2023Activity reportProject-TeamODYSSEY

RNSR: 202224252V
  • Research center Inria Centre at Rennes University
  • In partnership with:Université de Bretagne Occidentale, Ecole Nationale Supérieure Mines-Télécom 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


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. Computation-data 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]
  • Jean-Francois 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]

Post-Doctoral Fellows

  • Pierre-Marie 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 Caspar-Cohen [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 ever-increasing developments to simulate and observe the coupled ocean-atmosphere 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 observation-driven paradigms to develop and learn novel stochastic representations of the coupled ocean-atmosphere 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 ocean-atmosphere events and routes to rapid intensifications; (iii) the derivation of forefront deep-learning stochastic data assimilation techniques. The name Odyssey is a short-cut 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 multi-modal high-resolution 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 air-sea 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 high-resolution 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 high-frequency submesoscale motions estimation to extreme event hindcast and up to basin-scale dynamics reconstruction. At the base of this work is the design and validation of simplified models based on physics and data-driven reduced order models that allows for an optimal coupling with observations. At the same time, new uncertainty-handling 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 data-driven 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 sparse-in-time 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 real-world situations of interest. Today, data and models shall thus be combined to tackle uncertainty quantification and probabilistic ensemble forecasting issues, as advanced data-driven 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 data-model coupling functional still need to be specified or parameterized through dynamically-adapted basis functions, evolving parameters or covariance matrices. Our third credo is that the improved physical understanding of the multi-scale 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 space-time resolutions, differing passive and active microwave instruments, ...) observations, air-sea 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: upper-ocean dynamics, ocean-atmosphere 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 high-resolution sea surface temperature and ocean colour using multi-sensor and platform measurements. One may also cite the mapping of high sea winds from combined radiometer/scatterometer, including very-high 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 Sentinel-1 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 wide-swath 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 air-sea 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 multi-sensor data algorithm developments with advances in mining and learning from multi-modal observations, i.e. satellite and in-situ 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) sub-mesoscale variability and associated upper-ocean vertical exchange processes, known as “vertical exchange”, and finally (3) internal gravity wave variability (induced by winds, tides, and interactions of low-frequency currents with topography). Another central scientific objective is to explore and develop data-model-driven techniques in the context of extreme marine-atmosphere events, to provide new insights for air-sea 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 fine-scale 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 Navier-Stokes 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 well-posedness 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 high-dimension 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 multi-layer 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 data-driven and learning-based schemes and their interactions with model-based approaches, which constitute the state-of-the-art in ocean and atmosphere science. The general goal is to improve the understanding, modeling, forecasting and reconstruction of air-sea exchanges and upper ocean dynamics, as well as bottom turbulent processes, from the in-depth exploration of the existing observation and simulation data. We jointly explore three main complementary data-driven 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 model-driven 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 data-driven 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 partially-observed 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 physics-informed priors (e.g., stability, conservation laws, stochasticity, chaos...) into data-driven and hybrid representations, (ii) learning latent representations for oceanic flows and air-sea exchanges accounting for flow stochasticity, including extremes (iii) learning schemes when dealing with partially-observed, irregularly-sampled and noisy dynamics, (iv) the joint learning of data-driven 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, data-model 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 previously-launched projects. The new-generation wide-swath altimeter mission SWOT has been succesfully launched in December 2022, and provided a first round data that over-perform the expectations, opening very exciting and promising perspectives for the team.

7 New software, platforms, open data

  • Ronan Fablet : most softwares are available under free-license (licence Ceccil-C) 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: upper-ocean dynamics, ocean-atmosphere 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 short-term predictions and long-term projections, important efforts have been dedicated on targeting marine-atmosphere extreme events. Indeed, NWP re-analysis (e.g. ERA-5) generally poorly resolve extreme marine-atmosphere events and their surrounding environment. Such spatio-temporal inconsistencies and unreliability of global historical re-analyses 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), near-core surface wind structural properties are today still not precisely recorded and re-analyzed. Present-day available model-data 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 high-resolution ocean surface winds from all-weather 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 high-resolution measurements with best-track 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 marine-atmosphere extreme event

Participants: Alexis Mouche, Nicolas Reul, Jean-François Piollé.

