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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]

The accident at the Fukushima-Daiichi nuclear power plant 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 5 problem. In the case of Fukushima-Daiichi, a Bayesian inversion is particularly suitable because it allows errors to be modelled rigorously and a large amount 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 releases stems from the temporal representation of the source. To obtain a well time-resolved estimate, we implement a MCMC sampling algorithm within a Bayesian framework, the Reversible-Jump MCMC, in order to retrieve the distributions of the magnitude of the Fukushima-Daiichi 137Cs source as well as its temporal discretisation. In addition, we develop Bayesian methods allowing 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 137Cs 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 released reconstructed activity is estimated to be between 10 and 20 PBq, although it increases when taking into account the deposition measurements. Finally, the variable discretisation of the source term yields an almost hourly profile over certain intervals of high temporal variability, signaling 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 reducing prediction error in online, short-range forecast systems. We propose a novel, outer-loop optimization of the ensemble-variational formalism for applications in which forecast error dynamics are weakly nonlinear, such as synoptic meteorology. In order to rigorously derive our method and demonstrate its novelty, we review ensemble smoothers that appear throughout the literature in a unified Bayesian maximum-a-posteriori narrative, updating and simplifying some results. After mathematically deriving our technique, we systematically develop and inter-compare all studied schemes in the open-source Julia package DataAssimilationBenchmarks.jl, with pseudo-code provided for these methods. This high-performance numerical framework, supporting our mathematical results, produces extensive benchmarks that demonstrate the significant performance advantages of our proposed technique. In particular, our single-iteration ensemble Kalman smoother is shown both to improve prediction / posterior accuracy and to simultaneously reduce the leading order cost of iterative, sequential smoothers in a variety of relevant test cases for operational short-range forecasts. This long work is thus intended to present our novel single-iteration ensemble Kalman smoother, and to provide a theoretical and computational framework for the study of sequential, ensemble-variational Kalman filters and smoothers generally. [ABSTRACT FROM AUTHOR]

The implementation of current deep learning training algorithms is power-hungry, due to data transfer between memory and logic units. Oxide-based resistive random access memories (RRAMs) are outstanding candidates to implement in-memory computing, which is less power-intensive. Their weak RESET regime is particularly attractive for learning, as it allows tuning the resistance of the devices with remarkable endurance. However, the resistive change behavior in this regime suffers from many fluctuations and is particularly challenging to model, especially in a way compatible with tools used for simulating deep learning. In this work, we present a model of the weak RESET process in hafnium oxide RRAM and integrate this model within the PyTorch deep learning framework. Validated on experiments on a hybrid CMOS/RRAM technology, our model reproduces both the noisy progressive behavior and the device-to-device (D2D) variability. We use this tool to train binarized neural networks (BNNs) for the MNIST handwritten digit recognition task and the CIFAR-10 object classification task. We simulate our model with and without various aspects of device imperfections to understand their impact on the training process and identify that the D2D variability is the most detrimental aspect. The framework can be used in the same manner for other types of memories to identify the device imperfections that cause the most degradation, which can, in turn, be used to optimize the devices to reduce the impact of these imperfections. [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]

We examine the perturbation update step of the ensemble Kalman filters which rely on covariance localisation, and hence have the ability to assimilate non-local observations in geophysical models. We show that the updated perturbations of these ensemble filters are not to be identified with the main empirical orthogonal functions of the analysis covariance matrix, in contrast with the updated perturbations of the local ensemble transform Kalman filter (LETKF). Building on that evidence, we propose a new scheme to update the perturbations of a local ensemble square root Kalman filter (LEnSRF) with the goal to minimise the discrepancy between the analysis covariances and the sample covariances regularised by covariance localisation. The scheme has the potential to be more consistent and to generate updated members closer to the model's attractor (showing fewer imbalances). We show how to solve the corresponding optimisation problem and discuss its numerical complexity. The qualitative properties of the perturbations generated from this new scheme are illustrated using a simple one-dimensional covariance model. Moreover, we demonstrate on the discrete Lorenz–96 and continuous Kuramoto–Sivashinsky one-dimensional low-order models that the new scheme requires significantly less, and possibly none, multiplicative inflation needed to counteract imbalance, compared to the LETKF and the LEnSRF without the new scheme. Finally, we notice a gain in accuracy of the new LEnSRF as measured by the analysis and forecast root mean square errors, despite using well-tuned configurations where such gain is very difficult to obtain. [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. Focus is given to the distinction between strong and weak convergence of the numerical schemes, 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]

This paper studies multiplicative inflation: the complementary scaling of the state covariance in the ensemble Kalman filter (EnKF). Firstly, error sources in the EnKF are catalogued and discussed in relation to inflation; nonlinearity is given particular attention as a source of sampling error. In response, the "finite‐size" refinement known as the EnKF‐N is re‐derived via a Gaussian scale mixture, again demonstrating how it yields adaptive inflation. Existing methods for adaptive inflation estimation are reviewed, and several insights are gained from a comparative analysis. One such adaptive inflation method is selected to complement the EnKF‐N to make a hybrid that is suitable for contexts where model error is present and imperfectly parametrized. Benchmarks are obtained from experiments with the two‐scale Lorenz model and its slow‐scale truncation. The proposed hybrid EnKF‐N method of adaptive inflation is found to yield systematic accuracy improvements in comparison with the existing methods, albeit to a moderate degree. This paper studies multiplicative inflation: the complementary scaling of the state covariance in the ensemble Kalman filter (EnKF). Firstly, error sources in the EnKF are catalogued and discussed in relation to inflation; nonlinearity is given particular attention as a source of sampling error. In response, the "finite‐size" refinement known as the EnKF‐N is re‐derived via a Gaussian scale mixture, again demonstrating how it yields adaptive inflation. An extension is proposed that hybridizes the EnKF‐N with an existing adaptive inflation scheme, making it suitable also in the presence of model error. [ABSTRACT FROM AUTHOR]

