arXiv subjects

Bertrand Chapron

Publications and source records attributed to Bertrand Chapron.

At least 19 recordsLinked to original sources

arXiv2026

Sampling sea state using a diffusion model

Sea state prediction is essential for operational maritime applications and coupled earth system modeling, yet current spectral wave models remain computationally prohibitive for many use cases, including online coupling to climate simulations and making probabilistic (ensemble-based) predictions. While deep learning has recently demonstrated strong performance in weather forecasting, existing AI-based wave models are predominantly deterministic and largely limited to bulk variables such as significant wave height, leaving probabilistic sea state estimation largely unexplored. In this work, we propose a diffusion-based generative model for global sea state estimation that conditions on a relatively long history (5 days) of global wind forcing. This generative model directly samples the complex conditional distribution of sea state without autoregressive time-stepping. Unlike prior approaches, our framework naturally extends beyond bulk variables to estimate partition-related variables and derived quantities, such as Stokes drift and mean square slope. Trained on a 30-year global WAVEWATCH-III hindcast, the model achieves substantial computational acceleration compared with numerical spectral models while delivering skillful predictions and a calibrated ensemble spread for the bulk variables. Our results suggest that diffusion-based sea state sampling offers a promising path toward probabilistic wave forecasting and efficient coupling of sea state information into broader earth system models.

physics.ao-ph↗

arXiv2026

Take It or Leave It: Intent-Controlled Partial Optimal Transport

While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or uniform rejection rule. However, many applications call for more structured, pointwise rejection mechanisms, where the decision to leave mass unmatched depends on side-specific reliability, support geometry, or external information about which components should participate in the comparison. We introduce \emph{intent-controlled partial optimal transport} (IC-POT), a targeted generalization of partial transport that replaces the global rejection paradigm with pointwise rejection costs over both measures. We show that the resulting optimization problem admits a dual interpretation in terms of local acceptance thresholds and can be solved by recasting it as a balanced Kantorovich OT problem on an augmented support. Beyond theoretical analysis, we demonstrate the practical relevance of IC-POT in settings where rejection is driven by side information. In positive-unlabeled learning and open-partial domain adaptation, incorporating pointwise rejection rules that encode statistical structure improves fixed baseline pipelines. Finally, we motivate the use of IC-POT with a geophysical practical case: multi-modal satellite ocean measurements, for which physical and sensors priors naturally inform the rejection mechanism and define the retrieved comparable signal information.

cs.LG↗

arXiv2026

OceanSAR-2: A Universal Feature Extractor for SAR Ocean Observation

We present OceanSAR-2, the second generation of our foundation model for SAR-based ocean observation. Building on our earlier release, which pioneered self-supervised learning on Sentinel-1 Wave Mode data, OceanSAR-2 relies on improved SSL training and dynamic data curation strategies, which enhances performance while reducing training cost. OceanSAR-2 demonstrates strong transfer performance across downstream tasks, including geophysical pattern classification, ocean surface wind vector and significant wave height estimation, and iceberg detection. We release standardized benchmark datasets, providing a foundation for systematic evaluation and advancement of SAR models for ocean applications.

cs.LG↗

arXiv2025

Neural ocean forecasting from sparse satellite-derived observations: a case-study for SSH dynamics and altimetry data

We present an end-to-end deep learning framework for short-term forecasting of global sea surface dynamics based on sparse satellite altimetry data. Building on two state-of-the-art architectures: U-Net and 4DVarNet, originally developed for image segmentation and spatiotemporal interpolation respectively, we adapt the models to forecast the sea level anomaly and sea surface currents over a 7-day horizon using sequences of sparse nadir altimeters observations. The model is trained on data from the GLORYS12 operational ocean reanalysis, with synthetic nadir sampling patterns applied to simulate realistic observational coverage. The forecasting task is formulated as a sequence-to-sequence mapping, with the input comprising partial sea level anomaly (SLA) snapshots and the target being the corresponding future full-field SLA maps. We evaluate model performance using (i) normalized root mean squared error (nRMSE), (ii) averaged effective resolution, (iii) percentage of correctly predicted velocities magnitudes and angles, and benchmark results against the operational Mercator Ocean forecast product. Results show that end-to-end neural forecasts outperform the baseline across all lead times, with particularly notable improvements in high variability regions. Our framework is developed within the OceanBench benchmarking initiative, promoting reproducibility and standardized evaluation in ocean machine learning. These results demonstrate the feasibility and potential of end-to-end neural forecasting models for operational oceanography, even in data-sparse conditions.

