RESEARCH CENTRE

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

2023
ACTIVITY REPORT

Project-Team

ODYSSEY

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

Contents

Project-Team ODYSSEY

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

and extreme events.

3.1 Ocean observations analysis: upper-ocean dynamics, ocean-atmosphere interaction, waves
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Development and analysis of numerical and mathematical models of geophysical flows . .
3.3 Data/Models interactions and reduced order modelling . . . . . . . . . . . . . . . . . . . . .
3.4 AI models and methods for ocean data analysis . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Application domains

5 Social and environmental responsibility

6 Highlights of the year

7 New software, platforms, open data

8 New results

1

2

3

4

4
5
5
6

6

7

7

7

7

and extreme events.

8.1 Ocean observations analysis: upper-ocean dynamics, ocean-atmosphere interaction, waves
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7
8.2 Development and analysis of numerical and mathematical models of geophysical flows . . 11
8.3 Data/Models interactions and reduced order modelling . . . . . . . . . . . . . . . . . . . . . 17
8.4 AI models and methods for ocean data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 18

9 Bilateral contracts and grants with industry

20
9.1 Bilateral Grants with Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

10 Partnerships and cooperations

10.3 European initiatives

10.2.1 Visits to international teams

20
10.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
10.2 International research visitors
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.3.1 Horizon Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.3.2 H2020 projects
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.3.3 Other european programs/initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.4 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.5 Regional initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

11 Dissemination

24
11.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
11.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
11.1.2 Scientific events: selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
11.1.3 Journal
11.1.4 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.1.5 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.1.6 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
11.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
11.3 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

12 Scientific production

30
12.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
12.2 Publications of the year
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
12.3 Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Project ODYSSEY

1

Project-Team ODYSSEY

Creation of the Project-Team: 2022 March 01

Keywords

Computer sciences and digital sciences

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

2

Inria Annual Report 2023

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]

Project ODYSSEY

3

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 ob-
jectives: (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

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Inria Annual Report 2023

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 de-
veloped 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 physic-
ally relevant representations of geophysical dynamics accounting for the specificities and complex-
ities 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) representa-
tions.

3 Research program

A primary focus of the team intends to better characterize poorly known mechanisms of energy redis-
tribution 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 un-
derstanding 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 inter-

action, 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 oth-
ers, 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 meas-
urements. 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

Project ODYSSEY

5

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 variabil-
ity 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 geophys-

ical 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 tech-
niques 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. Fol-
lowing recent results on the application of particle filters to address these issues on high-dimension

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Inria Annual Report 2023

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 pos-
terior 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, forecast-
ing 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.

Project ODYSSEY

7

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 estim-

ating latent variables in dynamical systems.

8 New results

8.1 Ocean observations analysis: upper-ocean dynamics, ocean-atmosphere inter-

action, 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.

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Inria Annual Report 2023

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 ad-
vanced 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).

Project ODYSSEY

9

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

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Inria Annual Report 2023

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.

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Using outputs from the realistic high-resolution (d x ∼ 2 km) numerical simulation of the North Atlantic
Ocean “eNATL60”, we are analyzing the lifecycle of the internal tide field based on a vertical mode
decomposition of the dynamics. We analyse and quantify the impact of several processes affecting
the propagation of internal tides, such as topographic scattering and interaction with the mesoscale
dynamics, and show that their implications is very contrasted depending of the region considered. Overall,
all these mechanisms seems to participate to a transfer of energy towards smaller scale, hence ultimately
favouring the dissipation of energy. A paper has been published in the 2022 STUOD proceedings, and
another one has been submitted to JGR: Oceans.

In parallel, we focus on the surface signature of the internal tide and the incoherence (lack of regularity
in time). We show that the typical time of decorrelation varies between 1 month and 1 day, with shorter
time associated with regions of strong mesoscale activity and internal tide with the shortest horizontal
scale (i.e., high vertical mode number). A paper is about to be submitted to GRL.

Equatorial ocean coherent vortices with temperature anomalies

Participants: Noé Lahaye, Olivier Larroque.

In the context of the M2 internship of Olivier Larroque (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 geophys-

ical 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).

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Inria Annual Report 2023

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, zt op ], where Π2 is a two
, α ∈ [0, 1], an homogeneous boundary
dimensional torus, with an eddy vertical eddy viscosity of order z
condition at z = 0, and a Robin condition at z = zt op . We show the existence of weak solutions to this
boundary problem, distinguishing the cases 0 ≤ α < 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.

α

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 Tuc-

ciarone.

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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 repres-
entations 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.

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Inria Annual Report 2023

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 mod-
els 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 ap-
proximate 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)

Project ODYSSEY

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and computationally cheap parameterization. We are currently investigating the modification of the dif-
fusion (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 numer-
ics, 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.

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Inria Annual Report 2023

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

Project ODYSSEY

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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 demon-
strated 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 par-
tially 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.

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Inria Annual Report 2023

In another study, we investigated the calibration of the stochastic noise in order to guide the real-
izations 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 methodo-
logy 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 Tis-
sot.