The term 'asynchronous data assimilation' (ADA) refers to modifications of sequential data assimilation methods that take into consideration the observation time. In Sakov et al. [Tellus A, 62, 24-29 (2010)], a simple rule has been formulated for the ADA with the ensemble Kalman filter (EnKF). To assimilate scattered in time observations, one needs to calculate ensemble forecast observations using the forecast ensemble at observation time. Using then these ensemble observations in the EnKF update matches the optimal analysis in the linear perfect model case. In this note, we generalise this rule for the case of additive model error. [ABSTRACT FROM AUTHOR]

In this paper, a new continuous multilevel compact model for phase-change memory (PCM) is proposed. It is based on the modified rate equations with the introduction of a variable related to material melting. The model is evaluated using a large set of dynamic measurements and shows a good accuracy with a single model card. All fitting parameters are discussed, and their impacts are detailed. Full circuit simulation is performed. Good convergence and fast simulation time suggest that this new compact model can be exploited for PCM circuit design. [ABSTRACT FROM AUTHOR]

Recent studies have demonstrated that it is possible to combine machine learning with data assimilation to reconstruct the dynamics of a physical model partially and imperfectly observed. The surrogate model can be defined as an hybrid combination where a physical model based on prior knowledge is enhanced with a statistical model estimated by a neural network (NN). The training of the NN is typically done offline, once a large enough data set of model state estimates is available. By contrast, with online approaches the surrogate model is improved each time a new system state estimate is computed. Online approaches naturally fit the sequential framework encountered in geosciences where new observations become available with time. In a recent methodology paper, we have developed a new weak‐constraint 4D‐Var formulation which can be used to train a NN for online model error correction. In the present article, we develop a simplified version of that method, in the incremental 4D‐Var framework adopted by most operational weather centers. The simplified method is implemented in the European Center for Medium‐Range Weather Forecasts (ECMWF) Object‐Oriented Prediction System, with the help of a newly developed Fortran NN library, and tested with a two‐layer two‐dimensional quasi geostrophic model. The results confirm that online learning is effective and yields a more accurate model error correction than offline learning. Finally, the simplified method is compatible with future applications to state‐of‐the‐art models such as the ECMWF Integrated Forecasting System. Plain Language Summary: We have recently proposed a general framework for combining data assimilation (DA) and machine learning (ML) techniques to train a neural network for online model error correction. In the present article, we develop a simplified version of this online training method, compatible with future applications to more realistic models. Using numerical illustrations, we show that the new method is effective and yields a more accurate model error correction than the usual offline learning approach. The results show the potential of incorporating DA and ML tightly, and pave the way toward an application to the Integrated Forecasting System used for operational numerical weather prediction at the European Centre for Medium‐Range Weather Forecasts. Key Points: Variants of weak‐constraint 4D‐Var can be used to train neural networks for online model error correctionOnline learning yields a more accurate model error correction than offline learningThe new, simplified method, developed in the incremental 4D‐Var framework, can be easily applied in operational weather models [ABSTRACT FROM AUTHOR]

Emerging nonvolatile memories based on resistive switching mechanisms pull intense research and development efforts from both academia and industry. Oxide-based resistive random access memories (OxRAM) gather noteworthy performances, such as fast WRITE/READ speed, low power, high endurance, and large integration density that outperform conventional flash memories. To fully explore new design concepts, such as distributed memory in logic or biomimetic architectures, robust OxRAM compact models must be developed and implemented into electrical simulators to assess performances at a circuit level. In this paper, we propose a physics-based compact model used in electrical simulator for bipolar OxRAM memories. After uncovering the theoretical background and the set of relevant physical parameters, this model is confronted to experimental electrical data. The excellent agreement with these data suggests that this model can be confidently implemented into circuit simulators for design purpose. [ABSTRACT FROM PUBLISHER]

Abstract: Inverse modelling techniques can be used to estimate the amount of radionuclides and the temporal profile of the source term released in the atmosphere during the accident of the Fukushima Daiichi nuclear power plant in March 2011. In Winiarek et al. (2012b), the lower bounds of the caesium-137 and iodine-131 source terms were estimated with such techniques, using activity concentration measurements. The importance of an objective assessment of prior errors (the observation errors and the background errors) was emphasised for a reliable inversion. In such critical context where the meteorological conditions can make the source term partly unobservable and where only a few observations are available, such prior estimation techniques are mandatory, the retrieved source term being very sensitive to this estimation. We propose to extend the use of these techniques to the estimation of prior errors when assimilating observations from several data sets. The aim is to compute an estimate of the caesium-137 source term jointly using all available data about this radionuclide, such as activity concentrations in the air, but also daily fallout measurements and total cumulated fallout measurements. It is crucial to properly and simultaneously estimate the background errors and the prior errors relative to each data set. A proper estimation of prior errors is also a necessary condition to reliably estimate the a posteriori uncertainty of the estimated source term. Using such techniques, we retrieve a total released quantity of caesium-137 in the interval 11.6−19.3 PBq with an estimated standard deviation range of 15−20% depending on the method and the data sets. The “blind” time intervals of the source term have also been strongly mitigated compared to the first estimations with only activity concentration data. [Copyright &y& Elsevier]