physics.ao-ph↗

arXiv2025

Growth rate and energy dissipation in wind-forced breaking waves

We investigate the energy growth and dissipation of wind-forced breaking waves at high wind speed using direct numerical simulations of the coupled air-water Navier-Stokes equations. A turbulent wind boundary layer drives the growth of a pre-existing narrowband wave field until it breaks, transferring energy into the water column. Under sustained wind forcing, the wave field resumes growth. We separately analyze energy transfers during wave growth and breaking-induced dissipation. Energy transfers are dominated by pressure input during growth and turbulent dissipation during breaking. Wind input during growth is balanced with dissipation during breaking over an entire growing-breaking cycle. The wave growth rate scales with $(u_\ast/c)^2$, modulated by the wave steepness due to sheltering, and the energy dissipation follows the inertial scaling with wave slope at breaking, confirming the universality of the process. Following breaking, near-surface vertical turbulence dissipation profiles scale as $z^{-1}$, with their magnitude controlled by the breaking-induced dissipation.

physics.flu-dyn↗

arXiv2025

A Stochastic Ekman-Stokes Model for Coupled Ocean-Wave-Atmosphere Dynamics

Accurate representation of atmosphere-ocean boundary layers, including the interplay of turbulence, surface waves, and air-sea fluxes, remains a challenge in geophysical fluid dynamics, particularly for climate simulations. This study introduces a stochastic coupled Ekman-Stokes model (SCESM) developed within the physically consistent Location Uncertainty framework, explicitly incorporating random turbulent fluctuations and surface wave effects. The SCESM integrates established parameterizations for air-sea fluxes, turbulent viscosity, and Stokes drift, and its performance is rigorously assessed through ensemble simulations compared against observations from the LOTUS field experiment. A performance ranking analysis quantifies the impact of different model components, highlighting the critical role of explicit uncertainty representation in both oceanic and atmospheric dynamics for accurately capturing system variability. Among the tested configurations, the full model version -- including both Stokes drift and wave-induced mixing -- shows the best agreement with observations. Wave-induced mixing terms improve model performance, while wave-dependent surface roughness enhances air-sea fluxes but reduces the relative influence of wave-driven mixing. This fully coupled stochastic framework provides a foundation for advancing boundary layer parameterizations in large-scale climate models.

physics.ao-ph↗

arXiv2025

Efficient Self-Supervised Learning for Earth Observation via Dynamic Dataset Curation

Self-supervised learning (SSL) has enabled the development of vision foundation models for Earth Observation (EO), demonstrating strong transferability across diverse remote sensing tasks. While prior work has focused on network architectures and training strategies, the role of dataset curation, especially in balancing and diversifying pre-training datasets, remains underexplored. In EO, this challenge is amplified by the redundancy and heavy-tailed distributions common in satellite imagery, which can lead to biased representations and inefficient training. In this work, we propose a dynamic dataset pruning strategy designed to improve SSL pre-training by maximizing dataset diversity and balance. Our method iteratively refines the training set without requiring a pre-existing feature extractor, making it well-suited for domains where curated datasets are limited or unavailable. We demonstrate our approach on the Sentinel-1 Wave Mode (WV) Synthetic Aperture Radar (SAR) archive, a challenging dataset dominated by ocean observations. We train models from scratch on the entire Sentinel-1 WV archive spanning 10 years. Across three downstream tasks, our results show that dynamic pruning improves both computational efficiency and representation quality, leading to stronger transferability. We also release the weights of OceanSAR-1, the first model in the OceanSAR family, a series of foundation models for ocean observation and analysis using SAR imagery, at github.com/galeio-research/OceanSAR-models/.