Within the Marine-Atmosphere eXtreme Sensor Synergy (MAXSS) project, the team builds an advanced and unique workbench to more precisely study these ocean-atmosphere extreme events, from their generation to their impacts. Specifically, efforts have been dedicated to generate new 10-year-long databases:

  • Intercalibrated satellite surface winds in extreme conditions
  • A global 10-year multi-mission surface wind (MMW) derived from the merging of these inter-calibrated sensor wind estimates
  • A storm atlas of all-available Earth Observation (EO) data collected around tropical cyclones (TCs), extra-tropical storms (ETC), and polar lows (PLs)
  • An atlas of pre-storm upper ocean conditions, atmospheric forcing during the storms, and induced post-storm 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, non-linear 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 Caspar-Cohen, 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 spatio-temporal 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, high-resolution global numerical simulations (LLC4320, eNATL60). This year, we have pursued our analysis and valorization efforts following Zoé Caspar-Cohen's PhD thesis. A final article is in preparation (Caspar-Cohen 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 Ekman-Stokes 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 infinite-dimensional 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 time-delayed autocovariance exist, we construct a related Hilbert space and a Koopman-like operator that acts on it. We prove that the leading eigenvalues of the autocovariance matrix has one-to-one 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 weak-mixing property of the observables represented by the continuous spectrum.

Impact of oceanic meso- and submeso-scale 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 in-situ measurements of the EUREC4A experiment. We have shown that altimetry in the pre-SWOT 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 re-introducing some degree of non-hydrostatic 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 non-hydrostatic 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 ERA-5 reanalysis data as well as 80 members of the Community Earth System Model v2 large ensemble, we show that, over the North Atlantic (NA), altimetry-based 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 high-resolution realistic simulations

Participants: Adrien Bella, Noé Lahaye, Aurélien Ponte, Gilles Tissot.

Using outputs from the realistic high-resolution (dx2 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 (co-supervized 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 non-divergent, 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 beta-plane, by means of numerical simulations. A paper is currently under revision in the Journal of Fluid Mechanics.

Near-surface ocean dynamics

Participants: Claire Ménesguen.

We address the dynamics of the near-surface. 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 near-surface 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

Geometry-preserving Lie group integrators for differential equations on the manifold of symmetric positive definite matrices

Participants: Lucas Drumetz.

We have developed new methods – Geometry-preserving 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 ΓI. We approach the system by one that satisfies a friction Navier law at ΓI, and we show that when the friction coefficient goes to , the solutions converges to a solution of the initial system. We then write a numerical Schwarz-like coupling algorithm and run 2D-simulations, 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 Π2×[0,ztop], where Π2 is a two dimensional torus, with an eddy vertical eddy viscosity of order zα, α[0,1], an homogeneous boundary condition at z=0, and a Robin condition at z=ztop. We show the existence of weak solutions to this boundary problem, distinguishing the cases 0α<1 and α=1. Then we carry out several numerical simulations, showing the ability of our model to accurately reproduce profiles close to those predicted by the Monin-Oboukhov 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 non-linear 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

Very-high 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, high-frequency 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 along-track 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

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 large-scale 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 large-scale components by the small-scale velocity;(ii) a multiplicative noise representing small-scale energy backscattering; and (iii) a modified advection term related to the so-called 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 north-Atlantic circulation, we have shown that for different versions of the noise the QG LU model leads to improve long-terms statistics when compared to classical large-eddies 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 high-resolution data to learn a basis of the unresolved velocity field, on which the stochastic transport velocity is expressed. Time-harmonic property of DMD modes allowed us to perform a clean separation between time-differentiable and time-decorrelated components. Such random scheme is assessed on a quasi-geostrophic (QG) model and has been published in the STUOD proceedings.

Analysis of stochastic representation of Navier-Stokes equations.

Participants: Arnaud Debussche, Berenger Hug, Étienne Mémin.

In this study we analyze the theoretical properties of a stochastic representation of the incompressible Navier-Stokes 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 Navier-Stokes 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 Navier-Stokes equation. similarly to the grid convergence property of well-established large-eddies simulation strategies, this result brings some guarantee on the interpretation of the LU Navier-Stokes equations as a consistent large-scale model of the deterministic Navier-Stokes 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 well-posedness. The models we consider are intermediate between the incompressible 3D LU Navier-Stokes equations and the LU primitive equations with standard hydrostatic balance. Also, they are expected to be numerically tractable, while accounting well for non-hydrostatic phenomena. Our main result is the well-posedness 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 well-posedness result holds with rigid-lid 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 non-filtered 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 finite-dimensional Littlewood-Paley 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 small-scale 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 wave-current interaction.