Uncertainty quantification is critical in the inversion of CO2 surface fluxes from atmospheric concentration measurements. Here, we estimate the main hyperparameters of the error covariance matrices for a priori fluxes and CO2 concentrations, that is, the variances and the correlation lengths, using real, continuous hourly CO2 concentration data in the context of the Ring 2 experiment of the North American Carbon Program Mid Continent Intensive. Several criteria, namely maximum likelihood (ML), general cross-validation (GCV) and χ² test are compared for the first time under a realistic setting in a mesoscale CO2 inversion. It is shown that the optimal hyperparameters under the ML criterion assure perfect χ² consistency of the inverted fluxes. Inversions using the ML error variances estimates rather than the prescribed default values are less weighted by the observations, because the default values underestimate the model-data mismatch error, which is assumed to be dominated by the atmospheric transport error. As for the spatial correlation length in prior flux errors, the Ring 2 network is sparse for GCV, and this method fails to reach an optimum. In contrast, the ML estimate (e.g. an optimum of 20 km for the first week of June 2007) does not support long spatial correlations that are usually assumed in the default values. [ABSTRACT FROM AUTHOR]

Abstract: The review of major 3-D global and regional real-time air quality forecasting (RT-AQF) models in Part I identifies several areas of improvement in meteorological forecasts, chemical inputs, and model treatments of atmospheric physical, dynamic, and chemical processes. Part II highlights several recent scientific advances in some of these areas that can be incorporated into RT-AQF models to address model deficiencies and improve forecast accuracies. Current major numerical, statistical, and computational techniques to improve forecasting skills are assessed. These include bias adjustment techniques to correct biases in forecast products, chemical data assimilation techniques for improving chemical initial and boundary conditions as well as emissions, and ensemble forecasting approaches to quantify the uncertainties of the forecasts. Several case applications of current 3-D RT-AQF models with the state-of-the-science model treatments, a detailed urban process module, and an advanced combined ensemble/data assimilation technique are presented to illustrate current model skills and capabilities. Major technical challenges and research priorities are provided. A new generation of comprehensive RT-AQF model systems, to emerge in the coming decades, will be based on state-of-the-science 3-D RT-AQF models, supplemented with efficient data assimilation techniques and sophisticated statistical models, and supported with modern numerical/computational technologies and a suite of real-time observational data from all platforms. [Copyright &y& Elsevier]

Abstract: Real-time air quality forecasting (RT-AQF), a new discipline of the atmospheric sciences, represents one of the most far-reaching development and practical applications of science and engineering, poses unprecedented scientific, technical, and computational challenges, and generates significant opportunities for science dissemination and community participations. This two-part review provides a comprehensive assessment of the history, current status, major research and outreach challenges, and future directions of RT-AQF, with a focus on the application and improvement of three-dimensional (3-D) deterministic RT-AQF models. In Part I, major milestones in the history of RT-AQF are reviewed. The fundamentals of RT-AQF are introduced. Various RT-AQF techniques with varying degrees of sophistication and skills are described comparatively. Among all techniques, 3-D RT-AQF models with online-coupled meteorology–chemistry and their transitions from mesoscale to unified model systems across scales represent a significant advancement and would greatly enhance understanding of the underlying complex interplay of meteorology, emission, and chemistry from global to urban scales in the real atmosphere. Current major 3-D global and regional RT-AQF models in the world are reviewed in terms of model systems, component models, application scales, model inputs, forecast products, horizontal grid resolutions, and model treatments of chemistry and aerosol processes. An important trend of such models is their coupling with an urban model or a computational fluid dynamic model for urban/local scale applications at 1 km or less and with an exposure model to provide real-time public health assessment and exposure predictions. Evaluation protocols are described along with examinations of current forecasting skills and areas with large biases of major RT-AQF models. [Copyright &y& Elsevier]

Abstract: The International Monitoring System (IMS) radionuclide network enforces the Comprehensive Nuclear-Test-Ban Treaty which bans nuclear explosions. We have evaluated the potential of the IMS radionuclide network for inverse modelling of the source, whereas it is usually assessed by its detection capability. To do so, we have chosen the degrees of freedom for the signal (DFS), a well established criterion in remote sensing, in order to assess the performance of an inverse modelling system. Using a recent multiscale data assimilation technique, we have computed optimal adaptive grids of the source parameter space by maximising the DFS. This optimisation takes into account the monitoring network, the meteorology over one year (2009) and the relationship between the source parameters and the observations derived from the FLEXPART Lagrangian transport model. Areas of the domain where the grid-cells of the optimal adaptive grid are large emphasise zones where the retrieval is more uncertain, whereas areas where the grid-cells are smaller and denser stress regions where more source variables can be resolved. The observability of the globe through inverse modelling is studied in strong, realistic and small model error cases. The strong error and realistic error cases yield heterogeneous adaptive grids, indicating that information does not propagate far from the monitoring stations, whereas in the small error case, the grid is much more homogeneous. In all cases, several specific continental regions remain poorly observed such as Africa as well as the tropics, because of the trade winds. The northern hemisphere is better observed through inverse modelling (more than 60% of the total DFS) mostly because it contains more IMS stations. This unbalance leads to a better performance of inverse modelling in the northern hemisphere winter. The methodology is also applied to the subnetwork composed of the stations of the IMS network which measure noble gases. [Copyright &y& Elsevier]

A four-dimensional variational data assimilation system (4D-Var) is developed to retrieve carbon monoxide (CO) fluxes at regional scale, using an air quality network. The air quality stations that monitor CO are proximity stations located close to industrial, urban or traffic sources. The mismatch between the coarsely discretised Eulerian transport model and the observations, inferred to be mainly due to representativeness errors in this context, lead to a bias (average simulated concentrations minus observed concentrations) of the same order of magnitude as the concentrations. 4D-Var leads to a mild improvement in the bias because it does not adequately handle the representativeness issue. For this reason, a simple statistical subgrid model is introduced and is coupled to 4D-Var. In addition to CO fluxes, the optimisation seeks to jointly retrieve influence coefficients, which quantify each station's representativeness. The method leads to a much better representation of the CO concentration variability, with a significant improvement of statistical indicators. The resulting increase in the total inventory estimate is close to the one obtained from remote sensing data assimilation. This methodology and experiments suggest that information useful at coarse scales can be better extracted from atmospheric constituent observations strongly impacted by representativeness errors. [ABSTRACT FROM AUTHOR]

