Ensemble-based Data Assimilation Methods Research Articles

Projection of 4D seismic onto the ensemble observation subspace for data assimilation

Time-lapse (4D) seismic data offer valuable insights into fluid movements and pressure changes within reservoirs, thus aiding the updating of numerical models used in hydrocarbon recovery and geological CO2 storage. However, it is essential to characterize both the uncertainties in the data and the limitations in the forward model to effectively utilize this information. In the context of ensemble-based data assimilation methods, this objective is accomplished through the utilization of the data-error covariance matrix, denoted as Ce. The selection of an appropriate Ce is of paramount importance, as it determines the level of accuracy required to match the data and influences the relative weight assigned to various data sources and prior information during the computation of model updates.Despite significant efforts, the practical estimation of Ce, accounting for both data and model errors, remains a challenging task. This paper presents a novel methodology for estimating Ce within an ensemble-based 4D seismic data assimilation framework. The approach involves projecting observed seismic data onto the subspace defined by predicted data from the prior ensemble and estimating Ce based on the residuals—the difference between observed and projected 4D seismic data. The proposed methodology is tested through application with actual data from three real-world reservoir cases.

Assimilating AMSU-A Radiance Observations with an Ensemble Four-Dimensional Variational (En4DVar) Hybrid Data Assimilation System

Many ensemble-based data assimilation (DA) methods use observation space localization to mitigate the sampling errors due to the insufficient ensemble members. Observation space localization is simpler and more timesaving than model space localization in implementation, but more difficult to directly assimilate satellite radiance observations, a kind of non-local observations. The vertical locations of radiance observations are undetermined and the transmission of observational information is thereby obstructed. To determine the vertical coordinates of radiance observations, a weighted average hypsometry is proposed. Using this hypsometry, AMSU-A radiance observations are directly assimilated with an ensemble four-dimensional variational (En4DVar) DA system. It consists of a four-dimensional ensemble-variational (4DEnVar) system providing ensemble covariance and a 4DVar system. Observing system simulation experiments show that the hypsometry alleviates the degradations in the late period of medium-range forecast in the Northern Extratropics that occur in the traditional peak-based hypsometry. It obviously improves the analysis qualities and forecast skills of the En4DVar system and its two components, especially in the Southern Extratropics, when incorporating AMSU-A radiance observations. The improvement in the En4DVar-initialized forecast is comparable to that in the 4DVar-initialized forecast in the Southern Extratropics and Tropics. It indicates that a proper hypsometry enables efficient extraction of useful information from AMSU-A radiance observations by 4DEnVar with observation space localization. Therefore, the 4DEnVar provides high-quality ensemble covariances for En4DVar.

Benefit of vertical localization for sea surface temperature assimilation in isopycnal coordinate model

Sea surface temperature (SST) observations are a critical data set for long-term climate reconstruction. However, their assimilation with an ensemble-based data assimilation method can degrade performance in the ocean interior due to spurious covariances. Assimilation in isopycnal coordinates can delay the degradation, but it remains problematic for long reanalysis. We introduce vertical localization for SST assimilation in the isopycnal coordinate. The tapering functions are formulated empirically from a large pre-industrial ensemble. We propose three schemes: 1) a step function with a small localization radius that updates layers from the surface down to the first layer for which insignificant correlation with SST is found, 2) a step function with a large localization radius that updates layers down to the last layer for which significant correlation with SST is found, and 3) a flattop smooth tapering function. These tapering functions vary spatially and with the calendar month and are applied to isopycnal temperature and salinity. The impact of vertical localization on reanalysis performance is tested in identical twin experiments within the Norwegian Climate Prediction Model (NorCPM) with SST assimilation over the period 1980–2010. The SST assimilation without vertical localization greatly enhances performance in the whole water column but introduces a weak degradation at intermediate depths (e.g., 2,000–4,000 m). Vertical localization greatly reduces the degradation and improves the overall accuracy of the reanalysis, in particular in the North Pacific and the North Atlantic. A weak degradation remains in some regions below 2,000 m in the Southern Ocean. Among the three schemes, scheme 2) outperforms schemes 1) and 3) for temperature and salinity.

Maintaining the long-term accuracy of water distribution models with data assimilation methods: A comparative study

The upgrading of water supply services is calling for more accurate and adaptive numerical models to give insight into actual water distribution systems (WDSs), which underlines the importance of carefully calibrating model parameters. Due to unavoidable uncertainties in the calibration process such as measurement errors, errors in model parameters assumed to be known, and local-optimum of calibration algorithms, calibrated parameters could still contain non-negligible latent errors, and the calibrated model may not able to maintain its long-term accuracy when operating conditions change. To solve this problem, there is growing interest in adopting data assimilation (DA) methods to utilize more comprehensive information in long-term measurements to reduce the impact of uncertainties and maintain the accuracy and stability of calibrated models. In this study, two traditional calibration methods and four DA methods were tested and compared in two WDSs with different structures, which aims to form a general understanding of the behavior and applicability of different methods. The calibration results show that DA methods perform better than traditional methods and are more robust to different types of uncertainties, which provide an effective way to maintain the long-term accuracy of WDS models to enable better management of WDSs. Ensemble-based DA methods such as Particle Filter (PF) and Inferential-Measurement Kalman Filter (IMKF) performed well in the real-life system. They avoid linear approximation and can better estimate the impact of uncertainties to assimilate accurate correction information of the parameters. Gradient-based DA methods such as Extended Kalman Filter (EKF) and Variational Bayesian Adaptive Kalman Filter (VBAKF) have lower computational demand, but they are found to be less robust when dealing with large system uncertainties and nonlinearities.

