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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 satellite constellation in 2026 is expected to provide high-resolution images of CO2 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 CO2 plume low signal-to-noise ratio, due to the variability of 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 employ convolutional neural networks (CNN) 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 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. 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. [ABSTRACT FROM AUTHOR]

Under the Copernicus programme, an operational CO 2 Monitoring Verification and Support system (CO 2 MVS) is being developed and will exploit data from future satellites monitoring the distribution of CO 2 within the atmosphere. Methods for estimating CO 2 emissions from significant local emitters (hotspots; i.e. cities or power plants) can greatly benefit from the availability of such satellite images that display the atmospheric plumes of CO 2. Indeed, local emissions are strongly correlated to the size, shape, and concentration distribution of the corresponding plume, which is a visible consequence of the emission. The estimation of emissions from a given source can therefore directly benefit from the detection of its associated plumes in the satellite image. In this study, we address the problem of plume segmentation (i.e. the problem of finding all pixels in an image that constitute a city or power plant plume). This represents a significant challenge, as the signal from CO 2 plumes induced by emissions from cities or power plants is inherently difficult to detect, since it rarely exceeds values of a few parts per million (ppm) and is perturbed by variable regional CO 2 background signals and observation errors. To address this key issue, we investigate the potential of deep learning methods and in particular convolutional neural networks to learn to distinguish plume-specific spatial features from background or instrument features. Specifically, a U-Net algorithm, an image-to-image convolutional neural network with a state-of-the-art encoder, is used to transform an XCO 2 field into an image representing the positions of the targeted plume. Our models are trained on hourly 1 km simulated XCO 2 fields in the regions of Paris, Berlin, and several power plants in Germany. Each field represents the plume of the hotspot, with the background consisting of the signal of anthropogenic and biogenic CO 2 surface fluxes near to or far from the targeted source and the simulated satellite observation errors. The performance of the deep learning method is thereafter evaluated and compared with a plume segmentation technique based on thresholding in two contexts, namely (1) where the model is trained and tested on data from the same region and (2) where the model is trained and tested in two different regions. In both contexts, our method outperforms the usual segmentation technique based on thresholding and demonstrates its ability to generalise in various cases, with respect to city plumes, power plant plumes, and areas with multiple plumes. Although less accurate than in the first context, the ability of the algorithm to extrapolate on new geographical data is conclusive, paving the way to a promising universal segmentation model trained on a well-chosen sample of power plants and cities and able to detect the majority of the plumes from all of them. Finally, the highly accurate results for segmentation suggest the significant potential of convolutional neural networks for estimating local emissions from spaceborne imagery. [ABSTRACT FROM AUTHOR]

Under the Copernicus programme, an operational CO2 monitoring system (CO2MVS) is being developed and will exploit data from future satellites monitoring the amount of CO2 within the atmosphere. Methods for estimating CO2 emissions from significant local emitters (hotspots, i.e. cities or power plants) can greatly benefit from the availability of such satellite images, displaying atmospheric plumes of CO2. Indeed, local emissions are strongly correlated to the size, shape and concentrations distribution of the corresponding plume, the visible consequence of the emission. The estimation of emissions from a given source can therefore directly benefit from the detection of its associated plumes in the satellite image. In this study, we address the problem of plume segmentation, i.e. the problem of finding all pixels in an image that constitute a city or power plant plume. This represents a significant challenge, as the signal from CO2 plumes induced by emissions from cities or power plants is inherently difficult to detect since it rarely exceeds values of a few ppm and is perturbed by variable regional CO2 background signals and observation errors. To address this key issue, we investigate the potential of deep learning methods and in particular convolutional neural networks to learn to distinguish plume-specific spatial features from background or instrument features. Specifically, a U-net algorithm, an image-to-image convolutional neural network, with a state-of-the-art encoder, is used to transform an XCO2 field into an image representing the positions of the targeted plume. Our models are trained on hourly 1 km simulated XCO2 fields in the regions of Paris, Berlin and several German power plants. Each field represents the plume of the hotspot, the background consisting of the signal of anthropogenic and biogenic CO2 surface fluxes near or far from the targeted source and the simulated satellite observation errors. The performance of the deep learning method is thereafter evaluated and compared with a plume segmentation technique based on thresholding in two contexts: the first where the model is trained and tested on data from the same region, and the second where the model is trained and tested in two different regions. In both contexts, our method outperforms the usual segmentation technique based on thresholding and demonstrates its ability to generalise in various cases: city plumes, power plant plumes, and areas with multiple plumes. Although less accurate than in the first context, the ability of the algorithm to extrapolate on new geographical data is conclusive, paving the way to a promising universal segmentation model, trained on a well-chosen sample of power plants and cities, and able to detect the majority of the plumes from all of them. Finally, the highly accurate results for segmentation suggest a significant potential of convolutional neural networks for estimating local emissions from spaceborne imagery. [ABSTRACT FROM AUTHOR]