cs.CV↗

arXiv2025

Turbulence and energy dissipation from wave breaking

Wave breaking is a critical process in the upper ocean: an energy sink for the surface wave field and a source for turbulence in the ocean surface boundary layer. We apply a novel multi-layer numerical solver resolving upper-ocean dynamics over scales from O(50cm) to O(1km), including a broad-banded wave field and wave breaking. The present numerical study isolates the effect of wave breaking and allows us to study the surface layer in wave-influenced and wave-breaking-dominated regimes. Following our previous work showing wave breaking statistics in agreement with field observations, we extend the analysis to underwater breaking-induced turbulence and related dissipation (in freely decaying conditions). We observe a rich field of vorticity resulting from the turbulence generation by breaking waves. We discuss the vertical profiles of dissipation rate which are compared with field observations, and propose an empirical universal shape function. Good agreement is found, further demonstrating that wave breaking can dominate turbulence generation in the near-surface layer. We examine the dissipation from different angles: the global dissipation of the wave field computed from the decaying wave field, the spectral dissipation from the fifth moment of breaking front distribution, and a turbulence dissipation estimated from the underwater strain rate tensor. Finally, we consider how these different estimates can be understood as part of a coherent framework.

physics.flu-dyn↗

arXiv2024

Momentum fluxes in wind-forced breaking waves

We investigate the momentum fluxes between a turbulent air boundary layer and a growing-breaking wave field by solving the air-water two-phase Navier-Stokes equations through direct numerical simulations (DNS). A fully-developed turbulent airflow drives the growth of a narrowbanded wave field, whose amplitude increases until reaching breaking conditions. The breaking events result in a loss of wave energy, transferred to the water column, followed by renewed growth under wind forcing. We revisit the momentum flux analysis in a high-wind speed regime, characterized by the ratio of the friction velocity to wave speed $u_\ast/c$ in the range $[0.3-0.9]$, through the lens of growing-breaking cycles. The total momentum flux across the interface is dominated by pressure, which increases with $u_\ast/c$ during growth and reduces sharply during breaking. Drag reduction during breaking is linked to airflow separation, a sudden acceleration of the flow, an upward shift of the mean streamwise velocity profile, and a reduction in Reynolds shear stress. We characterize the reduction of pressure stress and flow acceleration through an aerodynamic drag coefficient by splitting the analysis between growing and breaking stages, treating them as separate sub-processes. While drag increases with $u_\ast/c$ during growth, it drops during breaking. Averaging over both stages leads to a saturation of the drag coefficient at high $u_\ast/c$, comparable to what is observed at high wind speeds in laboratory and field conditions. Our analysis suggests this saturation is controlled by breaking dynamics.

physics.flu-dyn↗

arXiv2024

WV-Net: A foundation model for SAR WV-mode satellite imagery trained using contrastive self-supervised learning on 10 million images

The European Space Agency's Copernicus Sentinel-1 (S-1) mission is a constellation of C-band synthetic aperture radar (SAR) satellites that provide unprecedented monitoring of the world's oceans. S-1's wave mode (WV) captures 20x20 km image patches at 5 m pixel resolution and is unaffected by cloud cover or time-of-day. The mission's open data policy has made SAR data easily accessible for a range of applications, but the need for manual image annotations is a bottleneck that hinders the use of machine learning methods. This study uses nearly 10 million WV-mode images and contrastive self-supervised learning to train a semantic embedding model called WV-Net. In multiple downstream tasks, WV-Net outperforms a comparable model that was pre-trained on natural images (ImageNet) with supervised learning. Experiments show improvements for estimating wave height (0.50 vs 0.60 RMSE using linear probing), estimating near-surface air temperature (0.90 vs 0.97 RMSE), and performing multilabel-classification of geophysical and atmospheric phenomena (0.96 vs 0.95 micro-averaged AUROC). WV-Net embeddings are also superior in an unsupervised image-retrieval task and scale better in data-sparse settings. Together, these results demonstrate that WV-Net embeddings can support geophysical research by providing a convenient foundation model for a variety of data analysis and exploration tasks.

cs.LG↗

arXiv2024

Neural variational Data Assimilation with Uncertainty Quantification using SPDE priors