Parameterization for coarse-resolution ocean modeling

Participants: Louis Thiry, Long Li, Étienne Mémin, Guillaume Roullet.

We work on simple parameterization for coarse-resolution oceanic models to replace computationally expensive high-resolution ocean models. We focus on the eddy-permitting 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 high-resolution reference solution. To test this new parameterization on a double-gyre quasi-geostrophic model, we are implementing a fast and portable python implementation of the multilayer quasi-geostrophic model. This study has been published in the STUOD proceedings. In another study we have explored a new discretization of the multi-layer quasi-geostrophic (QG) model that models implicitly the sub-grid-scale 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 non-oscillatory 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 hyper-viscosity. 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 machine-learning 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 discrete-time schemes

Participants: Pierre-Marie 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 coarse-scale 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 high-order discrete time evolution schemes for stochastic representation defined from stochastic transport.

Discrete numerical schemes for stochastic shallow water models under location uncertainty

Participants: Pierre-Marie 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 Navier-Stokes 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 Navier-Stokes 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 lift-up mechanism. In the present work, we focus on the study of streamwise-elongated structures, energetic in the buffer and logarithmic layers. In the buffer layer, elongated streamwise vortices, named rolls, are seen to result from coherent wave-wave 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 atmosphere-ocean momentum transfer, break ice floes, alter CO2 fluxes, and impact mixed-layer depth through Langmuir turbulence. In contrast to the goals of third-generation spectral models, the wave information needed for mixing, air-sea, and wave-ice-coupling is much less than a full directional wave spectrum. All present parameterizations – for wave-induced 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 next-generation Earth System Models (ESM). In that context, an alternative, cost-efficient wave modeling framework for air-sea interaction to enable the routine use of sea state-dependent air-sea flux parameterization in ESMs. In contrast to spectral models, the Particle-in-Cell for Efficient Swell Wave Model (PiCLES) is under developments targeting coupled atmosphere-ocean-sea ice modeling. Combining Lagrangian wave growth solutions with the Particle-In-Cell 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 50-200 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. Fox-Kemper and T. Protin (PhD)

8.3 Data/Models interactions and reduced order modelling

Data-driven methods for partially observed systems

Participants: Pierre Tandeo, Florian Sévellec.

In collaboration with Pierre Ailliot [Tandeo et al, 2023] and within a data-driven context, we have demonstrated our ability to obtain accurate and reliable predictions of a partially observed Lorenz-63 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 data-driven context, we focus on the Lorenz-63 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 large-scale 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 high-dimensional 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 large-scale 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 ad-hoc 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 1-layer rotating shallow water model, we study the evolution of an inertia-gravity wave interacting with a turbulent mesoscale jet. The resulting incoherent inertia-gravity 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 loss-of coherence of the inertia-gravity 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 inertia-gravity wave, given some knowledge of the mesoscale flow contribution. The latter is oriented towards the devise of data-assimilation 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 1-dimensional stochastic fields with turbulent velocity statistics

Participants: Carlos Granero Belinchon.

We define generative neural network architectures to model stochastic 1-dimensional 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.

Learning-based prediction of the particles catchment area of deep ocean sediment traps

Participants: Jonathan Gula, Ronan Fablet.

We have studied how fine-scale 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 high-resolution 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 ensemble-based 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 constant-in-time 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 wind-forced three-layers 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 subgrid-scale processes, and more broadly on learning corrections to a reference model in simulations of geophysical flows.We have applied an “a-posteriori” learning method introduced in (Frezat et al., 2022) to non-differentiable direct simulation codes. Our contributions explore both emulator-based methods (Frezat et al., 2023) and Euler-type approximations for computing the gradient of the a posteriori learning cost (Ouala et al., 2023).

Data-driven methods and End-to-end learning for data assimilation

Participants: Bertrand Chapron, Lucas Drumetz, Ronan Fablet, Etienne Mémin, Pierre Tandeo.

