A Wave Data Assimilation System based on the Ensemble Kalman Filter (EnKF) is implemented for the North Sea showing improved performance and physical consistency. We first show the EnKF implementation and illustrate the wave data assimilation system using identical twin experiments to assimilate synthetic observations from buoys. A sensitivity analysis shows that the ensemble size, assimilation frequency and observation uncertainty are relatively important settings. Lastly, the potential for assimilating satellite measurements was assessed by assimilating synthetic altimeter measurements with real pass-over tracks. In these experiments, the state contains the full wave spectrum, unlike in most existing schemes. The results show that wave spectra and integral variables beyond significant wave height show physically consistent updates for the buoy and satellite experiments, by assimilating only significant wave height. This is a key advantage of this implementation compared to the more widely used implementations in wave data assimilation. Although the satellite experiment performs slightly worse than the buoy experiment due to decreased temporal availability of measurements, the results underline the potential for assimilation of satellite altimeter measurements. Such a system provides a promising framework for future observation impact study using satellite altimeter measurements.

The present study proposes a novel data assimilation (DA) approach for estimating emission and wind direction parameters in an advection-diffusion model. This implementation aims to improve the prediction of a chemical transport model over long distances by updating the emission operator in the model using DA techniques. As a first step, we want to test the method in a small-scale scenario. A low-dimensional advection-diffusion model was utilized to evaluate the effectiveness of the proposed approach under various sampling observation numbers. The model’s emission and wind parameters are perturbed as a source of uncertainty. The parameters are sequentially estimated with the adjoint-free Ensemble Kalman filter with an augmented state vector. These sequential DA techniques exploit the ensemble of multiple model realizations to reduce uncertainty in the state and parameter representation. An associated stream function with a divergence-free condition controls the wind fields, and the estimation of this stream function through the assimilation process allows corrections of the wind fields without violating physical laws. The technique’s performance was compared against validation observations such as the Root-Mean Square (RMS), and it was found that the number of assimilated observations had a significant impact on the parameter estimations results. This study demonstrates the potential of the proposed DA approach for improving the prediction of transport in the advection-diffusion model through parameter estimation.

This paper presents a hybrid model to estimate the magnetic behaviour of a ferromagnetic structure. The mathematical-physical model has been developed using the Method of Moments combined with a hysteresis model. The mathematical model was derived by a linearisation of the hysteresis curve. The initial magnetic state of a ferromagnetic object is found through inverse computations, including regularisation techniques. The idea of dictionary regularisation is introduced to support the inverse computations with prescribed templates that reflect a priori knowledge of the typical shapes of magnetisation distributions. These templates are extracted from the Method of Moments. Data assimilation is used to update the model in time by means of measurements of the magnetic field near a ferromagnetic structure. The proposed hybrid model is implemented for a typical steel object and verified by means of numerical experiments and measurements in an experimental environment.

Accurately forecasting ozone levels that exceed specific thresholds is pivotal for mitigating adverse effects on both the environment and public health. However, predicting such ozone exceedances remains challenging due to the infrequent occurrence of high-concentration ozone data. This research, leveraging data from 57 German monitoring stations from 1999 to 2018, introduces an Enhanced Extreme Instance Augmentation Random Forest (EEIA-RF) approach that significantly improves the prediction of days when the maximum daily 8-hour average ozone concentrations exceed 120μg/m³. A pre-trained machine learning model is used to generate additional high-concentration data, which, combined with selectively reduced low-concentration data, forms a new dataset for training a refined model. This method achieved an improvement of at least 8% in the accuracy of predicting days with ozone exceedances across Germany. Our experiment underscores the approach's value in enhancing atmospheric modeling and supporting public health advisories and environmental policy-making related to ozone pollution.