The spatio-temporal interpolation of large geophysical datasets has historically been addressed by Optimal Interpolation (OI) and more sophisticated equation-based or data-driven Data Assimilation (DA) techniques. Recent advances in the deep learning community enables to address the interpolation problem through a neural architecture incorporating a variational data assimilation framework. The reconstruction task is seen as a joint learning problem of the prior involved in the variational inner cost, seen as a projection operator of the state, and the gradient-based minimization of the latter. Both prior models and solvers are stated as neural networks with automatic differentiation which can be trained by minimizing a loss function, typically the mean squared error between some ground truth and the reconstruction. Such a strategy turns out to be very efficient to improve the mean state estimation, but still needs complementary developments to quantify its related uncertainty. In this work, we use the theory of Stochastic Partial Differential Equations (SPDE) and Gaussian Processes (GP) to estimate both space-and time-varying covariance of the state. Our neural variational scheme is modified to embed an augmented state formulation with both state and SPDE parametrization to estimate. We demonstrate the potential of the proposed framework on a spatio-temporal GP driven by diffusion-based anisotropies and on realistic Sea Surface Height (SSH) datasets. We show how our solution reaches the OI baseline in the Gaussian case. For nonlinear dynamics, as almost always stated in DA, our solution outperforms OI, while allowing for fast and interpretable online parameter estimation.

stat.ML↗

arXiv2023

Alignments of Geophysical Fields: a differential geometry perspective

To estimate the displacements of physical state variables, the physics principles that govern the state variables must be considered. Technically, for a certain class of state variables, each state variable is associated to a tensor field. Ways displacement maps act on different state variables will then differ according to their associated different tensor field definitions. Displacement procedures can then explicitly ensure the conservation of certain physical quantities (total mass, total vorticity, total kinetic energy, etc.), and a differential-geometry-based optimisation formulated. Morphing with the correct physics, it is reasonable to apply the estimated displacement map to unobserved state variables, as long as the displacement maps are strongly correlated. This leads to a new nudging strategy using all-available observations to infer displacements of both observed and unobserved state variables. Using the proposed nudging method before applying ensemble data assimilation, numerical results show improved preservation of the intrinsic structure of underlying physical processes.

math.OC↗

arXiv2023

Online Calibration of Deep Learning Sub-Models for Hybrid Numerical Modeling Systems

Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and parameterization where they demonstrate great potential and often outperform traditional physical models. Most of these efforts in defining hybrid dynamical systems follow {offline} learning strategies in which the neural parameterization (called here sub-model) is trained to output an ideal correction. Yet, these hybrid models can face hard limitations when defining what should be a relevant sub-model response that would translate into a good forecasting performance. End-to-end learning schemes, also referred to as online learning, could address such a shortcoming by allowing the deep learning sub-models to train on historical data. However, defining end-to-end training schemes for the calibration of neural sub-models in hybrid systems requires working with an optimization problem that involves the solver of the physical equations. Online learning methodologies thus require the numerical model to be differentiable, which is not the case for most modeling systems. To overcome this difficulty and bypass the differentiability challenge of physical models, we present an efficient and practical online learning approach for hybrid systems. The method, called EGA for Euler Gradient Approximation, assumes an additive neural correction to the physical model, and an explicit Euler approximation of the gradients. We demonstrate that the EGA converges to the exact gradients in the limit of infinitely small time steps. Numerical experiments are performed on various case studies, including prototypical ocean-atmosphere dynamics. Results show significant improvements over offline learning, highlighting the potential of end-to-end online learning for hybrid modeling.

cs.LG↗

arXiv2023

Linear wave solutions of a stochastic shallow water model

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind or coming as the feedback of the ocean on the atmosphere and leading in a very fast way to the selection of some wavelength. This interwoven, yet simple, mechanism explains the emergence of typical wavelength associated to near inertial waves. Ensemble-mean waves that are not in phase with the random forcing are damped at an exponential rate, whose magnitude depends on the random forcing variance. Geostrophic adjustment is also interpreted as a statistical homogenization 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.

physics.flu-dyn↗

arXiv2023

Comparison of Stochastic Parametrization Schemes using Data Assimilation on Triad Models

In recent years, stochastic parametrizations have been ubiquitous in modelling uncertainty in fluid dynamics models. One source of model uncertainty comes from the coarse graining of the fine-scale data and is in common usage in computational simulations at coarser scales. In this paper, we look at two such stochastic parametrizations: the Stochastic Advection by Lie Transport (SALT) parametrization introduced by Holm and the Location Uncertainty (LU) parametrization introduced by Mémin. Whilst both parametrizations are available for full-scale models, we study their reduced order versions obtained by projecting them on a complex vector Fourier mode triad of eigenfunctions of the curl. Remarkably, these two parametrizations lead to the same reduced order model, which we term the helicity-preserving stochastic triad (HST). This reduced order model is then compared with an alternative model which preserves the energy of the system, and which is termed the energy preserving stochastic triad (EST). These low-dimensional models are ideal benchmark models for testing new Data Assimilation algorithms: they are easy to implement, exhibit diverse behaviours depending on the choice of the coefficients and come with natural physical properties such as the conservation of energy and helicity.

