Studies of atmospheric dispersion of pollutants on a local scale are increasingly performed with Computational Fluid Dynamics (CFD) simulations. However, CFD computations can be numerically expensive, and are often only performed on a limited number of situations. Machine learning approaches offer the possibility to build surrogate models, i.e. fast approximations to the CFD solver, allowing to quickly simulate new scenarios. Here, we propose a data-driven model that interpolates between CFD simulations with varying wind directions. The model combines a multi-layer perceptron and far-field vertical profiles of the atmosphere. We show that the use of far-field atmospheric profiles allows to improve the overall model performances but degrades the model with respect to the continuity principle. As a result, the knowledge of the continuity equation is embedded into the neural network via an additional term in the training loss. This allows to compensate for the error in the physical metrics induced by the far-field vertical profiles. The final model shows good performances in predicting atmospheric flow for new directions.

Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries. However, existing approaches implicitly assume a fixed domain size, which limits their ability to generalize at inference. In this work, we investigate domain extension, namely zero-shot inference on spatial domains that are significantly larger than those encountered during training. We argue that this setting fundamentally requires spatial locality and translation equivariance. We propose to implement this locality via a decomposable bias in the attention logits computation, enabling finely controllable locality while remaining fully decomposable into query-key inner products and directly compatible with optimized attention kernels. Combined with rotary positional embeddings, it enables expressive embeddings with controllable spatial support without altering the transformer architecture. We empirically show that our approach substantially improves zero-shot generalization to larger domains across two PDE benchmarks and a 3D industrial atmospheric flow application. Our code and datasets are available at https://github.com/cerea-daml/domain-extension.

Air flow modeling at a local scale is essential for applications such as pollutant dispersion modeling or wind farm modeling. To circumvent costly Computational Fluid Dynamics (CFD) computations, deep learning surrogate models have recently emerged as promising alternatives. However, in the context of urban air flow, deep learning models struggle to adapt to the high variations of the urban geometry and to large mesh sizes. To tackle these challenges, we introduce Anchored Branched Steady-state WInd Flow Transformer (AB-SWIFT), a transformer-based model with an internal branched structure uniquely designed for atmospheric flow modeling. We train our model on a specially designed database of atmospheric simulations around randomised urban geometries and with a mixture of unstable, neutral, and stable atmospheric stratifications. Our model reaches the best accuracy on all predicted fields compared to state-of-the-art transformers and graph-based models. Our code and data is available at https://github.com/cerea-daml/abswift.

Among the different types of atmospheric waves, infrasound corresponds to low-frequency acoustic waves that can propagate over thousands of kilometers within atmospheric waveguides formed between the surface and the middle-atmosphere (MA, 15-90 km) or the lower thermosphere (90-120 km). Infrasound is a technology used to monitor the atmosphere for the Comprehensive Nuclear-test Ban Treaty (CTBT). Infrasound stations of the International Monitoring System put in place to monitor compliance with CTBT continuously record infrasound waves, which can be seen as a tracer of the MA and lower thermosphere dynamics. At these altitudes, Numerical Weather Prediction (NWP) models are biased, notably due to the lack of observations to assimilate, especially for winds, or for instance due to an approximate representation of the impact of atmospheric gravity waves on the dynamics. We propose a method based on the observation of infrasound of oceanic origin, known as microbaroms, to evaluate and compare the performances of atmospheric models in the middle atmosphere. We present a complete processing chain that simulates microbarom arrivals at an infrasound station and that compares them to observations. It explicitly accounts for both the oceanic source emission mechanism and the atmospheric propagation. Beyond the atmospheric diagnostics enabled by this method, we have implemented our modeling of microbarom arrivals within a variational data assimilation (DA) framework to constrain wind and temperature atmospheric fields in the MA. As proof-of-concept, first DA synthetic experiments were conducted in simplified atmospheric configurations to demonstrate the added value of infrasound observations in constraining the MA dynamics.