BSTRACT When constraining surface emissions of air pollutants using inverse modelling one often encounters spurious corrections to the inventory at places where emissions and observations are colocated, referred to here as the colocalization problem. Several approaches have been used to deal with this problem: coarsening the spatial resolution of emissions; adding spatial correlations to the covariance matrices; adding constraints on the spatial derivatives into the functional being minimized; and multiplying the emission error covariance matrix by weighting factors. Intercomparison of methods for a carbon monoxide inversion over a city shows that even though all methods diminish the colocalization problem and produce similar general patterns, detailed information can greatly change according to the method used ranging from smooth, isotropic and short range modifications to not so smooth, non-isotropic and long range modifications. Poisson (non-Gaussian) and Gaussian assumptions both show these patterns, but for the Poisson case the emissions are naturally restricted to be positive and changes are given by means of multiplicative correction factors, producing results closer to the true nature of emission errors. Finally, we propose and test a new two-step, two-scale, fully Bayesian approach that deals with the colocalization problem and can be implemented for any prior density distribution. [ABSTRACT FROM AUTHOR]

Abstract: Ozone is a harmful air pollutant at ground level, and its concentrations are routinely measured with monitoring networks. The network design problem aims at determining the optimal positioning of the monitoring stations. In this study, the background stations of the French routine pollution monitoring network (BDQA) are partially redistributed over France under a set of design objectives. These background stations report ozone variations at large spatial scale comparable with that of a chemistry-transport model (CTM). The design criterion needs to be defined on a regular grid that covers France, where in general no ozone observations are available for validation. Geostatistical ozone estimation methods are used to extrapolate concentrations to these grid nodes. The geostatistical criteria are introduced to minimize the theoretical error of those geostatistical extrapolations. A physical criterion is also introduced to measure the ability of a network to represent a physical ozone field retrieved from CTM simulations using geostatistical extrapolation methods. A third type of criteria of geometrical nature, e.g. a maximal coverage of the design domain, are based uniquely on the distance between the network stations. To complete the network design methodology, a stochastic optimization method, simulated annealing, is employed in the algorithm to select optimally the stations. Significant improvement with all the proposed criteria has been found for the optimally redistributed network against the original background BDQA network. For instance, the relative improvements in the physical criterion value range from 21% to 32% compared to randomly relocated networks. Different design criteria lead to different optimally relocated networks. The optimal networks under physical criteria are the most heterogeneously distributed. More background stations are displaced to the coast, frontiers, and large urban agglomerations, e.g. Paris and Marseilles. The ozone heterogeneous fields are not as well reconstructed from optimal networks under geostatistical or geometrical criteria as from the optimal network obtained with the physical criterion. The values of the physical criterion for the geostatistically and geometrically optimal networks show deteriorations of about 8% and 17% respectively compared to that of the physically optimal network. [Copyright &y& Elsevier]

Abstract: Ozone is a harmful air pollutant at ground level, and its concentrations are measured with routine monitoring networks. Due to the heterogeneous nature of ozone fields, the spatial distribution of the ozone concentration measurements is very important. Therefore, the evaluation of distributed monitoring networks is of both theoretical and practical interests. In this study, we assess the efficiency of the ozone monitoring network over France (BDQA) by investigating a network reduction problem. We examine how well a subset of the BDQA network can represent the full network. The performance of a subnetwork is taken to be the root mean square error (rmse) of the hourly ozone mean concentration estimations over the whole network given the observations from that subnetwork. Spatial interpolations are conducted for the ozone estimation taking into account the spatial correlations. Several interpolation methods, namely ordinary kriging, simple kriging, kriging about the means, and consistent kriging about the means, are compared for a reliable estimation. Exponential models are employed for the spatial correlations. It is found that the statistical information about the means improves significantly the kriging results, and that it is necessary to consider the correlation model to be hourly-varying and daily stationary. The network reduction problem is solved using a simulated annealing algorithm. Significant improvements can be obtained through these optimizations. For instance, removing optimally half the stations leads to an estimation error of the order of the standard observational error (10 μg m−3). The resulting optimal subnetworks are dense in urban agglomerations around Paris (Île-de-France) and Nice (Côte d’Azur), where high ozone concentrations and strong heterogeneity are observed. The optimal subnetworks are probably dense near frontiers because beyond these frontiers there is no observation to reduce the uncertainty of the ozone field. For large rural regions, the stations are uniformly distributed. The fractions between urban, suburban and rural stations are rather constant for optimal subnetworks of larger size (beyond 100 stations). By contrast, for smaller subnetworks, the urban stations dominate. [Copyright &y& Elsevier]

This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from. [ABSTRACT FROM AUTHOR]

Abstract: In the event of an accidental atmospheric release of radionuclides from a nuclear power plant, accurate real-time forecasting of the activity concentrations of radionuclides is acutely required by the decision makers for the preparation of adequate countermeasures. Yet, the accuracy of the forecasted plume is highly dependent on the source term estimation. Inverse modelling and data assimilation techniques should help in that respect. However the plume can locally be thin and could avoid a significant part of the radiological monitoring network surrounding the plant. Deploying mobile measuring stations following the accident could help to improve the source term estimation. In this paper, a method is proposed for the sequential reconstruction of the plume, by coupling a sequential data assimilation algorithm based on inverse modelling with an observation targeting strategy. The targeting design strategy consists in seeking the optimal locations of the mobile monitors at time t + 1 based on all available observations up to time t. The performance of the sequential assimilation with and without targeting of observations has been assessed in a realistic framework. It focuses on the Bugey nuclear power plant (France) and its surroundings within 50 km from the plant. The existing surveillance network is used and realistic observational errors are assumed. The targeting scheme leads to a better estimation of the source term as well as the activity concentrations in the domain. The mobile stations tend to be deployed along plume contours, where activity concentration gradients are important. It is shown that the information carried by the targeted observations is very significant, as compared to the information content of fixed observations. A simple test on the impact of model error from meteorology shows that the targeting strategy is still very useful in a more uncertain context. [Copyright &y& Elsevier]

