: W. Llovel.
 PhD in progress: Arthur Coquereau, since 2022, “Assessing the Role of forced and internal Variability for the Ocean and climate Response in a changing climate”. Bourse région bretagne et UBO. Supervisor: Sévellec; cosupervisors: J.M. Hirschi et T. Huck.
 PhD defended: Joana Roussillon; defended 18/12/23, “Apprentissages profonds pour la reconstruction de séries temporelles de biomasse phytoplanctonique globale et l’étude des mécanismes physiquesbiogéochimiques sousjacents”, LOPS (Lucas Drumetz: cosupervisor)
 PhD in progress: Anthony Frion, “méthodes d’apprentissage de systèmes dynamiques et assimilation variationnelle basées données en utilisant l’opérateur de Koopman”, IMT Atlantique (Lucas Drumetz: supervisor).
 PhD in progress: P. Aimé, IMT ATlantique, supervisors: L.Drumetz, M. Dalla Mura (G ipsalab), T. Bajjouk (IFREMER), R. Garello (IMT Atlantique).
 PhD in progress: Hugo Georgenthum, IMT Atlantique, supervisors: L.Drumetz, J. Le Sommer (CNRS/IGE), D. Greenberg (HEREON), L. Drumetz (Odyssey) et R. Fablet (Odyssey).
 PhD in progress: Nafoual El Bekri, UBO, supervisors: L. Drumetz and F. Vermet (UBO/EURI A).
 PhD in progress: Adrien Stella, “Dynamique du phytoplancton et processus sousjacents dans l’océan Arctique sur la base d’observations et d’apprentissage profond”, LOPS & IMT Atlantique (Lucas Drumetz: cosupervisor)
 PhD in progress: Benoit Presse, since Sept. 2023, (UBO, ANR REPLICA). Pierre Tandeo: supervisor
 PhD in progress: Ewen Frogé, since Oct. 2022 (IMT, ANR Scales). Carlos Granero Belinchon: cosupervisor
 PhD in progress: Daria Botvynko (ENIB). Carlos Granero Belinchon: cosupervisor
 PhD in progress: T. Picard, “Datadriven MOdeling and sampling to MOnitor PARticle origins in deep sediment traps (Biological Carbon Pump), started in 2021. Supervisors: J. Gula, R. Fablet, L.Mémery.
 PhD defended: Simon Benaïchouche, IMT Atlantique, defended Sept. 2023, supervisors: F. Rousseau (IMT Atlantique/LATIM), C. Legoff (Eodyn) and R. Fablet (Odyssey)
 PhD in progress: J. Littaye, UBO, coencadrement avec L. Memery (CNRS/LEMAR) et R. Fablet
 PhD in progress: M. Zambra, IMT Atlantique, coencadrement avec D. Cazau (ENSTA Bretagne/IGE), N. Farrugia (IMT Atlantique/LabSTICC), A. Gense (NavalGroup) et R. Fablet (Odyssey)
 PhD defended: Quentin Febvre, IMT Atlantique, defended Dec. 2023. Supervisors: J. Le Sommer (CNRS/IGE), C. Ubelman (Datlas), R. Fablet (Odyssey)
 PhD in progress: P. Beauchot, ENSTA Bretagne,. Supervisors: F. Sévellec (CNRS/LOPS), A. Drémeau (ENSTA Bretagne/LabSTICC) and R. Fablet (Odyssey)
 PhD in progress: Arthur Avenas, IMT Atlantique. Supervisors: A. Mouche (Odyssey), P. Tandeo (Odyssey), J. Knaf (NOAA) and R. Fablet (Odyssey)
 PhD in progress: D. Botvinko, ENIB, supervisors: A. Benzinou (ENIB, LabSTICC), S. Van Gennip (MOi), C. GraneroBelinchon (Odyssey) and R. Fablet (Odyssey)
11.2.3 Juries

Etienne Mémin
:

PhD defenseBenjamin Dufée, Sept. 2023, Univ. Rennes

PhD defenseBastien Nony (rapporteur), Univ. Toulouse III Paul Sabatier, 20/01/2023

HdR defenseEhouarn Simon (rapporteur), Toulouse INP, 27/11/2023

PhD defense

Jocelyne Erhel
:

PhD defenseMohamed El Marouf, 17/03/2023 (examinatrice)

PhD defensePierre Seize, 13/03/2023 (examinatrice)

PhD defense
 Auréien Ponte : PhD defense of Arne Bedinger, Dec. 2023
 Claire Menesguen : PhD defense of Marcela Contreras, 27/11/2023

Xavier Carton

HDR defense
N. Kolodziejczyk, LOPS, UBO, 2023 (chairman).

HDR defense
P. Tandeo, IMT Atlantique, 2023 (referee).

HDR defense
C. Combot, LOPS, IFREMER, 2023 (examiner).