Abstract. Recent work has shown that the analysis operator in sequential data assimilation designed to track chaotic dynamics, can be learned with deep learning from the sole knowledge of a true state trajectory and observations thereof. This approach to learning the analysis is computationally more challenging, yet conceptually more fundamental than approaches that learn a direct mapping from forecasts and observations to the corresponding analysis increments. Such learned scheme has been demonstrated to achieve accuracy comparable to that of the ensemble Kalman filter when applied to low-order dynamics. Strikingly, the same accuracy can be reached with a single state forecast instead of an ensemble, hence bypassing the need to explicitly represent forecast uncertainty. In this study, we extend the investigation of such learned analysis operators beyond the preliminary experiments reported so far. First, we analyse the emergence of local patterns encoded in the operator, which accounts for the remarkable scalability of the approach to high-dimensional state spaces. Second, we assess the performance of the learned operators in stronger nonlinear regimes of the chaotic dynamics. We show that they can match the efficiency of the iterative ensemble Kalman filter, the baseline in this context, while avoiding the need for nonlinear iterative optimisation. Throughout the paper, we seek underlying reasons for the efficiency of the approach, drawing on insights from both machine learning and nonlinear data assimilation.

Urban and industrial areas are vulnerable to accidental releases of pollutants. To accurately determine the pollutant's plume position and affected areas, it is essential to estimate the atmospheric flow around the affected site. This flow can be precisely computed using numerical methods of Computational Fluid Dynamics (CFD). However, CFD computation is expensive and slow, making it unsuitable for emergency response. As reduced order approximations, machine learning surrogates offer a promising alternative as they are usually much faster; but they must first be trained on CFD-generated data. In this study, we propose a database of atmospheric simulations with varying meshes and atmospheric stability conditions. Meshes are built by randomly sampling buildings and positioning them in space. For each mesh, values of the Monin-Obukhov length and of the ground roughness are sampled, leading to different turbulent regimes and overall atmoshperic flow behaviour. We then train a MeshGraphNet on this database, i.e. a graph neural network built on the mesh structure. The performance of the trained neural network on unseen scenarios with different initial conditions has been evaluated and will be presented.

Developing operational data assimilation systems for sea-ice models is challenging, especially using a variational approach due to the absence of adjoint models. NeXtSIM, a sea-ice model based on a brittle rheology paradigm, enables high-fidelity simulations of sea-ice dynamics at mesoscale resolution (∼10 km) but lacks an adjoint. By training a neural network as an Arctic-wide emulator for sea-ice thickness based on mesoscale simulations with neXtSIM, we gain access to an adjoint. Building on this emulator and its adjoint, we introduce a four-dimensional variational (4D–Var) data assimilation system to correct the emulator's bias and to better position the marginal ice zone (MIZ). Firstly, we perform twin experiments to demonstrate the capabilities of this 4D–Var system and to evaluate two approximations of the background covariance matrix. These twin experiments demonstrate that the assimilation improves the positioning of the MIZ and enhances the forecast quality, achieving an average reduction in sea-ice thickness root-mean-squared error of 0.8 m compared to the free run. Secondly, we assimilate real CS2SMOS satellite retrievals with this system. While the assimilation of these rather smooth retrievals amplifies the loss of small-scale information in our system, it effectively corrects the forecast bias. The forecasts of our 4D–Var system achieve a similar performance as the operational sea-ice forecasting system neXtSIM-F. These results pave the way to the use of deep learning-based emulators for 4D–Var systems to improve sea-ice modeling.

In recent years, there has been significant progress in the development of fully data-driven global numerical weather prediction models. These machine learning weather prediction models have their strength, notably accuracy and low computational requirements, but also their weakness: they struggle to represent fundamental dynamical balances, and they are far from being suitable for data assimilation experiments. Hybrid modelling emerges as a promising approach to address these limitations. Hybrid models integrate a physics-based core component with a statistical component, typically a neural network, to enhance prediction capabilities. In this article, we propose to develop a model error correction for the operational Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts using a neural network. The neural network is initially pre-trained offline using a large dataset of operational analyses and analysis increments. Subsequently, the trained network is integrated into the IFS within the Object-Oriented Prediction System (OOPS) so as to be used in data assimilation and forecast experiments. It is then further trained online using a recently developed variant of weak-constraint 4D-Var. The results show that the pre-trained neural network already provides a reliable model error correction, which translates into reduced forecast errors in many conditions and that the online training further improves the accuracy of the hybrid model in many conditions.