Abstract: A numerically efficient methodology for the optimal design of monitoring networks aiming at the surveillance of accidental atmospheric release is proposed in this paper. In a realistic context, the design of such a network requires the knowledge of a database of potential dispersion accidents occurring in the domain of the study. An objective function measures the ability of a potential network to provide measurements in order to reconstruct any accidental plume taken from the database. In the optimisation of such cost functions with respect to networks, most of the computational time is spent in the evaluation of the function, especially if the accidents database is large. In this paper we show how to optimally reduce this database and how this affects the design via a mathematical expansion in the cost function. We introduce methods based on principal component analysis, which are rigorous when the cost function is of least-squares type. These methods are then tested and validated with success on the design of a radionuclides monitoring network to be deployed over France. This is the so-called Descartes network which will be operated by the French Institute for Radiation and Nuclear Safety. These techniques are then applied on Descartes to solve several issues that are computationally demanding, but are also of more general interest, such as: how should one sequentially deploy the stations of the network? How is affected the optimal network when other European potential radiological sources are taken into account? [Copyright &y& Elsevier]

In geophysical data assimilation, observations shed light on a control parameter space through a model, a statistical prior, and an optimal combination of these sources of information. This control space can be a set of discrete parameters, or, more often in geophysics, part of the state space, which is distributed in space and time. When the control space is continuous, it must be discretized for numerical modeling. This discretization, in this paper called a representation of this distributed parameter space, is always fixed a priori. In this paper, the representation of the control space is considered a degree of freedom on its own. The goal of the paper is to demonstrate that one could optimize it to perform data assimilation in optimal conditions. The optimal representation is then chosen over a large dictionary of adaptive grid representations involving several space and time scales. First, to motivate the importance of the representation choice, this paper discusses the impact of a change of representation on the posterior analysis of data assimilation and its connection to the reduction of uncertainty. It is stressed that in some circumstances (atmospheric chemistry, in particular) the choice of a proper representation of the control space is essential to set the data assimilation statistical framework properly. A possible mathematical framework is then proposed for multiscale data assimilation. To keep the developments simple, a measure of the reduction of uncertainty is chosen as a very simple optimality criterion. Using this criterion, a cost function is built to select the optimal representation. It is a function of the control space representation itself. A regularization of this cost function, based on a statistical mechanical analogy, guarantees the existence of a solution. This allows numerical optimization to be performed on the representation of control space. The formalism is then applied to the inverse modeling of an accidental release of an atmospheric contaminant at European scale, using real data. [ABSTRACT FROM AUTHOR]

The Institute of Radiation Protection and Nuclear Safety (France) is planning the set-up of an automatic nuclear aerosol monitoring network over the French territory. Each of the stations will be able to automatically sample the air aerosol content and provide activity concentration measurements on several radionuclides. This should help monitor the French and neighbouring countries nuclear power plants set. It would help evaluate the impact of a radiological incident occurring at one of these nuclear facilities. This paper is devoted to the spatial design of such a network. Here, any potential network is judged on its ability to extrapolate activity concentrations measured on the network stations over the whole domain. The performance of a network is quantitatively assessed through a cost function that measures the discrepancy between the extrapolation and the true concentration fields. These true fields are obtained through the computation of a database of dispersion accidents over one year of meteorology and originating from 20 French nuclear sites. A close to optimal network is then looked for using a simulated annealing optimisation. The results emphasise the importance of the cost function in the design of a network aimed at monitoring an accidental dispersion. Several choices of norm used in the cost function are studied and give way to different designs. The influence of the number of stations is discussed. A comparison with a purely geometric approach which does not involve simulations with a chemistry-transport model is performed. [Copyright &y& Elsevier]

Abstract: In this paper, we evaluate the potentialities of hafnium-aluminates (HfAlO) materials as possible candidates for the interpoly dielectrics of future Flash memory devices. HfAlO layers of different thicknesses and compositions are integrated in single-layers and in Oxide/HfAlO/Oxide (OHO) triple-layer stacks, and analyzed in terms of coupling and insulating capabilities. We demonstrate that increasing the Hf content allows reducing the leakage current at high voltages but it results in a stronger leakage current at low voltages. We also show that once normalized in electric fields, the leakage current characteristics are independent of the high-k thickness. The electron conduction modes in these materials, at different temperatures, are also investigated. The activation energy increases with the Hf concentration in the HfAlO alloy, resulting in a higher leakage current at elevated temperatures. Finally, it is demonstrated that the conduction in triple-layer stacks is limited by a Poole–Frenkel conduction in the high-k layers, while the trap contribution in the case of single-layers becomes dominant when the HfAlO layer is thicker than 8nm. [Copyright &y& Elsevier]

Abstract: This work contributes to improvement in consequences evaluation for a release of radioactivity to the atmosphere at local scale. An investigation of how such an improvement could be achieved with the help of variational data assimilation is presented. The measurements collected in a wind tunnel experiment are coupled to a Gaussian puff model. Capacity of finding the true source emission rate is tackled in the first place. Secondly, data assimilation is employed to accommodate the computed concentration profiles to the measured ones. Benefit from data assimilation is subject to the quantity of information contained in the measurements. Therefore, posterior analysis of the monitoring network is carried out and its quality assessed. [Copyright &y& Elsevier]