Project ODYSSEY

19

A methodological framework for ensemble-based estimation and simulation of high dimensional dy-
namical 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 diagon-
alizable 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 methodolo-
gical 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).

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Inria Annual Report 2023

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 inter-
actions 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: USA

Dates: mid-2022 – mid-2023

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

Mobility program/type of mobility: sabbatical

Project ODYSSEY

Etienne Mémin

Visited institution: Imperial College, London

Country: UK

Dates: January – February 2023

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

21

Mobility program/type of mobility: CNRS/Imperial Fellowship UMI Abraham De Moivre, Visiting pro-

fessor

Aurélien Ponte

Visited institution: University of Western Australia

Country: Australia

Dates: June – September 2023

Context of the visit: collaboration with Nicole Jones and Matthew Rayson in the context of the experi-

mental campaign carried out below the SWOT pass on the edge of the North Australian Plateau.

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

Florian Sévellec

Visited institution: University of Southampton

Country: UK

Context of the visit: visiting scientist

Pierre Tandeo

Visited institution: Univ. Buenos Aires (Argentine)

Country : Argentina

dates : February 27th – March 10th

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

Pierre Tandeo

Visited institution: Univ. Grenada

Country : Spain

dates : December 11th – 19th

Context of the visit: teaching: doctoral course in turbulence

10.3 European initiatives

10.3.1 Horizon Europe

• Florian Sévellec: EERIE – European Eddy Rich Earth System Models, PIs: Thomas Jung (Alfred
Wegner Intitute, Université de Bremen, Allemagne) and Malcolm Roberts (MetOffice, UK). F. Sével-
lec is co-investigator.

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Inria Annual Report 2023

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.

PPR MEDIATION

Participants:

Etienne Mémin, Carlos Granero Belinchon, Pierre Tandeo.

The MEDIATION project aims at improving and developping better numerical code of the ocean dynamics.
E. Mémin is 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”.

PPR CLIMArcTIC

Participants:

Florian Sévellec.

“From regional to global impacts of climate change in the Arctic : an interdisciplinary perspective” (procjet
“Océan 2030”, PI: C. Lique, LOPS Ifremer). F. Sévellec is in charge of WP1.

ANR Chair: OceaniX

Participants:

Ronan Fablet, Florian Sévellec.

“ 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)

Project ODYSSEY

ANR JCJC ModITO

Participants: Noé Lahaye.

23

"Modelling the Internal Tide in the Ocean" project aims at developing a data assimilation model for the
ocean internal tide field, in the context of the SWOT mission. (PI: N. Lahaye)

ANR JCJC SCALES

Participants: Carlos Granero Belinchon.

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

ANR JCJC DEEPER

Participants:

Jonathan Gula.

“Impacts of DEep submEsoscale Processes on the ocEan ciRculation” (PI: J. Gula), 2020 – 2025. The
goals of the DEEPER project are to quantify the impacts of deep submesoscale processes and internal
waves on mixing and water mass transformations. In addition, the DEEPER project will explore ways of
parameterizing these impacts using the latest advances in machine learning.

LEFE-IMAGO: ARVOR

Participants:

Florian Sévellec.

“Assessing the Role of forced and internal Variability for the Ocean and climate Response in a changing
climate” (PI: F. Sévellec), 2022–2024.

LEFE-GMMC: OASIS

Participants:

Florian Sévellec.

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

ALESE

Participants: Carlos Granero Belinchon.

ALESE is a MITI CNRS project

TOSCA CNES projects

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

nesguen

THEIA PI: C. Granero Belinchon

IMHOTEP PI: T. Penduff (IGE, CNRS) & W. Llovel (CNRS, LOPS). Participants: F. Sévellec

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Inria Annual Report 2023

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

ARED AMMSDO

Participants:

Étienne Mémin, Antoine Moneyron.

The Britany ARED project " Analyse Mathématique de Modèles Stochastiques réalistes de la Dynamique
Océanique" in collaboration with Arnaud Debussche (ENS/MINGUS) funds 50 percent of the PhD thesis
of Antoine Moneyron.

SAD AMIGAS

Participants:

Pierre Tandeo, Florian Sévellec.

“Analog Methods to Identify Global Atmospheric Simulations” (PI: P. Tandeo).

11 Dissemination

11.1 Promoting scientific activities

11.1.1 Scientific events: organisation

Member of the organizing committees

• Lucas Drumetz: Organization of a special session at GRETSI 2023, “Signal processing and AI for

environmental data”

• Carlos Granero Belinchon: Organiszation of Brest workshop on Environmental Physics and Signal

Processing – June 19th–21st 2023.

• Florian Sévellec: Organization of the AI4OAC workshop (Artificial Intelligence for Ocean, Atmo-
sphere, and Climate) as part of GDR “Défis théoriques pour les sciences du climat” and ANR chair
OceaniX, spring 2023, Brest, France.