HDR defense
G. Escobar, LEGOSUPS, 2023 (referee).

PhD defense
A. Cassianides, LOPS, UBO, 2023 (examiner).

PhD defense
M. Alday. LOPS, UBO, 2023 (examiner).

PhD defense
A. Barboni, LMDSHOMLOPS, ENS, 2023.

PhD defense
Joana Roussillon, LOPS. UBO, 2023 (chairman).

HDR defense
 Pierre Tandeo : PhD defense of J.Roussillon

Ronan Fablet
:

PhD defenseE. Moschos, Ecole Polytechnique, Feb. 2023

PhD defenseJ. Roux, Nantes Univ., July 2023

PhD defenseW. Podjelski, Univ. AixMarseille, Oct 2023

PhD defenseE. Meunier, Univ. Rennes, Dec 2023

PhD defenseI. Meraoumia, IPP, Dec 2023

PhD defenseJ. Roussillon, UBO, Dec 2023

HDR defenseA. Paiement, Univ. Touloun, March 2023

PhD defense
11.3 Popularization
 Jocelyne Erhel article interstices (citation HAL) avec une vidéo, publiée sur youtube, chaîne Inria / Interstices: "comment modéliser les épidémies ? (Le modèle SIR).
 Florian Sévellec Nombreuse activités grand public en presse papier et radio, groupe scolaire, etc.
 Pierre Tandeo Présentation grand public le 17 septembre 2023 à Menez Meur (Hanvec) intitulée “Le saumon atlantique, un patrimoine vivant menacé”, dans le cadre des journées du patrimoine du Parc Naturel Régional d'Armorique.
12 Scientific production
12.1 Major publications
 1 articleDeciphering the role of smallscale inhomogeneity on geophysical flow structuration: a stochastic approach.Journal of Physical Oceanography504April 2020, 9831003HALDOI
 2 articleCharacterization of internal tide incoherence : Eulerian versus Lagrangian perspectives.Journal of Physical Oceanography5262022, 12451259HALDOI
 3 articleLearning Variational Data Assimilation Models and Solvers.Journal of Advances in Modeling Earth Systems1310October 2021, article n° e2021MS002572HALDOI
 4 articleA posteriori learning for quasi‐geostrophic turbulence parametrization.Journal of Advances in Modeling Earth Systems2022, 135HALDOI
 5 articleInternal tide cycle and topographic scattering over the North MidAtlantic Ridge.Journal of Geophysical Research. Oceans12512November 2020HALDOI
 6 articleFluid flow dynamics under location uncertainty.Geophysical and Astrophysical Fluid Dynamics1082May 2014, 119146HALDOI
 7 articleStochastic linear modes in a turbulent channel flow.Journal of Fluid Mechanics912April 2021, 133HALDOI
12.2 Publications of the year
International journals
 8 articleAn iterative optimization scheme to accommodate inequality constraints in air quality geostatistical estimation of multivariate PM.HeliyonJune 2023, e17413HALDOI
 9 articleEnsemblebased 4DVarNet uncertacinty quantification for the reconstruction of sea surface height dynamics.Environmental Data Science22023, e18HALDOI
 10 article4DVarNetSSH: endtoend learning of variational interpolation schemes for nadir and wideswath satellite altimetry.Geoscientific Model Development1682023, 21192147HALDOI
 11 articleOn the existence of weak solutions for a family of unsteady rotational smagorinsky models.Pure and Applied Functional Analysis812023, 83102HAL
 12 articleDiagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discretetime schemes.Foundations of Data Science2023, 125HALDOI
 13 articleComparison of simulationbased algorithms for parameter estimation and state reconstruction in nonlinear statespace models.Discrete and Continuous Dynamical Systems  Series S1622023, 240264HALDOI
 14 articleReduction of raininduced errors for wind speed estimation on SAR observations using convolutional neural networks.IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing2023, 1  13HALDOI
 15 articleA consistent stochastic largescale representation of the NavierStokes equations.Journal of Mathematical Fluid Mechanics251February 2023, 132HALDOI
 16 articleEnsemble forecasts in reproducing kernel Hilbert space family.Physica D: Nonlinear PhenomenaDecember 2023, 134044HALDOI
 17 articleMultimodal 4DVarNets for the reconstruction of sea surface dynamics from SSTSSH synergies.IEEE Transactions on Geoscience and Remote Sensing612023, 114HALDOI
 18 articleNeural network based generation of a 1dimensional stochastic field with turbulent velocity statistics.Physica D: Nonlinear Phenomena458December 2023, 133997HALDOI
 19 articleMultiscale and Anisotropic Characterization of Images Based on Complexity: an Application to Turbulence.Physica D: Nonlinear Phenomena459March 2024, 134027HALDOI
 20 articleAnalytical Properties for a Stochastic Rotating Shallow Water Model Under Location Uncertainty.Journal of Mathematical Fluid Mechanics252February 2023, 29HALDOI