In this study, we investigate the fully multivariate state and parameter estimation through idealised simulations of a dynamics-only model that uses the novel Maxwell elasto-brittle (MEB) sea-ice rheology and in which we estimate not only the sea-ice concentration, thickness and velocity, but also its level of damage, internal stress and cohesion. Specifically, we estimate the air drag coefficient and the so-called damage parameter of the MEB model. Mimicking the realistic observation network with different combinations of observations, we demonstrate that various issues can potentially arise in a complex sea-ice model, especially in instances for which the external forcing dominates the model forecast error growth. Even though further investigation will be needed using an operational (a coupled dynamics–thermodynamics) sea-ice model, we show that, with the current observation network, it is possible to improve both the observed and the unobserved model state forecast and parameter accuracy. [ABSTRACT FROM AUTHOR]

This Letter deals with a self-consistent physical model for set/reset operations involved in unipolar resistive switching memories integrating a transition metal oxide. In this model, set operation is described in terms of a local electrochemical reduction of the oxide leading to the formation of metallic conductive filaments. Beside, reset operation relies on the thermally assisted destruction of the formed metallic filaments by Joule heating effect. An excellent agreement is demonstrated with numerous published experimental data suggesting that this model can be confidently implemented into circuit simulators for design purpose. [ABSTRACT FROM AUTHOR]

Large-scale fires in urban areas have highlighted the need to develop ways of assessing the risks posed by smoke plumes to people and the environment. One of the challenges is to quickly provide the authorities with information on the areas affected by the plume and the levels of pollutant concentration to which people may have been exposed. In this work, we develop an inverse modelling method to find the smoke source term of a large-scale fire by assimilating in-situ pollutant concentration measurements. A Bayesian method based on a Markov Chain Monte Carlo (MCMC) technique is considered to determine the source characteristics and their uncertainties. The source is described by a time-varying emission rate and an emission height. The latter, linked to the phenomenon of plume rise, is an important parameter for assessing the pollution impact in the vicinity of the fire. An inversion proposal that forces the system to choose a single emission height is introduced. These inverse methodologies are applied to the real case study of a major warehouse fire in Aubervilliers, near Paris, in 2021. In most cases of application, certain information, such as the pollution already present before the fire, may be difficult to estimate, particularly in an operational situation. Fine-tuning of the inverse method to make it more robust for transposition to future case studies are then discussed. • Inversion methods for estimating fire smoke height and emission rate. • Application to a real large-scale fire. • Emission height inversion proposal. [ABSTRACT FROM AUTHOR]

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. [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]

Air-pollution modelling at the local scale requires accurate meteorological inputs such as from the velocity field. These meteorological fields are generally simulated with microscale models (here Code_Saturne), which are forced with boundary conditions provided by larger scale models or observations. Local atmospheric simulations are very sensitive to the boundary conditions, whose accurate estimation is difficult but crucial. When observations of the wind speed and turbulence or pollutant concentration are available inside the domain, they provide supplementary information via data assimilation, to enhance the simulation accuracy by modifying the boundary conditions. Among the existing data assimilation methods, the iterative ensemble Kalman smoother (IEnKS) is adapted to urban-scale simulations. This method has already been found to increase the accuracy of wind-resource assessment. Here we assess the ability of the IEnKS method to improve scalar-dispersion modelling—an important component of air-quality modelling—by assimilating perturbed measurements inside the urban canopy. To test the data assimilation method in urban conditions, we use the observations provided by the Mock Urban Setting Test field campaign and consider cases with neutral and stable conditions, and the boundary conditions consisting of the horizontal velocity components and turbulence. We prove the capacity of the IEnKS method to assimilate observations of velocity as well as pollutant concentration. In both cases, the accuracy of pollutant concentration estimates is enhanced by 40–60%. We also show that assimilating both types of observations allows further improvements of turbulence predictions by the model. [ABSTRACT FROM AUTHOR]

The ensemble Kalman filter (EnKF) has been successfully applied to a wide range ofgeophysical systems. However, when the ensemble size is small, ensemble estimates areunreliable, which is why localisation has been introduced. In the EnKF, two types oflocalisation methods have emerged: domain localisation and covariance localisation. Domainlocalisation is simple to implement and yields parallelisable algorithms. On the other hand,EnKF algorithms using covariance localisation rely on a single global analysis with alocalised background covariance. Their implementation is in general more complex,especially in a deterministic context. At the same time, the ability to assimilatenon-local observations becomes increasingly important with the prominence ofsatellite observations. With domain localisation, non-local observations cannotbe assimilated without ad hoc approximations, which limits the accuracy of theanalysis. In this presentation, we discuss the implementation of covariance localisationin the deterministic EnKF using augmented ensemble during the analysis step,that is when the ensemble size during the analysis step is larger than during theforecast step. The focus is on two crucial points: the accurate representation ofa localised background covariance and the perturbation update. We identify andpresent two methods. The first is based on a factorisation property and alreadyknown in the literature under the term modulation. The second relies on randomisedsingular value decomposition and has not been applied in this context. The qualitativeproperties of both methods are illustrated using a simple one-dimensional covariancemodel. For both method, we then derive an ensemble square root Kalman filter withcovariance localisation (LEnSRF). We compare the performance of the resultingalgorithms using twin simulations of the Lorenz 1996 (L96) model. Finally, weintroduce a realistic extension of the LEnSRF that uses domain localisation in thehorizontal and covariance localisation in the vertical. Using twin simulations of amultilayer extension of the L96 model, we show that this approach is adequate toassimilate satellite radiances, for which domain localisation alone is insufficient. [ABSTRACT FROM AUTHOR]