History matching can play a key role in improving geological characterization and reducing the uncertainty of reservoir model predictions. Application of reservoir history matching is restricted by the huge computational cost by amongst others the many runs of the full model. Surrogate models with a reduced complexity are therefore used to reduce the computational demands. This paper presents an efficient surrogate-assisted deterministic inversion framework to primarily explore the possibility of applying deep neural network (DNN) surrogate to approximate the gradient of large-scale history matching by using auto-differentiation (AD). In combination with the deep neural network model, the AD enables us to evaluate the gradients efficiently in a parallel manner. Furthermore, the benefits of using stochastic gradient optimizers in the deep learning practice, instead of full gradient optimizers in conventional deterministic inversions, is investigated as well. Numerical experiments are conducted on a 3D benchmark reservoir model in the context of a water-flooding production scenario. The quantity of interest, e.g., dynamic saturation for an ensemble of test models, can be accurately predicted. The proposed surrogate-assisted inversion with stochastic gradient optimizer obtains a very quick convergence rate against the model and data noise for the high-dimensional history matching problem with a large number of data and parameters. In addition, we also conduct several comparisons and evaluations with our previously proposed projection-based subdomain POD-TPWL approach in terms of computational efficiency and accuracy. The subdomain POD-TPWL constructs a local surrogate model, which is repeatedly reconstructed a number of times for maintaining a satisfactory accuracy, while DNN constructs a global surrogate model based on the entire training data and generally does not require additional reconstructions. The subdomain POD-TPWL is very sensitive to how the domain is decomposed, increasing the training samples does not infinitely improve the history matching results by a fixed decomposition. Overall, these two kinds of surrogate models have demonstrated great potential in solving large-scale history matching problem. The DNN surrogate is particularly useful to generate multiple posteriors for model uncertainty quantification.

Imaging-type monitoring techniques are used in monitoring dynamic processes in many domains, including medicine, engineering, and geophysics. This paper aims to propose an efficient workflow for application of such data for the conditioning of simulation models. Such applications are very common in e.g. the geosciences, where large-scale simulation models and measured data are used to monitor the state of e.g. energy and water systems, predict their future behavior and optimize actions to achieve desired behavior of the system. In order to reduce the high computational cost and complexity of data assimilation workflows for high-dimensional parameter estimation, a residual-in-residual dense block extension of the U-Net convolutional network architecture is proposed, to predict time-evolving features in high-dimensional grids. The network is trained using high-fidelity model simulations. We present two examples of application of the trained network as a surrogate within an iterative ensemble-based workflow to estimate the static parameters of geological reservoirs based on binary-type image data, which represent fluid facies as obtained from time-lapse seismic surveys. The differences between binary images are parameterized in terms of distances between the fluid-facies boundaries, or fronts. We discuss the impact of the choice of network architecture, loss function, and number of training samples on the accuracy of results and on overall computational cost. From comparisons with conventional workflows based entirely on high-fidelity simulation models, we conclude that the proposed surrogate-supported hybrid workflow is able to deliver results with an accuracy equal to or better than the conventional workflow, and at significantly lower cost. Cost reductions are shown to increase with the number of samples of the uncertain parameter fields. The hybrid workflow is generic and should be applicable in addressing inverse problems in many geophysical applications as well as other engineering domains.

In this paper, we propose an efficient and practical implementation of the ensemble Kalman filter via shrinkage covariance matrix estimation. Our filter implementation combines information brought by an ensemble of model realizations, and that based on our prior knowledge about the dynamical system of interest. We perform the combination of both sources of information via optimal shrinkage factors. The method exploits the rank-deficiency of ensemble covariance matrices to provide an efficient and practical implementation of the analysis step in EnKF based formulations. Localization and inflation aspects are discussed, as well. Experimental tests are performed to assess the accuracy of our proposed filter implementation by employing an Advection Diffusion Model and an Atmospheric General Circulation Model. The experimental results reveal that the use of our proposed filter implementation can mitigate the impact of sampling noise, and even more, it can avoid the impact of spurious correlations during assimilation steps.

The use of low air quality networks has been increasing in recent years to study urban pollution dynamics. Here we show the evaluation of the operational Aburrá Valley’s low-cost network against the official monitoring network. The results show that the PM_2.5 low-cost measurements are very close to those observed by the official network. Additionally, the low-cost allows a higher spatial representation of the concentrations across the valley. We integrate low-cost observations with the chemical transport model Long Term Ozone Simulation-European Operational Smog (LOTOS-EUROS) using data assimilation. Two different configurations of the low-cost network were assimilated: using the whole low-cost network (255 sensors), and a high-quality selection using just the sensors with a correlation factor greater than 0.8 with respect to the official network (115 sensors). The official stations were also assimilated to compare the more dense low-cost network’s impact on the model performance. Both simulations assimilating the low-cost model outperform the model without assimilation and assimilating the official network. The capability to issue warnings for pollution events is also improved by assimilating the low-cost network with respect to the other simulations. Finally, the simulation using the high-quality configuration has lower error values than using the complete low-cost network, showing that it is essential to consider the quality and location and not just the total number of sensors. Our results suggest that with the current advance in low-cost sensors, it is possible to improve model performance with low-cost network data assimilation.