Project ODYSSEY

25

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 Lahayehas 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

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Inria Annual Report 2023

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 Reana-

lyses 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 Univer-
sity 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 océano-
graphiques”

• Jonathan Gula: Numerical modelling (M2 Marine Sciences, UBO) and Ocean Turbulence (M2

Marine Sciences, UBO).

Project ODYSSEY

27

• 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 uni-

versité 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 Occi-
dentale, France). Master Sciences des données océaniques (UBO-IMT Atlantique-ENSTA Bretagne),
responsabilité du cours “Data Science 1” ; statistiques descriptives, problèmes inverses, régres-
sion, 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

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Inria Annual Report 2023

• 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 simula-
tions 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. Sév-
ellec, 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 recon-
struction 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 assimila-
tion 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).

Project ODYSSEY

29

• 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).

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Inria Annual Report 2023

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

[1] W. Bauer, P. Chandramouli, B. Chapron, L. Li and E. Mémin. ‘Deciphering the role of small-scale
inhomogeneity on geophysical flow structuration: a stochastic approach’. In: Journal of Physical
Oceanography 50.4 (Apr. 2020), pp. 983–1003. DOI: 10.1175/JPO-D-19-0164.1. URL: https://h
al.inria.fr/hal-02398521.

[2] Z. Caspar-Cohen, A. Ponte, N. Lahaye, X. Carton, X. Yu and S. Le Gentil. ‘Characterization of internal
tide incoherence : Eulerian versus Lagrangian perspectives’. In: Journal of Physical Oceanography
52.6 (2022), pp. 1245–1259. DOI: 10.1175/JPO-D-21-0088.1. URL: https://hal.archives-ou
vertes.fr/hal-03514215.

[3] R. Fablet, B. Chapron, L. Drumetz, E. Mémin, O. Pannekoucke and F. Rousseau. ‘Learning Variational
Data Assimilation Models and Solvers’. In: Journal of Advances in Modeling Earth Systems 13.10
(Oct. 2021), article n° e2021MS002572. DOI: 10.1029/2021MS002572. URL: https://imt-atlant
ique.hal.science/hal-02906798.

[4] H. Frezat, J. Le Sommer, R. Fablet, G. Balarac and R. Lguensat. ‘A posteriori learning for quasi-
geostrophic turbulence parametrization’. In: Journal of Advances in Modeling Earth Systems (2022),
pp. 1–35. DOI: 10.1029/2022MS003124. URL: https://imt-atlantique.hal.science/hal-0
3808230.

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[5] N. Lahaye, J. Gula and G. Roullet. ‘Internal tide cycle and topographic scattering over the North
Mid-Atlantic Ridge’. In: Journal of Geophysical Research. Oceans 125.12 (12th Nov. 2020). DOI:
10.1029/2020JC016376. URL: https://hal.archives-ouvertes.fr/hal-03015814.

[6] E. Mémin. ‘Fluid flow dynamics under location uncertainty’. In: Geophysical and Astrophysical
Fluid Dynamics 108.2 (28th May 2014), pp. 119–146. DOI: 10.1080/03091929.2013.836190. URL:
https://hal.inria.fr/hal-00852874.

[7] G. Tissot, A. V. G. Cavalieri and E. Mémin. ‘Stochastic linear modes in a turbulent channel flow’.
In: Journal of Fluid Mechanics 912 (10th Apr. 2021), pp. 1–33. DOI: 10.1017/jfm.2020.1168. URL:
https://hal.inria.fr/hal-03081978.

12.2 Publications of the year

International journals

[8] M. Beauchamp and B. Bessagnet. ‘An iterative optimization scheme to accommodate inequality
constraints in air quality geostatistical estimation of multivariate PM’. In: Heliyon (June 2023),
e17413. DOI: 10.1016/j.heliyon.2023.e17413. URL: https://hal.science/hal-04140956.

[9] M. Beauchamp, Q. Febvre and R. Fablet. ‘Ensemble-based 4DVarNet uncertacinty quantification
for the reconstruction of sea surface height dynamics’. In: Environmental Data Science 2 (2023), e18.
DOI: 10.1017/eds.2023.19. URL: https://imt-atlantique.hal.science/hal-04147805.

[10] M. Beauchamp, Q. Febvre, H. Georgenthum and R. Fablet. ‘4DVarNet-SSH: end-to-end learning of
variational interpolation schemes for nadir and wide-swath satellite altimetry’. In: Geoscientific
Model Development 16.8 (2023), pp. 2119–2147. DOI: 10.5194/gmd-16-1-2023. URL: https://h
al.science/hal-04140934.

[11] L. C. Berselli, A. Kaltenbach, R. Lewandowski and M. R ˚užiˇcka. ‘On the existence of weak solutions
for a family of unsteady rotational smagorinsky models’. In: Pure and Applied Functional Analysis
8.1 (2023), pp. 83–102. URL: https://hal.science/hal-03333561.

[12] P.-M. Boulvard and E. Mémin. ‘Diagnostic of the Lévy area for geophysical flow models in view
of defining high order stochastic discrete-time schemes’. In: Foundations of Data Science (2023),
pp. 1–25. DOI: 10.3934/fods.2023011. URL: https://inria.hal.science/hal-04241686.