math.DS↗

arXiv2023

Physically Constrained Covariance Inflation from Location Uncertainty

Motivated by the concept of ``location uncertainty", initially introduced in \cite{Memin2013FluidFD}, a scheme is sought to perturb the ``location" of a state variable at every forecast time step. Further considering Brenier's theorem \cite{Brenier1991}, asserting that the difference of two positive density fields on the same domain can be represented by a transportation map, perturbations are demonstrated to consistently define a SPDE from the original PDE. It ensues that certain quantities, up to the user, are conserved at every time step. Remarkably, derivations following both the SALT \cite{Holm2015VariationalPF} and LU \cite{Memin2013FluidFD, Resseguier2016GeophysicalFU} settings, can be recovered from this perturbation scheme. Still, it opens broader applicability since it does not explicitly rely on Lagrangian mechanics or Newton's laws of force. For illustration, a stochastic version of the thermal shallow water equation is presented.

math.OC↗

arXiv2023

Inversion of sea surface currents from satellite-derived SST-SSH synergies with 4DVarNets

Satellite altimetry is a unique way for direct observations of sea surface dynamics. This is however limited to the surface-constrained geostrophic component of sea surface velocities. Ageostrophic dynamics are however expected to be significant for horizontal scales below 100~km and time scale below 10~days. The assimilation of ocean general circulation models likely reveals only a fraction of this ageostrophic component. Here, we explore a learning-based scheme to better exploit the synergies between the observed sea surface tracers, especially sea surface height (SSH) and sea surface temperature (SST), to better inform sea surface currents. More specifically, we develop a 4DVarNet scheme which exploits a variational data assimilation formulation with trainable observations and {\em a priori} terms. An Observing System Simulation Experiment (OSSE) in a region of the Gulf Stream suggests that SST-SSH synergies could reveal sea surface velocities for time scales of 2.5-3.0 days and horizontal scales of 0.5$^\circ$-0.7$^\circ$, including a significant fraction of the ageostrophic dynamics ($\approx$ 47\%). The analysis of the contribution of different observation data, namely nadir along-track altimetry, wide-swath SWOT altimetry and SST data, emphasizes the role of SST features for the reconstruction at horizontal spatial scales ranging from \nicefrac{1}{20}$^\circ$ to \nicefrac{1}{4}$^\circ$.

physics.ao-ph↗

arXiv2023

Multimodal 4DVarNets for the reconstruction of sea surface dynamics from SST-SSH synergies

Due to the irregular space-time sampling of sea surface observations, the reconstruction of sea surface dynamics is a challenging inverse problem. While satellite altimetry provides a direct observation of the sea surface height (SSH), which relates to the divergence-free component of sea surface currents, the associated sampling pattern prevents from retrieving fine-scale sea surface dynamics, typically below a 10-day time scale. By contrast, other satellite sensors provide higher-resolution observations of sea surface tracers such as sea surface temperature (SST). Multimodal inversion schemes then arise as an appealing strategy. Though theoretical evidence supports the existence of an explicit relationship between sea surface temperature and sea surface dynamics under specific dynamical regimes, the generalization to the variety of upper ocean dynamical regimes is complex. Here, we investigate this issue from a physics-informed learning perspective. We introduce a trainable multimodal inversion scheme for the reconstruction of sea surface dynamics from multi-source satellite-derived observations. The proposed 4DVarNet schemes combine a variational formulation involving trainable observation and a priori terms with a trainable gradient-based solver. We report an application to the reconstruction of the divergence-free component of sea surface dynamics from satellite-derived SSH and SST data. An observing system simulation experiment for a Gulf Stream region supports the relevance of our approach compared with state-of-the-art schemes. We report relative improvement greater than 50% compared with the operational altimetry product in terms of root mean square error and resolved space-time scales. We discuss further the application and extension of the proposed approach for the reconstruction and forecasting of geophysical dynamics from irregularly-sampled satellite observations.

eess.IV↗