 21 articleContinuous boundary condition at the interface for twocoupled fluids.Applied Mathematics Letters1352023, article n°108393HALDOI
 22 articleStochastic Data‐Driven Parameterization of Unresolved Eddy Effects in a Baroclinic Quasi‐Geostrophic Model.Journal of Advances in Modeling Earth Systems152February 2023, 125HALDOI
 23 articleGaussian mixture models for the optimal sparse sampling of offshore wind resource.Wind Energy Science852023, 771  786HALDOI
 24 articleAn “objective” definition of potential vorticity. Generalized evolution equation and application to the study of coastal upwelling instability.Ocean ModellingNovember 2023, 102287HALDOI
 25 articleBounded nonlinear forecasts of partially observed geophysical systems with physicsconstrained deep learning.Physica D: Nonlinear Phenomena446April 2023, 133630HALDOI
 26 articleExtending the extended dynamic mode decomposition with latent observables: the latent EDMD framework.Machine Learning: Science and Technology42May 2023, 025018HALDOI
 27 articleHigh resolution seafloor thermometry for internal wave and upwelling monitoring using Distributed Acoustic Sensing.Sci.Rep.1312023, 17459HALDOI
 28 articleA MultiMode Convolutional Neural Network to reconstruct satellitederived chlorophylla time series in the global ocean from physical drivers.Frontiers in Marine Science10March 2023, 120HALDOI
 29 articleThe open ocean kinetic energy cascade is strongest in late winter and spring.Communications Earth & Environment4November 2023, 450HALDOI
 30 articleDatadriven reconstruction of partially observed dynamical systems.Nonlinear Processes in Geophysics302June 2023, 129  137HALDOI
 31 articleInputoutput analysis of the stochastic NavierStokes equations: application to turbulent channel flow.Physical Review Fluids832023, 118HALDOI
 32 articleCautionary tales from the mesoscale eddy transport tensor.Ocean Modelling1822023, 102172HALDOI
 33 articleWavelet‐Based Wavenumber Spectral Estimate of Eddy Kinetic Energy: Idealized Quasi‐Geostrophic Flow.Journal of Advances in Modeling Earth Systems153March 2023, 1619  1644HALDOI
International peerreviewed conferences
 34 inproceedingsLearning Neural Optimal Interpolation Models and Solvers.Lecture Notes in Computer Science book series (LNCS)ICCS 2023  23rd International Conference on Computational Science10476Lecture Notes in Computer SciencePrague, Czech RepublicSpringer Nature SwitzerlandJune 2023, 367381HALDOI
 35 inproceedingsSlicedWasserstein on Symmetric Positive Definite Matrices for M/EEG Signals.ICML 2023  Fortieth International Conference on Machine LearningHonololu, United States2023, 129HAL
 36 inproceedingsGeometrypreserving lie group integrators for differential equations on the manifold of symmetric positive definite matrices.GSI 2023  6th International Conference on Geometric Science of Information 23Saint Malo, FranceAugust 2023, 118HAL
 37 inproceedingsLeveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data.ICASSP 2023  IEEE International Conference on Acoustics, Speech and Signal ProcessingRhodes, GreeceJune 2023HALDOI
 38 inproceedingsTrainable dynamical estimation of abovesurface wind speed using underwater passive acoustics.OCEANS 2023  LimerickLimerick, IrelandIEEE2023, 16HALDOI
Conferences without proceedings
 39 inproceedingsObservationonly learning of 4DVarNet neural schemes for the reconstruction of sea surface turbidity dynamics from gappy satellite images.EGU 2023  European Geophysical UnionVienna, AustriaMay 2023, 11HALDOI
 40 inproceedingsAn Oceanoacoustic Simulation Framework for the Design of Lagrangian Systems Drifting in Mesoscale and Submesoscale Currents.IEEE OCEANS 2023Biloxi, France2023, 18HAL
 41 inproceedingsDeep Learning for Ship Classification on Medium Resolution SAR Imagery.SeaSAR 2023  workshop on Coastal and Marine applications of SARlongyearbyen, Norway2023, 13HAL
 42 inproceedingsDatadriven reconstruction of partially observed dynamical systems.ICIAM 2023  10th International Congress on Industrial and Applied MathematicsTokyo, JapanAugust 2023HAL
 43 inproceedingsDatadriven reconstruction of partially observed dynamical systems.RIKEN 2023  14th workshop on Data AssimilationKobe, JapanAugust 2023HAL
 44 inproceedingsEstimating Dynamical Models using Machine Learning and Data Assimilation.IMTAtlantique & Kyoto University & RIKEN joint Data Assimilation workshopKobe, JapanAugust 2023HAL