In case of an accidental radioactive release, the Institute for Radiological Protection and Nuclear Safety (IRSN) uses atmospheric dispersion models to assess radiological consequences for human health and environment. The accuracy of the models results is highly dependent on the meteorological fields and the source term, including the location, the duration, the magnitude and the isotopic composition of the release. Inverse modeling methods have proven to be efficient in assessing source term. The authors have developed an inverse method based on a variational approach and applied it to the Fukushima accident using dose rate measurements and air concentration measurements. The method has been extended to deal with minor detection events where the source location is usually unknown.Variational methods are suitable in operational use since they are able of quickly providing an optimal solution. However, unlike Bayesian methods, the quantification of the uncertainties of the source term assessed is usually not easily accessible. Indeed, Bayesian inverse methods are developed in order to efficiently sample the distributions of the parameters of the source, thus allowing to get a complete characterization of the source. In September 2017, small amounts of 106Ru have been observed in Europe without knowledge on the origin of the release. Although concentrations levels were too low to pose any health and environmental issues, the widespread detection suggested that the source term must have been quite high. Monte Carlo Markov Chains (MCMC) have been applied to reconstruct the 106Ru source using Metropolis Hastings (MH) algorithms based on the Bayesian inference. The distributions of the parameters associated to the source and the observations errors are presented. Convergence analysis of the MCMC methods have been studied and point out that chains with small number of parameters are drawing distributions consistent with the results obtained using variational methods. Moreover, the computational time required by the method is suitable for operational use. Nevertheless, chains of large number of parameters are providing problems of convergence. In particularly, chains can stuck in local minima during the localization of the source, notably because of the unequal distribution of the observations over the continent. To overcome this difficulty, other Bayesian methods are proposed to accelerate the convergence of the MCMC algorithm. [ABSTRACT FROM AUTHOR]

Is it possible to emulate a numerical model from noisy and sparse observations? How realisticand skillful can it be? A popular way to produce data-driven models from a set of observations is to applymachine-learning methods. These approaches proved efficient for chaotic systemsusing various machine learning algorithms such as, for instance, deep-learningor reservoir computing. In most of previous works, these approaches were usedwith a noisy-free, completely observed, state vector, and their performance wasevaluated on short-term predictability skills. When it comes to noisy and sparseobservations, data assimilation techniques provide the natural tools to produce an optimalestimation of the state of a system, provided a numerical model, is available (thoughimperfect). In this work, we consider the case in which noisy and partial observations of a givenphenomena are available but the evolution model is unknown. The idea is to applymachine-learning and data assimilation algorithms alternatively to learn the underlyingdynamics of the system. First, the data assimilation procedure completes the state estimate,which is then used as a training set for machine learning. Reciprocally, the machinelearning-based model is used as the forward dynamical model in the data assimilationframework. The sequence is reiterated with increasing complexity of the machine learningmodel. This combined approach is tested numerically in a twin experiments setup with chaoticmodels. The machine learning algorithm used in this work is a convolutional neural networkarchitecture (CNN) whereas the data assimilation scheme is an ensemble Kalman filter (usingthe finite-size variant to avoid the inflation: EnKF-N). The resulting CNN showed bothforecast skills and abilities to reproduce the "climate" (i.e. spectral properties and statisticalmoments) of the underlying dynamical model on long-term simulations. Perspectives towardslarge-scale systems will be discussed on the basis of the benchmarks presented. [ABSTRACT FROM AUTHOR]

Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from its output, resorting in particular to neural networks and deep learning techniques. We will show how the same goal can be directly achieved using data assimilation techniques without leveraging on machine learning software libraries, with a view to high-dimensional models. The dynamics of a model are learned from its observation and an ordinary differential equation (ODE) representation of this model is inferred using a recursive nonlinear regression. Because the method is embedded in a Bayesian data assimilation framework, it can learn from partial and noisy observations of a state trajectory of the physical model. Moreover, a space-wise local representation of the ODE system is introduced and is key to deal with high-dimensional models. The method is illustrated on several chaotic discrete and continuous models of various dimensions, with or without noisy observations, with the goal to identify or improve the model dynamics, build a surrogate or reduced model, or produce forecasts from mere observations of the physical model.It has recently been suggested that neural network architectures could be interpreted as dynamical systems. Reciprocally, we show that our ODE representations are reminiscent of deep learning architectures. Furthermore, numerical analysis considerations on stability shed light on the assets and limitations of the method. [ABSTRACT FROM AUTHOR]

In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages highresolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrization model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrization is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases, the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model. [ABSTRACT FROM AUTHOR]

Data assimilation combines forecasts from a numerical model with observations. Most of the current data assimilation algorithms consider the model and observation error terms as additive Gaussian noise, specified by their covariance matrices Q and R, respectively. These error covariances, and specifically their respective amplitudes, determine the weights given to the background (i.e., the model forecasts) and to the observations in the solution of data assimilation algorithms (i.e., the analysis). Consequently, Q and R matrices significantly impact the accuracy of the analysis. This review aims to present and to discuss, with a unified framework, different methods to jointly estimate the Q and R matrices using ensemble-based data assimilation techniques. Most of the methods developed to date use the innovations, defined as differences between the observations and the projection of the forecasts onto the observation space. These methods are based on two main statistical criteria: 1) the method of moments, in which the theoretical and empirical moments of the innovations are assumed to be equal, and 2) methods that use the likelihood of the observations, themselves contained in the innovations. The reviewed methods assume that innovations are Gaussian random variables, although extension to other distributions is possible for likelihood-based methods. The methods also show some differences in terms of levels of complexity and applicability to high-dimensional systems. The conclusion of the review discusses the key challenges to further develop estimation methods for Q and R. These challenges include taking into account time-varying error covariances, using limited observational coverage, estimating additional deterministic error terms, or accounting for correlated noise. [ABSTRACT FROM AUTHOR]

