Reduction of rain-induced errors for wind speed estimation on SAR observations using convolutional neural networks

Synthetic Aperture Radar is known to be able to provide high-resolution estimates of surface wind speed. These estimates usually rely on a Geophysical Model Function (GMF) that has difficulties accounting for non-wind processes such as rain events. Convolutional neural network, on the other hand, have the capacity to use contextual information and have demonstrated their ability to delimit rainfall areas. By carefully building a large dataset of SAR observations from the Copernicus Sentinel-1 mission, collocated with both GMF and atmospheric model wind speeds as well as rainfall estimates, we were able to train a wind speed estimator with reduced errors under rain. Collocations with in-situ wind speed measurements from buoys show a root mean square error that is reduced by 27% (resp. 45%) under rainfall estimated at more than 1 mm/h (resp. 3 mm/h). These results demonstrate the capacity of deep learning models to correct rain-related errors in SAR products.

Scale-aware neural calibration for wide swath altimetry observations

Sea surface height (SSH) is a key geophysical parameter for monitoring and studying meso-scale surface ocean dynamics. For several decades, the mapping of SSH products at regional and global scales has relied on nadir satellite altimeters, which provide one-dimensional-only along-track satellite observations of the SSH. The Surface Water and Ocean Topography (SWOT) mission deploys a new sensor that acquires for the first time wide-swath two-dimensional observations of the SSH. This provides new means to observe the ocean at previously unresolved spatial scales. A critical challenge for the exploiting of SWOT data is the separation of the SSH from other signals present in the observations. In this paper, we propose a novel learning-based approach for this SWOT calibration problem. It benefits from calibrated nadir altimetry products and a scale-space decomposition adapted to SWOT swath geometry and the structure of the different processes in play. In a supervised setting, our method reaches the state-of-the-art residual error of ~1.4cm while proposing a correction on the entire spectral from 10km to 1000k

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}$^\circ$.

Neural Fields for Fast and Scalable Interpolation of Geophysical Ocean Variables

Optimal Interpolation (OI) is a widely used, highly trusted algorithm for interpolation and reconstruction problems in geosciences. With the influx of more satellite missions, we have access to more and more observations and it is becoming more pertinent to take advantage of these observations in applications such as forecasting and reanalysis. With the increase in the volume of available data, scalability remains an issue for standard OI and it prevents many practitioners from effectively and efficiently taking advantage of these large sums of data to learn the model hyperparameters. In this work, we leverage recent advances in Neural Fields (NerFs) as an alternative to the OI framework where we show how they can be easily applied to standard reconstruction problems in physical oceanography. We illustrate the relevance of NerFs for gap-filling of sparse measurements of sea surface height (SSH) via satellite altimetry and demonstrate how NerFs are scalable with comparable results to the standard OI. We find that NerFs are a practical set of methods that can be readily applied to geoscience interpolation problems and we anticipate a wider adoption in the future.

Deep learning for Lagrangian drift simulation at the sea surface

We address Lagrangian drift simulation in geophysical dynamics and explore deep learning approaches to overcome known limitations of state-of-the-art model-based and Markovian approaches in terms of computational complexity and error propagation. We introduce a novel architecture, referred to as DriftNet, inspired from the Eulerian Fokker-Planck representation of Lagrangian dynamics. Numerical experiments for Lagrangian drift simulation at the sea surface demonstrates the relevance of DriftNet w.r.t. state-of-the-art schemes. Benefiting from the fully-convolutional nature of Drift-Net, we explore through a neural inversion how to diagnose modelderived velocities w.r.t. real drifter trajectories.

Learning Neural Optimal Interpolation Models and Solvers

The reconstruction of gap-free signals from observation data is a critical challenge for numerous application domains, such as geoscience and space-based earth observation, when the available sensors or the data collection processes lead to irregularly-sampled and noisy observations. Optimal interpolation (OI), also referred to as kriging, provides a theoretical framework to solve interpolation problems for Gaussian processes (GP). The associated computational complexity being rapidly intractable for n-dimensional tensors and increasing numbers of observations, a rich literature has emerged to address this issue using ensemble methods, sparse schemes or iterative approaches. Here, we introduce a neural OI scheme. It exploits a variational formulation with convolutional auto-encoders and a trainable iterative gradient-based solver. Theoretically equivalent to the OI formulation, the trainable solver asymptotically converges to the OI solution when dealing with both stationary and non-stationary linear spatio-temporal GPs. Through a bi-level optimization formulation, we relate the learning step and the selection of the training loss to the theoretical properties of the OI, which is an unbiased estimator with minimal error variance. Numerical experiments for 2D+t synthetic GP datasets demonstrate the relevance of the proposed scheme to learn computationally-efficient and scalable OI models and solvers from data. As illustrated for a real-world interpolation problems for satellite-derived geophysical dynamics, the proposed framework also extends to non-linear and multimodal interpolation problems and significantly outperforms state-of-the-art interpolation methods, when dealing with very high missing data rates.