[13] T. T. T. Chau, P. Ailliot, V. Monbet and P. Tandeo. ‘Comparison of simulation-based algorithms for
parameter estimation and state reconstruction in nonlinear state-space models’. In: Discrete and
Continuous Dynamical Systems - Series S 16.2 (2023), pp. 240–264. DOI: 10.3934/dcdss.2022054.
URL: https://imt-atlantique.hal.science/hal-03616079.

[14] A. Colin, P. Tandeo, C. Peureux, R. Husson and R. Fablet. ‘Reduction of rain-induced errors for wind
speed estimation on SAR observations using convolutional neural networks’. In: IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensing (2023), pp. 1–13. DOI: 10.1109
/jstars.2023.3291236. URL: https://imt-atlantique.hal.science/hal-04149533.

[15] A. Debussche, B. Hug and E. Mémin. ‘A consistent stochastic large-scale representation of the
Navier-Stokes equations’. In: Journal of Mathematical Fluid Mechanics 25.1 (Feb. 2023), pp. 1–32.
DOI: 10.1007/s00021-023-00764-0. URL: https://inria.hal.science/hal-03724396.

[16] B. Dufée, B. Hug, É. Mémin and G. Tissot. ‘Ensemble forecasts in reproducing kernel Hilbert space
family’. In: Physica D: Nonlinear Phenomena (Dec. 2023), p. 134044. DOI: 10.1016/j.physd.2023
.134044. URL: https://inria.hal.science/hal-04366698.

[17] R. Fablet, Q. Febvre and B. Chapron. ‘Multimodal 4DVarNets for the reconstruction of sea surface
dynamics from SST-SSH synergies’. In: IEEE Transactions on Geoscience and Remote Sensing 61
(2023), pp. 1–14. DOI: 10.1109/TGRS.2023.3268006. URL: https://imt-atlantique.hal.sc
ience/hal-03928368.

[18] C. Granero-Belinchon. ‘Neural network based generation of a 1-dimensional stochastic field with
turbulent velocity statistics’. In: Physica D: Nonlinear Phenomena 458 (4th Dec. 2023), p. 133997.
DOI: 10.1016/j.physd.2023.133997. URL: https://hal.science/hal-03861273.

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[19] C. Granero-Belinchon, S. G. Roux and N. B. Garnier. ‘Multiscale and Anisotropic Characterization of
Images Based on Complexity: an Application to Turbulence’. In: Physica D: Nonlinear Phenomena
459 (1st Mar. 2024), p. 134027. DOI: 10.1016/j.physd.2023.134027. URL: https://hal.scien
ce/hal-04190553.

[20] O. Lang, D. Crisan and É. Mémin. ‘Analytical Properties for a Stochastic Rotating Shallow Water
Model Under Location Uncertainty’. In: Journal of Mathematical Fluid Mechanics 25.2 (20th Feb.
2023), p. 29. DOI: 10.1007/s00021-023-00769-9. URL: https://inria.hal.science/hal-03
832450.

[21] F. Legeais and R. Lewandowski. ‘Continuous boundary condition at the interface for twocoupled
fluids’. In: Applied Mathematics Letters 135 (2023), article n°108393. DOI: 10.1016/j.aml.2022.1
08393. URL: https://hal.science/hal-03694918.

[22] L. Li, B. Deremble, N. Lahaye and E. Mémin. ‘Stochastic Data-Driven Parameterization of Unre-
solved Eddy Effects in a Baroclinic Quasi-Geostrophic Model’. In: Journal of Advances in Modeling
Earth Systems 15.2 (Feb. 2023), pp. 1–25. DOI: 10.1029/2022ms003297. URL: https://inria.ha
l.science/hal-04022844.

[23] R. Marcille, M. Thiébaut, P. Tandeo and J.-F. Filipot. ‘Gaussian mixture models for the optimal
sparse sampling of offshore wind resource’. In: Wind Energy Science 8.5 (2023), pp. 771–786. DOI:
10.5194/wes-8-771-2023. URL: https://imt-atlantique.hal.science/hal-04131337.

[24] Y. Morel, G. Morvan, R. Benshila, L. Renault, J. Gula and F. Auclair. ‘An “objective” definition of
potential vorticity. Generalized evolution equation and application to the study of coastal upwelling
instability’. In: Ocean Modelling (Nov. 2023), p. 102287. DOI: 10.1016/j.ocemod.2023.102287.
URL: https://hal.science/hal-04274117.

[25]

S. Ouala, S. Brunton, B. Chapron, A. Pascual, F. Collard, L. Gaultier and R. Fablet. ‘Bounded nonlinear
forecasts of partially observed geophysical systems with physics-constrained deep learning’. In:
Physica D: Nonlinear Phenomena 446 (Apr. 2023), p. 133630. DOI: 10.1016/j.physd.2022.13363
0. URL: https://imt-atlantique.hal.science/hal-04171040.