We developed several data-driven 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 mid-term 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 multi-spectral and panchromatic data.

We are also developing original end-to-end 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 inference-type formulations (Lafon et al., 2023) and stochastic PDE-type 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], short-term 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 4DVarNET-OFDA 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

  • EUREC4A-OA: Improving the representation of small-scale nonlinear ocean-atmosphere interactions in Climate Models by innovative joint observing and modelling approaches. JPl-Ocean project, 2020-2024. 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 & LOCEAN-IPSL). 2020-2024. 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:
  • Dates:
    mid-2022 – mid-2023
  • Context of the visit:
    collaboration in the group of James C. McWilliams
  • Mobility program/type of mobility:
Etienne Mémin
  • Visited institution:
    Imperial College, London
  • Country:
  • 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:
  • 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:
  • 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 co-investigator.

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, 2023-2028

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 co-PI and R. Fablet and L. Drumetz participate to WP1.


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 co-PI 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”.


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.

“ Physics-Informed 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)


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)


Participants: Carlos Granero Belinchon.

“ Statistical ChAracterization of multi-scaLE complex Systems with information theory ” (PI: C. Granero Belinchon)


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.


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.


Participants: Florian Sévellec.

“Ocean state Analog in-SItu analyses System (PI: N. Kolodziejczyk – CNAP, LOPS), 2022–2024


Participants: Carlos Granero Belinchon.

ALESE is a MITI CNRS project

TOSCA CNES projects
    (SWOT science team). Participants: A. Ponte (PI), J. Gula, N. Lahaye, P. Tandeo, R. Fablet, C. Menesguen
    PI: C. Granero Belinchon
    PI: T. Penduff (IGE, CNRS) & W. Llovel (CNRS, LOPS). Participants: F. Sévellec
Inrae-Inria 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 non-linear dynamical systems for ensemble methods”) consists in expressing the Koopman operator associated with a high-dimensional geophysical dynamical system in a family of reproducing kernel Hilbert spaces. The interest is to learn the non-linear dynamics, locally in the phase space, in order to solve efficiently ensemble data assimilation problems. Multi-layer quasi-geostrophic models representative of the Gulf stream area is considered in this work.

10.5 Regional initiatives


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.


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.
    • “End-to-end and physics-informed 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 LEFE-MANU, 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 socio-écosystèmes 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” (UBO-IMT Atlantique-ENSTA 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 (UBO-IMT Atlantique-ENSTA 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 high-fidelity 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 small-scale ocean variability", supervisors: Aurélien Ponte, François-Xavier Socheleau, Florent Le Courtois
  • PhD in progress: Mariana Lage (Helmhotz-Zentrum Hereon - Germany), 2021-2024, « Small-scale variability of turbulence and stratification in the Surface Mixed Layer », Supervisors: Claire Menesguen, Jeff Carpenter
  • PhD in progress: Yao Meng (Exeter), 2021-2024. « 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 mixed-layer”, 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 ARED-ISblue (région Bretagne) et UBO. Supervisors: F. Sévellec; co-supervisors: 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. Co-supervisors: F. Sévellec, R. Fablet
  • PhD in progress: Erwan Oulhen, thèse, since 2021, “Ocean state Analog in-SItu 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 1993-2020”. Bourse CNES and UBO. supervisor: F. Sévellec and co-supervisor: 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; co-supervisors: 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 physiques-biogéochimiques sous-jacents”, LOPS (Lucas Drumetz: co-supervisor)
  • 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 ipsa-lab), 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 sous-jacents dans l’océan Arctique sur la base d’observations et d’apprentissage profond”, LOPS & IMT Atlantique (Lucas Drumetz: co-supervisor)
  • 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: co-supervisor
  • PhD in progress: Daria Botvynko (ENIB). Carlos Granero Belinchon: co-supervisor
  • PhD in progress: T. Picard, “Data-driven 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, co-encadrement avec L. Memery (CNRS/LEMAR) et R. Fablet
  • PhD in progress: M. Zambra, IMT Atlantique, co-encadrement avec D. Cazau (ENSTA Bretagne/IGE), N. Farrugia (IMT Atlantique/Lab-STICC), 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/Lab-STICC) 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, Lab-STICC), S. Van Gennip (MOi), C. Granero-Belinchon (Odyssey) and R. Fablet (Odyssey)