A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating a hidden, possibly chaotic, dynamics and (ii) predicting its future states. The method applies alternatively a data assimilation step, here an ensemble Kalman filter, and a neural network. Data assimilation is used to combine optimally a surrogate model with sparse noisy data. The resulting analysis is spatially complete and can thus be used as a training set by the neural network to upgrade the surrogate model. The two steps are then repeated iteratively. Numerical experiments have been carried out using the chaotic Lorenz 96, a 40-variables model, proving both convergence and statistical skills. The skill metrics include the short-term forecast skills out to two Lyapunov times, the retrieval of positive Lyapunov exponents and the power density spectrum. The sensitivity of the method to critical setup parameters is also presented: forecast skills decrease smoothly with increased observational noise but drops abruptly if less then half of the model domain is observed. The synergy demonstrated with a low-dimensional system is encouraging for more sophisticated dynamics and motivates further investigation to merge data assimilation and machine learning. [ABSTRACT FROM AUTHOR]

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the best possible stochastic parameterization from noisy data. State-of-the-art sequential estimation methods such as Kalman and particle filters do not achieve this goal successfully because both suffer from the collapse of the posterior distribution of the parameters. To overcome this intrinsic limitation, we propose two statistical learning methods. They are based on the combination of the ensemble Kalman filter (EnKF) with either the expectation-maximization (EM) or the Newton-Raphson (NR) used to maximize a likelihood associated to the parameters to be estimated. The EM and NR are applied primarily in the statistics and machine learning communities and are brought here in the context of data assimilation for the geosciences. The methods are derived using a Bayesian approach for a hidden Markov model and they are applied to infer deterministic and stochastic physical parameters from noisy observations in coarse-grained dynamical models. Numerical experiments are conducted using the Lorenz-96 dynamical system with one and two scales as a proof of concept. The imperfect coarse-grained model is modelled through a one-scale Lorenz-96 system in which a stochastic parameterization is incorporated to represent the small-scale dynamics. The algorithms are able to identify the optimal stochastic parameterization with good accuracy under moderate observational noise. The proposed EnKF-EM and EnKF-NR are promising efficient statistical learning methods for developing stochastic parameterizations in high-dimensional geophysical models. [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]

We introduce a proof of concept to parametrise the unresolved subgrid scale of sea-ice dynamics with deep learning techniques. Instead of parametrising single processes, a single neural network is trained to correct all model variables at the same time. This data-driven approach is applied to a regional sea-ice model that accounts exclusively for dynamical processes with a Maxwell elasto-brittle rheology. Driven by an external wind forcing in a 40km×200km domain, the model generates examples of sharp transitions between unfractured and fully fractured sea ice. To correct such examples, we propose a convolutional U-Net architecture which extracts features at multiple scales. We test this approach in twin experiments: the neural network learns to correct forecasts from low-resolution simulations towards high-resolution simulations for a lead time of about 10 min. At this lead time, our approach reduces the forecast errors by more than 75% , averaged over all model variables. As the most important predictors, we identify the dynamics of the model variables. Furthermore, the neural network extracts localised and directional-dependent features, which point towards the shortcomings of the low-resolution simulations. Applied to correct the forecasts every 10 min, the neural network is run together with the sea-ice model. This improves the short-term forecasts up to an hour. These results consequently show that neural networks can correct model errors from the subgrid scale for sea-ice dynamics. We therefore see this study as an important first step towards hybrid modelling to forecast sea-ice dynamics on an hourly to daily timescale. [ABSTRACT FROM AUTHOR]

The iterative ensemble Kalman filter (IEnKF) in a deterministic framework was introduced in Sakov et al. [Mon. Wea. Rev. 140: 1988–2004 ( )] to extend the ensemble Kalman filter (EnKF) and improve its performance in mildly up to strongly nonlinear cases. However, the IEnKF assumes that the model is perfect. This assumption simplified the update of the system at a time different from the observation time, which made it natural to apply the IEnKF for smoothing. In this study, we generalize the IEnKF to the case of an imperfect model with additive model error. The new method called IEnKF‐Q conducts a Gauss–Newton minimization in ensemble space. It combines the propagated analysed ensemble anomalies from the previous cycle and model noise ensemble anomalies into a single ensemble of anomalies, and by doing so takes an algebraic form similar to that of the IEnKF. The performance of the IEnKF‐Q is tested in a number of experiments with the Lorenz'96 model, which show that the method consistently outperforms both the EnKF and the IEnKF naively modified to accommodate additive model noise. [ABSTRACT FROM AUTHOR]

In the next few years, numerous satellites with high-resolution instruments dedicated to the imaging of atmospheric gaseous compounds will be launched, to finely monitor emissions of greenhouse gases and pollutants. Processing the resulting images of plumes from cities and industrial plants to infer the emissions of these sources can be challenging. In particular traditional atmospheric inversion techniques, relying on objective comparisons to simulations with atmospheric chemistry transport models, may poorly fit the observed plume due to modelling errors rather than due to uncertainties in the emissions. The present article discusses how these images can be adequately compared to simulated concentrations to limit the weight of modelling errors due to the meteorology used to analyse the images. For such comparisons, the usual pixel-wise L2 norm may not be suitable, since it does not linearly penalise a displacement between two identical plumes. By definition, such a metric considers a displacement as an accumulation of significant local amplitude discrepancies. This is the so-called double penalty issue. To avoid this issue, we propose three solutions: (i) compensate for position error, due to a displacement, before the local comparison; (ii) use non-local metrics of density distribution comparison; and (iii) use a combination of the first two solutions. All the metrics are evaluated using first a catalogue of analytical plumes and then more realistic plumes simulated with a mesoscale Eulerian atmospheric transport model, with an emphasis on the sensitivity of the metrics to position error and the concentration values within the plumes. As expected, the metrics with the upstream correction are found to be less sensitive to position error in both analytical and realistic conditions. Furthermore, in realistic cases, we evaluate the weight of changes in the norm and the direction of the four-dimensional wind fields in our metric values. This comparison highlights the link between differences in the synoptic-scale winds direction and position error. Hence the contribution of the latter to our new metrics is reduced, thus limiting misinterpretation. Furthermore, the new metrics also avoid the double penalty issue. [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]