This paper presents the development and application of a deep-learning-based method for inverting CO2 atmospheric plumes from power plants using satellite imagery of the CO2 total column mixing ratios (XCO2). We present an end-to-end convolutional neural network (CNN) approach, processing the satellite XCO2 images to derive estimates of the power plant emissions, that is resilient to missing data in the images due to clouds or to the partial view of the plume owing to the limited extent of the satellite swath. The CNN is trained and validated exclusively on CO2 simulations from eight power plants in Germany in 2015. The evaluation on this synthetic dataset shows an excellent CNN performance with relative errors close to 20 %, which is only significantly affected by substantial cloud cover. The method is then applied to 39 images of the XCO2 plumes from nine power plants, acquired by the Orbiting Carbon Observatory-3 Snapshot Area Maps (OCO3 SAMs), and the predictions are compared to average annual reported emissions. The results are very promising, showing a relative difference in the predictions to reported emissions only slightly higher than the relative error diagnosed from the experiments with synthetic images. Furthermore, analysis of the area of the images in which the CNN-based inversion extracts the information for the quantification of the emissions, based on integrated-gradient techniques, demonstrates that the CNN effectively identifies the location of the plumes in the OCO-3 SAM images. This study demonstrates the feasibility of applying neural networks that have been trained on synthetic datasets for the inversion of atmospheric plumes in real satellite imagery from XCO2 and provides the tools for future applications.

Data assimilation for weather forecasting is commonly achieved by combining model state “trajectories” for example, daily temperature series with observations. However, for processes requiring long‐term statistics, such as climate projections in climate models, the emphasis is on capturing the long‐term state distribution (i.e., frequency and possible values of temperature over a range) rather than individual trajectories. This study introduces a probabilistic framework for parameter inference based on the probability distribution functions of state variables, using the Lorenz ’96 (L96) system as a toy model to demonstrate the proof of concept. We develop a distribution emulator for the L96 system using conditional normalizing flow models. This emulator replicates the state distributions without the need to unroll the entire series of state trajectories. Building on this emulator, a distribution‐driven framework for model parameter inference is presented, including uncertainty quantification. Finally, an application of the proposed framework for distribution matching, extreme value estimation and joint quantile analysis is discussed, highlighting its potential for current climate models and data analysis.

Due to the lack of observations, Numerical Weather Prediction (NWP) models are poorly constrained in the Middle Atmosphere (MA ~10-90km) and thus significantly biased [1]. Infrasounds of oceanic origin (microbaroms) propagate across thousands of kilometers and integrate information on the MA dynamical state and particularly on winds. Thus, we investigate how to assess the performance of NWP models in the MA through simulations and global and continuous observations of microbaroms. Infrasound observations are processed using an adaptation of the MCML [2] algorithm to obtain the azimuthal distribution of microbarom amplitudes at the International Monitoring System Norwegian infrasound station I37NO. These observations are compared to simulations where modelled distribution account for the antenna response relative to MCML processing.Simulations of microbaroms arrival are carried for the year 2021 by combining a microbarom source model [3] and two propagation methods: a semi-empirical law using a single atmospheric profile and Parabolic Equation (PE) range-dependent propagation simulation accounting for the 3D atmosphere. Yearly comparisons through an optimal transport metric using atmospheric specification from different atmospheric models highlight the limitations of the semi-empirical law for a NWP model performance evaluation.Atmospheric models are thus assessed building on the PE propagation simulations and first conclusions on models relative performances are derived over specific periods of interest, including a sudden stratospheric warming. While the current work focuses on the evaluation of NWP models, it will also allow to define a method relying on microbarom observations to improve these models through Data Assimilation. [1] Le Pichon, A., Assink, J. D., Heinrich, P., Blanc, E., Charlton-Perez, A., Lee, C. F., Keckhut, P., Hauchecorne, A., Rüfenacht, R., Kämpfer, N., et al. (2015), Comparison of co-located independent ground-based middle atmospheric wind and temperature measurements with numerical weather prediction models, J. Geophys. Res. Atmos., 120, 8318–8331, doi:10.1002/2015JD023273.[2] B Poste, M Charbit, A Le Pichon, C Listowski, F Roueff, J Vergoz, The multichannel maximum-likelihood (MCML) method: a new approach for infrasound detection and wave parameter estimation, Geophysical Journal International, Volume 232, Issue 2, February 2023, Pag-es 1099–1112, https://doi.org/10.1093/gji/ggac377[3] De Carlo, M., Accensi, M., Ardhuin, F., and Le Pichon, A.: ARROW (AtmospheRic InfRasound by Ocean Waves): a new real-time product for global ambient noise monitoring., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7564, https://doi.org/10.5194/egusphere-egu22-7564, 2022.