[26] S. Ouala, B. Chapron, F. Collard, L. Gaultier and R. Fablet. ‘Extending the extended dynamic
mode decomposition with latent observables: the latent EDMD framework’. In: Machine Learning:
Science and Technology 4.2 (2nd May 2023), p. 025018. DOI: 10.1088/2632-2153/acccd6. URL:
https://imt-atlantique.hal.science/hal-04171039.

[27]

[28]

J. D. Pelaez Quiñones, A. Sladen, A. Ponte, I. Lior, J. P. Ampuero, D. Rivet, S. Meulé, F. Bouchette,
I. Pairaud and P. Coyle. ‘High resolution seafloor thermometry for internal wave and upwelling
monitoring using Distributed Acoustic Sensing’. In: Sci.Rep. 13.1 (2023), p. 17459. DOI: 10.1038/s
41598-023-44635-0. URL: https://hal.science/hal-04245550.

J. Roussillon, R. Fablet, T. Gorgues, L. Drumetz, J. Littaye and E. Martinez. ‘A Multi-Mode Convolu-
tional Neural Network to reconstruct satellite-derived chlorophyll-a time series in the global ocean
from physical drivers’. In: Frontiers in Marine Science 10 (16th Mar. 2023), pp. 1–20. DOI: 10.3389
/fmars.2023.1077623. URL: https://imt-atlantique.hal.science/hal-04171042.

[29] R. Schubert, O. Vergara and J. Gula. ‘The open ocean kinetic energy cascade is strongest in late
winter and spring’. In: Communications Earth & Environment 4 (30th Nov. 2023), p. 450. DOI:
10.1038/s43247-023-01111-x. URL: https://hal.univ-brest.fr/hal-04398529.

[30] P. Tandeo, P. Ailliot and F. Sévellec. ‘Data-driven reconstruction of partially observed dynamical
systems’. In: Nonlinear Processes in Geophysics 30.2 (9th June 2023), pp. 129–137. DOI: 10.5194/np
g-30-129-2023. URL: https://imt-atlantique.hal.science/hal-04131312.

[31] G. Tissot, A. V. G. Cavalieri and E. Mémin. ‘Input-output analysis of the stochastic Navier-Stokes
equations: application to turbulent channel flow’. In: Physical Review Fluids 8.3 (2023), pp. 1–18.
DOI: 10.1103/PhysRevFluids.8.033904. URL: https://inria.hal.science/hal-0402289
6.

[32] T. Uchida, D. Balwada, Q. Jamet, W. K. Dewar, B. Deremble, T. Penduff and J. Le Sommer. ‘Cautionary
tales from the mesoscale eddy transport tensor’. In: Ocean Modelling 182 (2023), p. 102172. DOI:
10.1016/j.ocemod.2023.102172. URL: https://hal.science/hal-04213098.

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[33] T. Uchida, Q. Jamet, A. C. Poje, W. K. Dewar and B. Deremble. ‘Wavelet-Based Wavenumber Spectral
Estimate of Eddy Kinetic Energy: Idealized Quasi-Geostrophic Flow’. In: Journal of Advances in
Modeling Earth Systems 15.3 (Mar. 2023), pp. 1619–1644. DOI: 10 . 1029 / 2022ms003399. URL:
https://hal.science/hal-04380844.

International peer-reviewed conferences

[34] M. Beauchamp, Q. Febvre, J. Thompson, H. Georgenthum and R. Fablet. ‘Learning Neural Optimal
Interpolation Models and Solvers’. In: Lecture Notes in Computer Science book series (LNCS). ICCS
2023 - 23rd International Conference on Computational Science. Vol. 10476. Lecture Notes in
Computer Science. Prague, Czech Republic: Springer Nature Switzerland, 26th June 2023, pp. 367–
381. DOI: 10.1007/978-3-031-36027-5_28. URL: https://imt-atlantique.hal.science
/hal-04231248.

[35] C. Bonet, B. Malézieux, A. Rakotomamonjy, L. Drumetz, T. Moreau, M. Kowalski and N. Courty.
‘Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals’. In: ICML 2023 -
Fortieth International Conference on Machine Learning. Honololu, United States, 2023, pp. 1–29.
URL: https://cnrs.hal.science/hal-04250921.

[36] L. Drumetz, A. Reiffers-Masson, N. El Bekri and F. Vermet. ‘Geometry-preserving lie group integ-
rators for differential equations on the manifold of symmetric positive definite matrices’. In: GSI
2023 - 6th International Conference on Geometric Science of Information 23. Saint Malo, France,
30th Aug. 2023, pp. 1–18. URL: https://imt-atlantique.hal.science/hal-03815325.

[37] A. Frion, L. Drumetz, M. Dalla Mura, G. Tochon and A. Aissa El Bey. ‘Leveraging Neural Koopman
Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data’. In:
ICASSP 2023 - IEEE International Conference on Acoustics, Speech and Signal Processing. Rhodes,
Greece, 4th June 2023. DOI: 10.1109/ICASSP49357.2023.10094919. URL: https://imt-atlan
tique.hal.science/hal-03895087.