11.2.3 Juries

  • Etienne Mémin :
    • PhD defense
      Benjamin Dufée, Sept. 2023, Univ. Rennes
    • PhD defense
      Bastien Nony (rapporteur), Univ. Toulouse III Paul Sabatier, 20/01/2023
    • HdR defense
      Ehouarn Simon (rapporteur), Toulouse INP, 27/11/2023
  • Jocelyne Erhel :
    • PhD defense
      Mohamed El Marouf, 17/03/2023 (examinatrice)
    • PhD defense
      Pierre Seize, 13/03/2023 (examinatrice)
  • 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, LEGOS-UPS, 2023 (referee).
    • PhD defense
      A. Cassianides, LOPS, UBO, 2023 (examiner).
    • PhD defense
      M. Alday. LOPS, UBO, 2023 (examiner).
    • PhD defense
      A. Barboni, LMD-SHOM-LOPS, ENS, 2023.
    • PhD defense
      Joana Roussillon, LOPS. UBO, 2023 (chairman).
  • Pierre Tandeo : PhD defense of J.Roussillon
  • Ronan Fablet :
    • PhD defense
      E. Moschos, Ecole Polytechnique, Feb. 2023
    • PhD defense
      J. Roux, Nantes Univ., July 2023
    • PhD defense
      W. Podjelski, Univ. Aix-Marseille, Oct 2023
    • PhD defense
      E. Meunier, Univ. Rennes, Dec 2023
    • PhD defense
      I. Meraoumia, IPP, Dec 2023
    • PhD defense
      J. Roussillon, UBO, Dec 2023
    • HDR defense
      A. Paiement, Univ. Touloun, March 2023