Sea ice plays an important role in stabilising the Earth system. Yet, representing its dynamics remains a major challenge for models, as the underlying processes are scale-invariant and highly anisotropic. This poses a dilemma: physics-based models that faithfully reproduce the observed dynamics are computationally costly, while efficient AI models sacrifice realism. Here, to resolve this dilemma, we introduce GenSIM, the first generative AI model to predict the evolution of the full Arctic sea-ice state at 12-hour increments. Trained for sub-daily forecasting on 20 years of sea-ice-ocean simulation data, GenSIM makes realistic predictions for 30 years, while reproducing the dynamical properties of sea ice with its leads and ridges and capturing long-term trends in the sea-ice volume. Notably, although solely driven by atmospheric reanalysis, GenSIM implicitly learns hidden signatures of multi-year ice-ocean interaction. Therefore, generative AI can extrapolate from sub-daily forecasts to decadal simulations, while retaining physical consistency.

The current generation of sea-ice models with Brittle rheologies can represent the observed temporal and spatial scaling of the sea-ice dynamics at resolutions of around 10 km. However, running those models is expensive, which can prohibit their use in coupled Earth system models. The promising results of neural networks for the fast prediction of the sea-ice extent or sea-ice thickness offer an opportunity to remedy this shortcoming. Here, we present the development of a data-driven sea-ice model based on generative deep learning that predicts together the sea-ice velocities, concentration, thickness, and damage. Trained with more than twenty years of simulation data from neXtSIM, the model can extrapolate to previously unseen conditions, thereby exceeding the performance of baseline models. Relying on deterministic data-driven models can lead to overly smoothed predictions, caused by a loss of small-scale information. This is why the ability to perform stochastic predictions can be instrumental to the success of data-driven sea-ice models. To generate stochastic predictions with neural networks, we employ denoising diffusion models. We show that they can predict the uncertainty that remains unexplained by deterministic models. Furthermore, diffusion models can recover the information at all scales. This resolves the issues with the smoothing effects and results in sharp predictions even for longer horizons. Therefore, we see a huge potential of generative deep learning for sea-ice modelling, which can pave the way towards the use of data-driven models within coupled Earth system models.

A novel generation of sea-ice models with elasto-brittle rheologies, such as neXtSIM, can represent sea-ice processes with an unprecedented accuracy at the mesoscale for resolutions of around 10 km. As these models are computationally expensive, we introduce supervised deep learning techniques for surrogate modeling of the sea-ice thickness from neXtSIM simulations. We adapt a convolutional U-Net architecture to an Arctic-wide setup by taking the land–sea mask with partial convolutions into account. Trained to emulate the sea-ice thickness at a lead time of 12 h, the neural network can be iteratively applied to predictions for up to 1 year. The improvements of the surrogate model over a persistence forecast persist from 12 h to roughly 1 year, with improvements of up to 50 % in the forecast error. Moreover, the predictability gain for the sea-ice thickness measured against the daily climatology extends to over 6 months. By using atmospheric forcings as additional input, the surrogate model can represent advective and thermodynamical processes which influence the sea-ice thickness and the growth and melting therein. While iterating, the surrogate model experiences diffusive processes which result in a loss of fine-scale structures. However, this smoothing increases the coherence of large-scale features and thereby the stability of the model. Therefore, based on these results, we see huge potential for surrogate modeling of state-of-the-art sea-ice models with neural networks.

We make the first steps towards diffusion models for unconditional generation of multivariate and Arctic-wide sea-ice states. While targeting to reduce the computational costs by diffusion in latent space, latent diffusion models also offer the possibility to integrate physical knowledge into the generation process. We tailor latent diffusion models to sea-ice physics with a censored Gaussian distribution in data space to generate data that follows the physical bounds of the modelled variables. Our latent diffusion models reach similar scores as the diffusion model trained in data space, but they smooth the generated fields as caused by the latent mapping. While enforcing physical bounds cannot reduce the smoothing, it improves the representation of the marginal ice zone. Therefore, for large-scale Earth system modelling, latent diffusion models can have many advantages compared to diffusion in data space if the significant barrier of smoothing can be resolved.