 45 inproceedingsNarrowing Uncertainties of Climate Projections using Datadriven Methods: the AMOC Case Study.NHM 2023: 6th International Workshop on Nonhydrostatic ModelsSapporo, JapanSeptember 2023, 113HAL
Scientific books
Scientific book chapters
 48 inbookInternal Tides Energy Transfers and Interactions with the Mesoscale Circulation in Two Contrasted Areas of the North Atlantic.11Stochastic Transport in Upper Ocean Dynamics IIMathematics of Planet EarthSpringer Nature SwitzerlandAugust 2024, 116HALDOI
 49 inbookModeling Under Location Uncertainty: A Convergent LargeScale Representation of the NavierStokes Equations.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 1526HALDOI
 50 inbookObservationBased Noise Calibration: An Efficient Dynamics for the Ensemble Kalman Filter.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 4356HALDOI
 51 inbookStochastic Parameterization with Dynamic Mode Decomposition.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 179193HALDOI
 52 inbookComparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models.Chapron, B., Crisan, D., Holm, D., Mémin, E., Radomska, A. (eds) Stochastic Transport in Upper Ocean Dynamics II. STUOD 2022. Part of the Mathematics of Planet Earth book series (MPE,volume 11). Springer, Cham. Print ISBN 9783031400933 Online ISBN 9783031400940. https://doi.org/10.1007/9783031400940_7. pp.1591912024HALDOI
 53 inbookCorrelated Structures in a Balanced Motion Interacting with an Internal Wave.11Stochastic Transport in Upper Ocean Dynamics IIMathematics of Planet EarthSpringer Nature SwitzerlandAugust 2024, 207222HALDOI
 54 inbookLinear Wave Solutions of a Stochastic Shallow Water Model.Chapron, B., Crisan, D., Holm, D., Mémin, E., Radomska, A. (eds) Stochastic Transport in Upper Ocean Dynamics II. STUOD 2022. Part of the Mathematics of Planet Earth book series (MPE,volume 11). Springer, Cham. Print ISBN 9783031400933 Online ISBN 9783031400940. https://doi.org/10.1007/9783031400940_10. pp.2232452024HALDOI
 55 inbookModified (Hyper)Viscosity for CoarseResolution Ocean Models.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 273285HALDOI
 56 inbookStochastic Compressible Navier–Stokes Equations Under Location Uncertainty.11Stochastic Transport in Upper Ocean Dynamics IIMathematics of Planet EarthSpringer Nature SwitzerlandAugust 2024, 293319HALDOI
 57 inbookData Driven Stochastic Primitive Equations with Dynamic Modes Decomposition.11Stochastic Transport in Upper Ocean Dynamics IIMathematics of Planet EarthSpringer Nature SwitzerlandAugust 2024, 321336HALDOI
 58 inbookPrimitive Equations Under Location Uncertainty: Analytical Description and Model Development.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 287300HALDOI
Doctoral dissertations and habilitation theses
 59 thesisData assimilation for stochastic ocean models.Université de RennesSeptember 2023HAL
Reports & preprints
 60 miscSingular boundary condition for a degenerated turbulent toy model.January 2024HAL
 61 miscTKE model involving the distance to the wall. Part 1: the relaxed case.2023HAL
 62 miscNeural SPDE solver for uncertainty quantification in highdimensional spacetime dynamics.November 2023HAL
 63 miscTimechanged normalizing flows for accurate SDE modeling.December 2023HAL
 64 miscSurface boundary layers through a scalar equation with an eddy viscosity vanishing at the ground.2023HAL
 65 miscInversion of sea surface currents from satellitederived SSTSSH synergies with 4DVarNets.2023HAL
 66 miscTraining neural mapping schemes for satellite altimetry with simulation data.2023HALDOI
 67 miscScaleaware neural calibration for wide swath altimetry observations.2023HALDOI
 68 miscA multiscale and multicriteria Generative Adversarial Network to synthesize 1dimensional turbulent fields.2023HAL
 69 miscA VAE approach to sample multivariate extremes.2023HAL
 70 miscA Nonlinear Elliptic Equation with a Degenerate Diffusion and a Source Term in L 1.January 2024HAL
 71 miscAutomated Ship Detection and Characterization in Sentinel2 Images: A Comprehensive Approach.December 2023HAL
 72 miscOnline machinelearning forecast uncertainty estimation for sequential data assimilation.2023HALDOI
Other scientific publications
 73 inproceedingsSparse SPDE priors for uncertainty quantification of neural variational schemes.ISDA 2023: 23rd International Conference on Intelligent Systems Design and ApplicationsBologne (ITA), Italy2023HAL
12.3 Other
Scientific popularization
 74 articleDes modèles numériques pour aider à contrôler une épidémie.IntersticesFebruary 2023HAL