[38] M. Zambra, D. Cazau, N. Farrugia, A. Gensse, S. Pensieri, R. Bozzano and R. Fablet. ‘Trainable dy-
namical estimation of above-surface wind speed using underwater passive acoustics’. In: OCEANS
2023 - Limerick. Limerick, Ireland: IEEE, 2023, pp. 1–6. DOI: 10.1109/OCEANSLimerick52467.20
23.10244715. URL: https://ensta-bretagne.hal.science/hal-04296291.

Conferences without proceedings

[39] C. Dorffer, F. Jourdin, D. Mouillot, R. Devillers and R. Fablet. ‘Observation-only learning of 4DVarNet
neural schemes for the reconstruction of sea surface turbidity dynamics from gappy satellite
images’. In: EGU 2023 - European Geophysical Union. Vienna, Austria, 15th May 2023, pp. 1–1. DOI:
10.5194/egusphere-egu23-15977. URL: https://hal.science/hal-04363493.

[40] M. Grangeon, F.-X. Socheleau, A. Ponte, F. Le Courtois and B. Kinda. ‘An Oceano-acoustic Simula-
tion Framework for the Design of Lagrangian Systems Drifting in Mesoscale and Sub-mesoscale
Currents’. In: IEEE OCEANS 2023. Biloxi, France, 2023, pp. 1–8. URL: https://imt-atlantique
.hal.science/hal-04190600.

[41] B. L. Moujahid, V. Rodolphe, H. Guillaume and R. Fablet. ‘Deep Learning for Ship Classification on
Medium Resolution SAR Imagery’. In: SeaSAR 2023 - workshop on Coastal and Marine applications
of SAR. longyearbyen, Norway, 2023, pp. 1–3. URL: https://hal.science/hal-04277648.

[42] P. Tandeo. ‘Data-driven reconstruction of partially observed dynamical systems’. In: RIKEN 2023 -
14th workshop on Data Assimilation. Kobe, Japan, 30th Aug. 2023. URL: https://imt-atlantiqu
e.hal.science/hal-04193129.

[43] P. Tandeo. ‘Data-driven reconstruction of partially observed dynamical systems’. In: ICIAM 2023 -
10th International Congress on Industrial and Applied Mathematics. Tokyo, Japan, 23rd Aug. 2023.
URL: https://imt-atlantique.hal.science/hal-04193127.

[44] P. Tandeo. ‘Estimating Dynamical Models using Machine Learning and Data Assimilation’. In: IMT-
Atlantique & Kyoto University & RIKEN joint Data Assimilation workshop. Kobe, Japan, 28th Aug.
2023. URL: https://imt-atlantique.hal.science/hal-04193130.

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Inria Annual Report 2023

[45] P. Tandeo, P. Le Bras, F. Sévellec, P. Ailliot and J. Ruiz. ‘Narrowing Uncertainties of Climate Projections
using Data-driven Methods: the AMOC Case Study’. In: NHM 2023: 6th International Workshop on
Nonhydrostatic Models. Sapporo, Japan, 2nd Sept. 2023, pp. 1–13. URL: https://imt-atlantiqu
e.hal.science/hal-04193133.

Scientific books

[46] B. Chapron, D. Crisan, D. Holm, E. Mémin and A. Radomska. Stochastic Transport in Upper Ocean
Dynamics II. Vol. 11. Mathematics of Planet Earth. Springer Nature Switzerland, 2024. DOI: 10.100
7/978-3-031-40094-0. URL: https://inria.hal.science/hal-04354387.

[47] B. Chapron, D. Crisan, D. D. Holm, E. Mémin and A. Radomska. Stochastic Transport in Upper
Ocean Dynamics. Vol. 10. Mathematics of Planet Earth. Springer International Publishing, 2023.
DOI: 10.1007/978-3-031-18988-3. URL: https://inria.hal.science/hal-04356202.

Scientific book chapters

[48] A. Bella, N. Lahaye and G. Tissot. ‘Internal Tides Energy Transfers and Interactions with the Meso-
scale Circulation in Two Contrasted Areas of the North Atlantic’. In: Stochastic Transport in Upper
Ocean Dynamics II. Vol. 11. Mathematics of Planet Earth. Springer Nature Switzerland, 4th Aug.
2024, pp. 1–16. DOI: 10.1007/978-3-031-40094-0_1. URL: https://inria.hal.science/ha
l-04357365.

[49] A. Debussche, B. Hug and E. Mémin. ‘Modeling Under Location Uncertainty: A Convergent Large-
Scale Representation of the Navier-Stokes Equations’. In: Stochastic Transport in Upper Ocean
Dynamics. Vol. 10. Mathematics of Planet Earth. Springer International Publishing, 24th Sept. 2023,
pp. 15–26. DOI: 10.1007/978-3-031-18988-3_2. URL: https://hal.science/hal-03910767.