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple residual convolutional neural network, while assuming the dynamics to be known. Experiments are performed with the Lorenz 96 dynamics, which display spatiotemporal chaos and for which solid benchmarks for DA performance exist. The accuracy of the states obtained from the learned analysis approaches that of the best possibly tuned ensemble Kalman filter and is far better than that of variational DA alternatives. Critically, this can be achieved while propagating even just a single state in the forecast step. We investigate the reason for achieving ensemble filtering accuracy without an ensemble. We diagnose that the analysis scheme actually identifies key dynamical perturbations, mildly aligned with the unstable subspace, from the forecast state alone, without any ensemble-based covariances representation. This reveals that the analysis scheme has learned some multiplicative ergodic theorem associated to the DA process seen as a non-autonomous random dynamical system.

The quantification of emissions of greenhouse gases and air pollutants through the inversion of plumes in satellite images remains a complex problem that current methods can only assess with significant uncertainties. The anticipated launch of the CO2M (Copernicus Anthropogenic Carbon Dioxide Monitoring) satellite constellation in 2026 is expected to provide high-resolution images of CO2 (carbon dioxide) column-averaged mole fractions (XCO2), opening up new possibilities. However, the inversion of future CO2 plumes from CO2M will encounter various obstacles. A challenge is the low CO2 plume signal-to-noise ratio due to the variability in the background and instrumental errors in satellite measurements. Moreover, uncertainties in the transport and dispersion processes further complicate the inversion task. To address these challenges, deep learning techniques, such as neural networks, offer promising solutions for retrieving emissions from plumes in XCO2 images. Deep learning models can be trained to identify emissions from plume dynamics simulated using a transport model. It then becomes possible to extract relevant information from new plumes and predict their emissions. In this paper, we develop a strategy employing convolutional neural networks (CNNs) to estimate the emission fluxes from a plume in a pseudo-XCO2 image. Our dataset used to train and test such methods includes pseudo-images based on simulations of hourly XCO2, NO2 (nitrogen dioxide), and wind fields near various power plants in eastern Germany, tracing plumes from anthropogenic and biogenic sources. CNN models are trained to predict emissions from three power plants that exhibit diverse characteristics. The power plants used to assess the deep learning model's performance are not used to train the model. We find that the CNN model outperforms state-of-the-art plume inversion approaches, achieving highly accurate results with an absolute error about half of that of the cross-sectional flux method and an absolute relative error of ∼ 20 % when only the XCO2 and wind fields are used as inputs. Furthermore, we show that our estimations are only slightly affected by the absence of NO2 fields or a detection mechanism as additional information. Finally, interpretability techniques applied to our models confirm that the CNN automatically learns to identify the XCO2 plume and to assess emissions from the plume concentrations. These promising results suggest a high potential of CNNs in estimating local CO2 emissions from satellite images.

We propose denoising diffusion models for data-driven representation learning of dynamical systems. In this type of generative deep learning, a neural network is trained to denoise and reverse a diffusion process, where Gaussian noise is added to states from the attractor of a dynamical system. Iteratively applied, the neural network can then map samples from isotropic Gaussian noise to the state distribution. We showcase the potential of such neural networks in proof-of-concept experiments with the Lorenz 1963 system. Trained for state generation, the neural network can produce samples that are almost indistinguishable from those on the attractor. The model has thereby learned an internal representation of the system, applicable for different tasks other than state generation. As a first task, we fine-tune the pre-trained neural network for surrogate modelling by retraining its last layer and keeping the remaining network as a fixed feature extractor. In these low-dimensional settings, such fine-tuned models perform similarly to deep neural networks trained from scratch. As a second task, we apply the pre-trained model to generate an ensemble out of a deterministic run. Diffusing the run, and then iteratively applying the neural network, conditions the state generation, which allows us to sample from the attractor in the run's neighbouring region. To control the resulting ensemble spread and Gaussianity, we tune the diffusion time and, thus, the sampled portion of the attractor. While easier to tune, this proposed ensemble sampler can outperform tuned static covariances in ensemble optimal interpolation. Therefore, these two applications show that denoising diffusion models are a promising way towards representation learning for dynamical systems.