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

12.2 Publications of the year

International journals

  • 8 articleM.Maxime Beauchamp and B.Bertrand Bessagnet. An iterative optimization scheme to accommodate inequality constraints in air quality geostatistical estimation of multivariate PM.HeliyonJune 2023, e17413HALDOI
  • 9 articleM.Maxime Beauchamp, Q.Quentin Febvre and R.Ronan Fablet. Ensemble-based 4DVarNet uncertacinty quantification for the reconstruction of sea surface height dynamics.Environmental Data Science22023, e18HALDOI
  • 10 articleM.Maxime Beauchamp, Q.Quentin Febvre, H.Hugo Georgenthum and R.Ronan Fablet. 4DVarNet-SSH: end-to-end learning of variational interpolation schemes for nadir and wide-swath satellite altimetry.Geoscientific Model Development1682023, 2119--2147HALDOI
  • 11 articleL. C.Luigi C Berselli, A.Alex Kaltenbach, R.Roger Lewandowski and M.Michael Růžička. On the existence of weak solutions for a family of unsteady rotational smagorinsky models.Pure and Applied Functional Analysis812023, 83-102HAL
  • 12 articleP.-M.Pierre-Marie Boulvard and E.Etienne Mémin. Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes.Foundations of Data Science2023, 1-25HALDOI
  • 13 articleT. T.Thi Tuyet Trang Chau, P.Pierre Ailliot, V.Valérie Monbet and P.Pierre Tandeo. Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models.Discrete and Continuous Dynamical Systems - Series S1622023, 240-264HALDOI
  • 14 articleA.Aurélien Colin, P.Pierre Tandeo, C.Charles Peureux, R.Romain Husson and R.Ronan Fablet. Reduction of rain-induced 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.Arnaud Debussche, B.Berenger Hug and E.Etienne Mémin. A consistent stochastic large-scale representation of the Navier-Stokes equations.Journal of Mathematical Fluid Mechanics251February 2023, 1-32HALDOI
  • 16 articleB.Benjamin Dufée, B.Bérenger Hug, É.Étienne Mémin and G.Gilles Tissot. Ensemble forecasts in reproducing kernel Hilbert space family.Physica D: Nonlinear PhenomenaDecember 2023, 134044HALDOI
  • 17 articleR.Ronan Fablet, Q.Quentin Febvre and B.Bertrand Chapron. Multimodal 4DVarNets for the reconstruction of sea surface dynamics from SST-SSH synergies.IEEE Transactions on Geoscience and Remote Sensing612023, 1-14HALDOI
  • 18 articleC.Carlos Granero-Belinchon. Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics.Physica D: Nonlinear Phenomena458December 2023, 133997HALDOI
  • 19 articleC.Carlos Granero-Belinchon, S. G.Stéphane G. Roux and N.Nicolas B. Garnier. Multiscale and Anisotropic Characterization of Images Based on Complexity: an Application to Turbulence.Physica D: Nonlinear Phenomena459March 2024, 134027HALDOI
  • 20 articleO.Oana Lang, D.Dan Crisan and É.Étienne Mémin. Analytical Properties for a Stochastic Rotating Shallow Water Model Under Location Uncertainty.Journal of Mathematical Fluid Mechanics252February 2023, 29HALDOI
  • 21 articleF.François Legeais and R.Roger Lewandowski. Continuous boundary condition at the interface for twocoupled fluids.Applied Mathematics Letters1352023, article n°108393HALDOI
  • 22 articleL.Long Li, B.Bruno Deremble, N.Noé Lahaye and E.Etienne Mémin. Stochastic Data‐Driven Parameterization of Unresolved Eddy Effects in a Baroclinic Quasi‐Geostrophic Model.Journal of Advances in Modeling Earth Systems152February 2023, 1-25HALDOI
  • 23 articleR.Robin Marcille, M.Maxime Thiébaut, P.Pierre Tandeo and J.-F.Jean-François Filipot. Gaussian mixture models for the optimal sparse sampling of offshore wind resource.Wind Energy Science852023, 771 - 786HALDOI
  • 24 articleY.Yves Morel, G.Guillaume Morvan, R.Rachid Benshila, L.Lionel Renault, J.Jonathan Gula and F.Francis Auclair. An “objective” definition of potential vorticity. Generalized evolution equation and application to the study of coastal upwelling instability.Ocean ModellingNovember 2023, 102287HALDOI
  • 25 articleS.Said Ouala, S.Steven Brunton, B.Bertrand Chapron, A.Ananda Pascual, F.Fabrice Collard, L.Lucile Gaultier and R.Ronan Fablet. Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning.Physica D: Nonlinear Phenomena446April 2023, 133630HALDOI
  • 26 articleS.Said Ouala, B.Bertrand Chapron, F.Fabrice Collard, L.Lucile Gaultier and R.Ronan Fablet. Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework.Machine Learning: Science and Technology42May 2023, 025018HALDOI
  • 27 articleJ. D.Julián David Pelaez Quiñones, A.Anthony Sladen, A.Aurelien Ponte, I.Itzhak Lior, J. P.Jean Paul Ampuero, D.Diane Rivet, S.Samuel Meulé, F.Frédéric Bouchette, I.Ivane Pairaud and P.Paschal Coyle. High resolution seafloor thermometry for internal wave and upwelling monitoring using Distributed Acoustic Sensing.Sci.Rep.1312023, 17459HALDOI
  • 28 articleJ.Joana Roussillon, R.Ronan Fablet, T.Thomas Gorgues, L.Lucas Drumetz, J.Jean Littaye and E.Elodie Martinez. A Multi-Mode Convolutional Neural Network to reconstruct satellite-derived chlorophyll-a time series in the global ocean from physical drivers.Frontiers in Marine Science10March 2023, 1-20HALDOI
  • 29 articleR.René Schubert, O.Oscar Vergara and J.Jonathan Gula. The open ocean kinetic energy cascade is strongest in late winter and spring.Communications Earth & Environment4November 2023, 450HALDOI
  • 30 articleP.Pierre Tandeo, P.Pierre Ailliot and F.Florian Sévellec. Data-driven reconstruction of partially observed dynamical systems.Nonlinear Processes in Geophysics302June 2023, 129 - 137HALDOI
  • 31 articleG.Gilles Tissot, A. V.André V. G. Cavalieri and E.Etienne Mémin. Input-output analysis of the stochastic Navier-Stokes equations: application to turbulent channel flow.Physical Review Fluids832023, 1-18HALDOI
  • 32 articleT.Takaya Uchida, D.Dhruv Balwada, Q.Quentin Jamet, W. K.William K Dewar, B.Bruno Deremble, T.Thierry Penduff and J.Julien Le Sommer. Cautionary tales from the mesoscale eddy transport tensor.Ocean Modelling1822023, 102172HALDOI
  • 33 articleT.Takaya Uchida, Q.Quentin Jamet, A. C.Andrew C Poje, W. K.William K Dewar and B.Bruno Deremble. Wavelet‐Based Wavenumber Spectral Estimate of Eddy Kinetic Energy: Idealized Quasi‐Geostrophic Flow.Journal of Advances in Modeling Earth Systems153March 2023, 1619 - 1644HALDOI