[50] B. Dufée, E. Mémin and D. Crisan. ‘Observation-Based Noise Calibration: An Efficient Dynam-
ics for the Ensemble Kalman Filter’. In: Stochastic Transport in Upper Ocean Dynamics. Vol. 10.
Mathematics of Planet Earth. Springer International Publishing, 24th Sept. 2023, pp. 43–56. DOI:
10.1007/978-3-031-18988-3_4. URL: https://hal.science/hal-03910764.

[51] L. Li, E. Mémin and G. Tissot. ‘Stochastic Parameterization with Dynamic Mode Decomposition’.
In: Stochastic Transport in Upper Ocean Dynamics. Vol. 10. Mathematics of Planet Earth. Springer
International Publishing, 24th Sept. 2023, pp. 179–193. DOI: 10.1007/978-3-031-18988-3_11.
URL: https://hal.science/hal-03910774.

[52] A. Lobbe, D. Crisan, D. Holm, E. Mémin, O. Lang and C. Bertrand. ‘Comparison of Stochastic
Parametrization Schemes Using Data Assimilation on Triad Models’. In: 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. h t t p s : // d o i . o r g / 1 0 . 1 0 0 7
/ 9 7 8 -3 -0 3 1 -4 0 0 9 4 -0 _7. pp.159-191. 2024. DOI: 10.1007/978-3-031-40094-0_7. URL:
https://hal.science/hal-04309730.

[53]

I. Maingonnat, G. Tissot and N. Lahaye. ‘Correlated Structures in a Balanced Motion Interacting
with an Internal Wave’. In: Stochastic Transport in Upper Ocean Dynamics II. Vol. 11. Mathematics
of Planet Earth. Springer Nature Switzerland, 4th Aug. 2024, pp. 207–222. DOI: 10.1007/978-3-03
1-40094-0_9. URL: https://inria.hal.science/hal-04357375.

[54] E. Mémin, L. Li, N. Lahaye, G. Tissot and B. Chapron. ‘Linear Wave Solutions of a Stochastic Shallow
Water Model’. In: 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. h t t p s : // d o i . o r g / 1 0 . 1 0 0 7 / 9 7 8 - 3 - 0 3 1 - 4 0 0 9 4 - 0 _10. pp.223-245.
2024. DOI: 10.1007/978-3-031-40094-0_10. URL: https://hal.science/hal-04309729.

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[55] L. Thiry, L. Li and E. Mémin. ‘Modified (Hyper-)Viscosity for Coarse-Resolution Ocean Models’.
In: Stochastic Transport in Upper Ocean Dynamics. Vol. 10. Mathematics of Planet Earth. Springer
International Publishing, 24th Sept. 2023, pp. 273–285. DOI: 10.1007/978-3-031-18988-3_17.
URL: https://hal.science/hal-03910773.

[56] G. Tissot, É. Mémin and Q. Jamet. ‘Stochastic Compressible Navier–Stokes Equations Under Loca-
tion Uncertainty’. In: Stochastic Transport in Upper Ocean Dynamics II. Vol. 11. Mathematics of
Planet Earth. Springer Nature Switzerland, 4th Aug. 2024, pp. 293–319. DOI: 10.1007/978-3-031-
40094-0_14. URL: https://inria.hal.science/hal-04356221.

[57] F. Tucciarone, E. Mémin and L. Li. ‘Data Driven Stochastic Primitive Equations with Dynamic
Modes Decomposition’. In: Stochastic Transport in Upper Ocean Dynamics II. Vol. 11. Mathematics
of Planet Earth. Springer Nature Switzerland, 4th Aug. 2024, pp. 321–336. DOI: 10.1007/978-3-03
1-40094-0_15. URL: https://inria.hal.science/hal-04356242.

[58] F. Tucciarone, E. Mémin and L. Li. ‘Primitive Equations Under Location Uncertainty: Analytical
Description and Model Development’. In: Stochastic Transport in Upper Ocean Dynamics. Vol. 10.
Mathematics of Planet Earth. Springer International Publishing, 24th Sept. 2023, pp. 287–300. DOI:
10.1007/978-3-031-18988-3_18. URL: https://hal.science/hal-03910760.

Doctoral dissertations and habilitation theses

[59] B. Dufée. ‘Data assimilation for stochastic ocean models’. Université de Rennes, 29th Sept. 2023.

URL: https://theses.hal.science/tel-04292176.

Reports & preprints

[60] C. Amrouche, L. C. Berselli, F. Legeais, G. Leloup and R. Lewandowski. Singular boundary condition
for a degenerated turbulent toy model. 8th Jan. 2024. URL: https://hal.science/hal-04143082.

[61] C. Amrouche, G. Leloup and R. Lewandowski. TKE model involving the distance to the wall. Part 1:

the relaxed case. 2023. URL: https://hal.science/hal-04111072.

[62] M. Beauchamp, R. Fablet and H. Georgenthum. Neural SPDE solver for uncertainty quantification
in high-dimensional space-time dynamics. 2nd Nov. 2023. URL: https://imt.hal.science/hal-
04265487.

[63] N. E. Bekri, L. Drumetz and F. Vermet. Time-changed normalizing flows for accurate SDE modeling.