4DVarNet-SSH: end-to-end learning of variational interpolation schemes for nadir and wide-swath satellite altimetry

The reconstruction of sea surface currents from satellite altimeter data is a key challenge in spatial oceanography, especially with the upcoming wide-swath SWOT (Surface Ocean and Water Topography) altimeter mission. Operational systems however generally fail to retrieve mesoscale dynamics for horizontal scales below 100km and time-scale below 10 days. Here, we address this challenge through the 4DVarnet framework, an end-to-end neural scheme backed on a variational data assimilation formulation. We introduce a parametrization of the 4DVarNet scheme dedicated to the space-time interpolation of satellite altimeter data. Within an observing system simulation experiment (NATL60), we demonstrate the relevance of the proposed approach both for nadir and nadir+swot altimeter configurations for two contrasted case-study regions in terms of upper ocean dynamics. We report relative improvement with respect to the operational optimal interpolation between 30% and 60% in terms of reconstruction error. Interestingly, for the nadir+swot altimeter configuration, we reach resolved space-time scales below 70km and 7days. The code is open-source to enable reproductibility and future collaborative developments. Beyond its applicability to large-scale domains, we also address uncertainty quantification issues and generalization properties of the proposed learning setting. We discuss further future research avenues and extensions to other ocean data assimilation and space oceanography challenges.

Learning-based estimation of in-situ wind speed from underwater acoustics

Wind speed retrieval at sea surface is of primary importance for scientific and operational applications. Besides weather models, in-situ measurements and remote sensing technologies, especially satellite sensors, provide complementary means to monitor wind speed. As sea surface winds produce sounds that propagate underwater, underwater acoustics recordings can also deliver fine-grained wind-related information. Whereas model-driven schemes, especially data assimilation approaches, are the state-of-the-art schemes to address inverse problems in geoscience, machine learning techniques become more and more appealing to fully exploit the potential of observation datasets. Here, we introduce a deep learning approach for the retrieval of wind speed time series from underwater acoustics possibly complemented by other data sources such as weather model reanalyses. Our approach bridges data assimilation and learning-based frameworks to benefit both from prior physical knowledge and computational efficiency. Numerical experiments on real data demonstrate that we outperform the state-of-the-art data-driven methods with a relative gain up to 16% in terms of RMSE. Interestingly, these results support the relevance of the time dynamics of underwater acoustic data to better inform the time evolution of wind speed. They also show that multimodal data, here underwater acoustics data combined with ECMWF reanalysis data, may further improve the reconstruction performance, including the robustness with respect to missing underwater acoustics data.

Rain Rate Estimation with SAR using NEXRAD measurements with Convolutional Neural Networks

Remote sensing of rainfall events is critical for both operational and scientific needs, including for example weather forecasting, extreme flood mitigation, water cycle monitoring, etc. Ground-based weather radars, such as NOAA's Next-Generation Radar (NEXRAD), provide reflectivity and precipitation measurements of rainfall events. However, the observation range of such radars is limited to a few hundred kilometers, prompting the exploration of other remote sensing methods, paricularly over the open ocean, that represents large areas not covered by land-based radars. For a number of decades, C-band SAR imagery such a such as Sentinel-1 imagery has been known to exhibit rainfall signatures over the sea surface. However, the development of SAR-derived rainfall products remains a challenge. Here we propose a deep learning approach to extract rainfall information from SAR imagery. We demonstrate that a convolutional neural network, such as U-Net, trained on a colocated and preprocessed Sentinel-1/NEXRAD dataset clearly outperforms state-of-the-art filtering schemes. Our results indicate high performance in segmenting precipitation regimes, delineated by thresholds at 1, 3, and 10 mm/h. Compared to current methods that rely on Koch filters to draw binary rainfall maps, these multi-threshold learning-based models can provide rainfall estimation for higher wind speeds and thus may be of great interest for data assimilation weather forecasting or for improving the qualification of SAR-derived wind field data.

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.