International peer-reviewed conferences

  • 34 inproceedingsM.Maxime Beauchamp, Q.Quentin Febvre, J.Joseph Thompson, H.Hugo Georgenthum and R.Ronan Fablet. Learning 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, 367-381HALDOI
  • 35 inproceedingsC.Clément Bonet, B.Benoît Malézieux, A.Alain Rakotomamonjy, L.Lucas Drumetz, T.Thomas Moreau, M.Matthieu Kowalski and N.Nicolas Courty. Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals.ICML 2023 - Fortieth International Conference on Machine LearningHonololu, United States2023, 1-29HAL
  • 36 inproceedingsL.Lucas Drumetz, A.Alexandre Reiffers-Masson, N.Naoufal El Bekri and F.Franck Vermet. Geometry-preserving 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, 1-18HAL
  • 37 inproceedingsA.Anthony Frion, L.Lucas Drumetz, M.Mauro Dalla Mura, G.Guillaume Tochon and A.Abdeldjalil Aissa El Bey. Leveraging 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 inproceedingsM.Matteo Zambra, D.Dorian Cazau, N.Nicolas Farrugia, A.Alexandre Gensse, S.Sara Pensieri, R.Roberto Bozzano and R.Ronan Fablet. Trainable dynamical estimation of above-surface wind speed using underwater passive acoustics.OCEANS 2023 - LimerickLimerick, IrelandIEEE2023, 1-6HALDOI

Conferences without proceedings

  • 39 inproceedingsC.Clément Dorffer, F.Frédéric Jourdin, D.David Mouillot, R.Rodolphe Devillers and R.Ronan Fablet. Observation-only learning of 4DVarNet neural schemes for the reconstruction of sea surface turbidity dynamics from gappy satellite images.EGU 2023 - European Geophysical UnionVienna, AustriaMay 2023, 1-1HALDOI
  • 40 inproceedingsM.Mathis Grangeon, F.-X.François-Xavier Socheleau, A.Aurélien Ponte, F.Florent Le Courtois and B.Bazile Kinda. An Oceano-acoustic Simulation Framework for the Design of Lagrangian Systems Drifting in Mesoscale and Sub-mesoscale Currents.IEEE OCEANS 2023Biloxi, France2023, 1-8HAL
  • 41 inproceedingsB. L.Bou Laouz Moujahid, V.Vadaine Rodolphe, H.Hajduch Guillaume and R.Ronan Fablet. Deep Learning for Ship Classification on Medium Resolution SAR Imagery.SeaSAR 2023 - workshop on Coastal and Marine applications of SARlongyearbyen, Norway2023, 1-3HAL
  • 42 inproceedingsP.Pierre Tandeo. Data-driven reconstruction of partially observed dynamical systems.ICIAM 2023 - 10th International Congress on Industrial and Applied MathematicsTokyo, JapanAugust 2023HAL
  • 43 inproceedingsP.Pierre Tandeo. Data-driven reconstruction of partially observed dynamical systems.RIKEN 2023 - 14th workshop on Data AssimilationKobe, JapanAugust 2023HAL
  • 44 inproceedingsP.Pierre Tandeo. Estimating Dynamical Models using Machine Learning and Data Assimilation.IMT-Atlantique & Kyoto University & RIKEN joint Data Assimilation workshopKobe, JapanAugust 2023HAL
  • 45 inproceedingsP.Pierre Tandeo, P.Pierre Le Bras, F.Florian Sévellec, P.Pierre Ailliot and J.Juan Ruiz. Narrowing Uncertainties of Climate Projections using Data-driven Methods: the AMOC Case Study.NHM 2023: 6th International Workshop on Nonhydrostatic ModelsSapporo, JapanSeptember 2023, 1-13HAL