22nd Dec. 2023. URL: https://hal.science/hal-04370186.

[64] L. C. Berselli, F. Legeais and R. Lewandowski. Surface boundary layers through a scalar equation with

an eddy viscosity vanishing at the ground. 2023. URL: https://hal.science/hal-03877325.

[65] R. Fablet, B. Chapron, J. L. Sommer and F. Sévellec. Inversion of sea surface currents from satellite-
derived SST-SSH synergies with 4DVarNets. 2023. URL: https://imt-atlantique.hal.science
/hal-03928366.

[66] Q. Febvre, J. L. Sommer, C. Ubelmann and R. Fablet. Training neural mapping schemes for satellite
altimetry with simulation data. 2023. DOI: 10.48550/arXiv.2309.14350. URL: https://hal.s
cience/hal-04312218.

[67] Q. Febvre, C. Ubelmann, J. L. Sommer and R. Fablet. Scale-aware neural calibration for wide swath
altimetry observations. 2023. DOI: 10.48550/arXiv.2302.04497. URL: https://hal.science
/hal-04312228.

[68] C. Granero-Belinchon and M. Cabeza Gallucci. A multiscale and multicriteria Generative Ad-
versarial Network to synthesize 1-dimensional turbulent fields. 2023. URL: https://hal.science
/hal-04173074.

[69] N. Lafon, P. Naveau and R. Fablet. A VAE approach to sample multivariate extremes. 2023. URL:

https://hal.science/hal-04013214.

[70] G. Leloup and R. Lewandowski. A Nonlinear Elliptic Equation with a Degenerate Diffusion and a

Source Term in L 1. 13th Jan. 2024. URL: https://hal.science/hal-04392244.

36

Inria Annual Report 2023

[71] B.-L. Moujahid, V. Rodolphe, H. Guillaume and R. Fablet. Automated Ship Detection and Character-
ization in Sentinel-2 Images: A Comprehensive Approach. Dec. 2023. URL: https://hal.science
/hal-04359761.

[72] M. Sacco, M. Pulido, J. Ruiz and P. Tandeo. Online machine-learning forecast uncertainty estimation
for sequential data assimilation. 2023. DOI: 10.48550/arXiv.2305.08874. URL: https://imt-a
tlantique.hal.science/hal-04195361.

Other scientific publications

[73] M. Beauchamp, H. Georgenthum and R. Fablet. ‘Sparse SPDE priors for uncertainty quantification
of neural variational schemes’. In: ISDA 2023: 23rd International Conference on Intelligent Systems
Design and Applications. Bologne (ITA), Italy, 2023. URL: https://imt.hal.science/hal-0423
6738.

12.3 Other

Scientific popularization

[74]

J. Erhel. ‘Des modèles numériques pour aider à contrôler une épidémie’. In: Interstices (15th Feb.
2023). URL: https://hal.science/hal-03999597.
<scratchpad>
- Main topic: Ocean Dynamics and Research Centre at Inria
- Key points: Research on ocean dynamics, climate change, and ocean-atmosphere interactions
- Structure: Document divided into sections on Project-Team, Domain, Theme, Research Program, Application Domains, Social and Environmental Responsibility, Highlights of the Year, New Software, Platforms, Open Data, New Results, Bilateral Contracts and Grants, Partnerships and Cooperations, Dissemination, and Scientific Production
- Potential artifacts to ignore: Web-related elements, links, and unnecessary text
</scratchpad>

After analyzing the document, I have identified the following key points:

* The research centre at Inria is focused on ocean dynamics and climate change, with a strong emphasis on ocean-atmosphere interactions.
* The project, ODYSSEY, aims to improve our understanding of ocean dynamics and climate change by developing new methods for ocean-atmosphere interactions and improving numerical models of ocean dynamics.
* The research programme includes four methodological axes: Ocean observations analysis, Development and analysis of numerical and mathematical models of geophysical flows, Data/Models interactions and reduced order modelling, and AI models and methods for ocean data analysis.
* The application domains of the research include geophysical environmental flows, related to ocean dynamics.
* The team has made significant progress in recent years, including the development of new numerical schemes, the analysis of stochastic models, and the application of machine learning techniques to ocean data analysis.

<final_summary>
The Inria Research Centre at Rennes is focused on ocean dynamics and climate change, with a strong emphasis on ocean-atmosphere interactions. The ODYSSEY project aims to improve our understanding of ocean dynamics and climate change by developing new methods for ocean-atmosphere interactions and improving numerical models of ocean dynamics. The research programme includes four methodological axes and has made significant progress in recent years, including the development of new numerical schemes and the application of machine learning techniques to ocean data analysis.
The Inria Research Centre at Rennes is focused on ocean dynamics and climate change, with a strong emphasis on ocean-atmosphere interactions. The ODYSSEY project aims to improve our understanding of ocean dynamics and climate change by developing new methods for ocean-atmosphere interactions and improving numerical models of ocean dynamics. The research programme includes four methodological axes and has made significant progress in recent years, including the development of new numerical schemes and the application of machine learning techniques to ocean data analysis.