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The accident at the Fukushima Daiichi nuclear power plant (NPP) yielded massive and rapidly varying atmospheric radionuclide releases. The assessment of these releases and of the corresponding uncertainties can be performed using inverse modelling methods that combine an atmospheric transport model with a set of observations and have proven to be very effective for this type of problem. In the case of the Fukushima Daiichi NPP, a Bayesian inversion is particularly suitable because it allows errors to be modelled rigorously and a large number of observations of different natures to be assimilated at the same time. More specifically, one of the major sources of uncertainty in the source assessment of the Fukushima Daiichi NPP releases stems from the temporal representation of the source. To obtain a well-time-resolved estimate, we implement a sampling algorithm within a Bayesian framework – the reversible-jump Markov chain Monte Carlo – in order to retrieve the distributions of the magnitude of the Fukushima Daiichi NPP caesium 137 (137 Cs) source as well as its temporal discretization. In addition, we develop Bayesian methods that allow us to combine air concentration and deposition measurements as well as to assess the spatio-temporal information of the air concentration observations in the definition of the observation error matrix. These methods are applied to the reconstruction of the posterior distributions of the magnitude and temporal evolution of the 137 Cs release. They yield a source estimate between 11 and 24 March as well as an assessment of the uncertainties associated with the observations, the model, and the source estimate. The total reconstructed release activity is estimated to be between 10 and 20 PBq, although it increases when the deposition measurements are taken into account. Finally, the variable discretization of the source term yields an almost hourly profile over certain intervals of high temporal variability, signalling identifiable portions of the source term. [ABSTRACT FROM AUTHOR]

Ensemble variational methods form the basis of the state of the art for nonlinear, scalable data assimilation, yet current designs may not be cost-effective for real-time, short-range forecast systems. We propose a novel estimator in this formalism that is designed for applications in which forecast error dynamics is weakly nonlinear, such as synoptic-scale meteorology. Our method combines the 3D sequential filter analysis and retrospective reanalysis of the classic ensemble Kalman smoother with an iterative ensemble simulation of 4D smoothers. To rigorously derive and contextualize our method, we review related ensemble smoothers in a Bayesian maximum a posteriori narrative. We then develop and intercompare these schemes in the open-source Julia package DataAssimilationBenchmarks.jl, with pseudo-code provided for their implementations. This numerical framework, supporting our mathematical results, produces extensive benchmarks demonstrating the significant performance advantages of our proposed technique. Particularly, our single-iteration ensemble Kalman smoother (SIEnKS) is shown to improve prediction/analysis accuracy and to simultaneously reduce the leading-order computational cost of iterative smoothing in a variety of test cases relevant for short-range forecasting. This long work presents our novel SIEnKS and provides a theoretical and computational framework for the further development of ensemble variational Kalman filters and smoothers. [ABSTRACT FROM AUTHOR]

Relatively little attention has been given to the impact of discretization error on twin experiments in the stochastic form of the Lorenz-96 equations when the dynamics are fully resolved but random. We study a simple form of the stochastically forced Lorenz-96 equations that is amenable to higher-order time-discretization schemes in order to investigate these effects. We provide numerical benchmarks for the overall discretization error, in the strong and weak sense, for several commonly used integration schemes and compare these methods for biases introduced into ensemble-based statistics and filtering performance. The distinction between strong and weak convergence of the numerical schemes is focused on, highlighting which of the two concepts is relevant based on the problem at hand. Using the above analysis, we suggest a mathematically consistent framework for the treatment of these discretization errors in ensemble forecasting and data assimilation twin experiments for unbiased and computationally efficient benchmark studies. Pursuant to this, we provide a novel derivation of the order 2.0 strong Taylor scheme for numerically generating the truth twin in the stochastically perturbed Lorenz-96 equations. [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]

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]