Scientific books

  • 46 bookB.Bertrand Chapron, D.Dan Crisan, D. D.Darryl D. Holm, E.Etienne Mémin and A.Anna Radomska. Stochastic Transport in Upper Ocean Dynamics.10Mathematics of Planet EarthSpringer International Publishing2023HALDOI
  • 47 bookB.Bertrand Chapron, D.Dan Crisan, D.Darryl Holm, E.Etienne Mémin and A.Anna Radomska. Stochastic Transport in Upper Ocean Dynamics II.11Mathematics of Planet EarthSpringer Nature Switzerland2024HALDOI

Scientific book chapters

  • 48 inbookA.Adrien Bella, N.Noé Lahaye and G.Gilles Tissot. Internal 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, 1-16HALDOI
  • 49 inbookA.Arnaud Debussche, B.Berenger Hug and E.Etienne Mémin. Modeling Under Location Uncertainty: A Convergent Large-Scale Representation of the Navier-Stokes Equations.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 15-26HALDOI
  • 50 inbookB.Benjamin Dufée, E.Etienne Mémin and D.Dan Crisan. Observation-Based Noise Calibration: An Efficient Dynamics for the Ensemble Kalman Filter.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 43-56HALDOI
  • 51 inbookL.Long Li, E.Etienne Mémin and G.Gilles Tissot. Stochastic Parameterization with Dynamic Mode Decomposition.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 179-193HALDOI
  • 52 inbookA.Alexander Lobbe, D.Dan Crisan, D.Darryl Holm, E.Etienne Mémin, O.Oana Lang and C.Chapron Bertrand. Comparison 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 978-3-031-40093-3 Online ISBN 978-3-031-40094-0. https://doi.org/10.1007/978-3-031-40094-0_7. pp.159-1912024HALDOI
  • 53 inbookI.Igor Maingonnat, G.Gilles Tissot and N.Noé Lahaye. Correlated Structures in a Balanced Motion Interacting with an Internal Wave.11Stochastic Transport in Upper Ocean Dynamics IIMathematics of Planet EarthSpringer Nature SwitzerlandAugust 2024, 207-222HALDOI
  • 54 inbookE.Etienne Mémin, L.Long Li, N.Noe Lahaye, G.Gilles Tissot and B.Bertrand Chapron. Linear 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 978-3-031-40093-3 Online ISBN 978-3-031-40094-0. https://doi.org/10.1007/978-3-031-40094-0_10. pp.223-2452024HALDOI
  • 55 inbookL.Louis Thiry, L.Long Li and E.Etienne Mémin. Modified (Hyper-)Viscosity for Coarse-Resolution Ocean Models.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 273-285HALDOI
  • 56 inbookG.Gilles Tissot, É.Étienne Mémin and Q.Quentin Jamet. Stochastic Compressible Navier–Stokes Equations Under Location Uncertainty.11Stochastic Transport in Upper Ocean Dynamics IIMathematics of Planet EarthSpringer Nature SwitzerlandAugust 2024, 293-319HALDOI
  • 57 inbookF.Francesco Tucciarone, E.Etienne Mémin and L.Long Li. Data Driven Stochastic Primitive Equations with Dynamic Modes Decomposition.11Stochastic Transport in Upper Ocean Dynamics IIMathematics of Planet EarthSpringer Nature SwitzerlandAugust 2024, 321-336HALDOI
  • 58 inbookF.Francesco Tucciarone, E.Etienne Mémin and L.Long Li. Primitive Equations Under Location Uncertainty: Analytical Description and Model Development.10Stochastic Transport in Upper Ocean DynamicsMathematics of Planet EarthSpringer International PublishingSeptember 2023, 287-300HALDOI

Doctoral dissertations and habilitation theses

  • 59 thesisB.Benjamin Dufée. Data assimilation for stochastic ocean models.Université de RennesSeptember 2023HAL

Reports & preprints

Other scientific publications

  • 73 inproceedingsM.Maxime Beauchamp, H.Hugo Georgenthum and R.Ronan Fablet. Sparse 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 articleJ.Jocelyne Erhel. Des modèles numériques pour aider à contrôler une épidémie.IntersticesFebruary 2023HAL