A reduced order modeling algorithm for the estimation of space varying parameter patterns in numerical models is proposed. In this approach domain decomposition is applied to construct separate approximations to the numerical model in every subdomain. We introduce a new local parameterization that decouples the computational cost of the algorithm from the number of global principal components and therefore provides attractive scaling for models with a very large number of uncertain parameter patterns. By defining uncertain parameter patterns only in the various subdomains the number of full order simulation required for the derivation of the reduced order models can be reduced drastically. To avoid non-smoothness at the boundaries of the subdomains, the optimal local parameters patterns are projected onto global parameter patterns. The computational effort of the new methodology hardly increases when the number of parameter patterns increases. The number of training models depends primarily on the maximum number of local parameters in a subdomain, which can be decreased by refining the domain decomposition. We apply the new algorithm to a large-scale reservoir model parameter estimation problem. In this application 282 parameters could be estimated using only 90 full order model runs.

Emission inversion using data assimilation fundamentally relies on having the correct assumptions about the emission background error covariance. A perfect covariance accounts for the uncertainty based on prior knowledge and is able to explain differences between model simulations and observations. In practice, emission uncertainties are constructed empirically; hence, a partially unrepresentative covariance is unavoidable. Concerning its complex parameterization, dust emissions are a typical example where the uncertainty could be induced from many underlying inputs, e.g., information on soil composition and moisture, land cover and erosive wind velocity, and these can hardly be taken into account together. This paper describes how an adjoint model can be used to detect errors in the emission uncertainty assumptions. This adjoint-based sensitivity method could serve as a supplement of a data assimilation inverse modeling system to trace back the error sources in case large observation-minus-simulation residues remain after assimilation based on empirical background covariance.

The method follows an application of a data assimilation emission inversion for an extreme severe dust storm over East Asia <span classCombining double low line"cit"idCombining double low line"xref_paren.1">(<a hrefCombining double low line"#bib1.bibx31">Jin et al.</a>, <a hrefCombining double low line"#bib1.bibx31">2019</a><a hrefCombining double low line"#bib1.bibx31">b</a>)</span>. The assimilation system successfully resolved observation-minus-simulation errors using satellite AOD observations in most of the dust-affected regions. However, a large underestimation of dust in Northeast China remained despite the fact that the assimilated measurements indicated severe dust plumes there. An adjoint implementation of our dust simulation model is then used to detect the most likely source region for these unresolved dust loads. The backward modeling points to the Horqin desert as the source region, which was indicated as a non-source region by the existing emission scheme. The reference emission and uncertainty are then reconstructed over the Horqin desert by assuming higher surface erodibility. After the emission reconstruction, the emission inversion is performed again, and the posterior dust simulations and reality are now in much closer harmony. Based on our results, it is advised that emission sources in dust transport models include the Horqin desert as a more active source region.

A data assimilation system for the LOTOS-EUROS chemical transport model has been implemented to improve the simulation and forecast of PM₁₀ and PM_2.5 in a densely populated urban valley of the tropical Andes. The Aburrá Valley in Colombia was used as a case study, given data availability and current environmental issues related to population expansion. The data assimilation system is an Ensemble Kalman filter with covariance localization based on specification of uncertainties in the emissions. Observations assimilated were obtained from a surface network for the period March–April of 2016, a period of one of the worst air quality crisis in recent history of the region. In a first series of experiments, the spatial length scale of the covariance localization and the temporal length scale of the stochastic model for the emission uncertainty were calibrated to optimize the assimilation system. The calibrated system was then used in a series of assimilation experiments, where simulation of particulate matter concentrations was strongly improved during the assimilation period, which also improved the ability to accurately forecast PM₁₀ and PM_2.5 concentrations over a period of several days.