An elastic framework for ensemble-based large-scale data assimilation

Prediction of chaotic systems relies on a floating fusion of sensor data (observations) with a numerical model to decide on a good system trajectory and to compensate non-linear feedback effects. Ensemble-based data assimilation (DA) is a major method for this concern depending on propagating an ensemble of perturbed model realizations. In this paper, we develop an elastic, online, fault-tolerant and modular framework called Melissa-DA for large-scale ensemble-based DA. Melissa-DAallows elastic addition or removal of compute resources for state propagation at runtime. Dynamic load balancing based on list scheduling ensures efficient execution. Online processing of the data produced by ensemble members enables to avoid the I/O bottleneck of file-based approaches. Our implementation embeds the PDAF parallel DA engine, enabling the use of various DA methods. Melissa-DAcan support extra ensemble-based DA methods by implementing the transformation of member background states into analysis states. Experiments confirm the excellent scalability of Melissa-DA, propagating 16,384 members for a regional hydrological critical zone assimilation relying on the ParFlow model on a domain with about 4 M grid cells. The same use case was ported to the PDAF state-of-the-art DA framework relying on a MPI approach. A comparison with Melissa-DA at 2500 members on 20,000 cores shows our approach is about 50% faster per assimilation cycle.

Parameter Estimation Using Adaptive Observations Toward Maximum Total Variance Reduction With Ensemble Adjustment Kalman Filter

In real applications, one common issue of parameter estimation using ensemble-based data assimilation methods is the accumulation of sampling errors when a large number of observations are used to update single-value parameters. In this article, a new parameter estimation method which assimilates a large number of observations to estimate the states while assimilates adaptive observations to update the parameters is introduced. The observations resulting in maximum total variance reduction to the parameter ensembles are identified to perform parameter estimation. To validate this new method, the two-scale Lorenz-96 model is used to generate true states, while a parameterized one-scale Lorenz-96 model is used to perform state and parameter estimation experiments. The comparison between state estimation and parameter estimation with fixed or adaptive observations shows the new method can be more effective in estimating the model parameters and providing more accurate analyses. This method also shows its potential to be used in the data assimilation with large general circulation models to better produce reanalyzes.

Multi-source information fused generative adversarial network model and data assimilation based history matching for reservoir with complex geologies

For reservoirs with complex non-Gaussian geological characteristics, such as carbonate reservoirs or reservoirs with sedimentary facies distribution, it is difficult to implement history matching directly, especially for the ensemble-based data assimilation methods. In this paper, we propose a multi-source information fused generative adversarial network (MSIGAN) model, which is used for parameterization of the complex geologies. In MSIGAN, various information such as facies distribution, microseismic, and inter-well connectivity, can be integrated to learn the geological features. And two major generative models in deep learning, variational autoencoder (VAE) and generative adversarial network (GAN) are combined in our model. Then the proposed MSIGAN model is integrated into the ensemble smoother with multiple data assimilation (ESMDA) method to conduct history matching. We tested the proposed method on two reservoir models with fluvial facies. The experimental results show that the proposed MSIGAN model can effectively learn the complex geological features, which can promote the accuracy of history matching.

Data assimilation of volcanic aerosol observations using FALL3D+PDAF

Abstract. Modelling atmospheric dispersal of volcanic ash and aerosols is becoming increasingly valuable for assessing the potential impacts of explosive volcanic eruptions on buildings, air quality, and aviation. Management of volcanic risk and reduction of aviation impacts can strongly benefit from quantitative forecasting of volcanic ash. However, an accurate prediction of volcanic aerosol concentrations using numerical modelling relies on proper estimations of multiple model parameters which are prone to errors. Uncertainties in key parameters such as eruption column height and physical properties of particles or meteorological fields represent a major source of error affecting the forecast quality. The availability of near-real-time geostationary satellite observations with high spatial and temporal resolutions provides the opportunity to improve forecasts in an operational context by incorporating observations into numerical models. Specifically, ensemble-based filters aim at converting a prior ensemble of system states into an analysis ensemble by assimilating a set of noisy observations. Previous studies dealing with volcanic ash transport have demonstrated that a significant improvement of forecast skill can be achieved by this approach. In this work, we present a new implementation of an ensemble-based data assimilation (DA) method coupling the FALL3D dispersal model and the Parallel Data Assimilation Framework (PDAF). The FALL3D+PDAF system runs in parallel, supports online-coupled DA, and can be efficiently integrated into operational workflows by exploiting high-performance computing (HPC) resources. Two numerical experiments are considered: (i) a twin experiment using an incomplete dataset of synthetic observations of volcanic ash and (ii) an experiment based on the 2019 Raikoke eruption using real observations of SO2 mass loading. An ensemble-based Kalman filtering technique based on the local ensemble transform Kalman filter (LETKF) is used to assimilate satellite-retrieved data of column mass loading. We show that this procedure may lead to nonphysical solutions and, consequently, conclude that LETKF is not the best approach for the assimilation of volcanic aerosols. However, we find that a truncated state constructed from the LETKF solution approaches the real solution after a few assimilation cycles, yielding a dramatic improvement of forecast quality when compared to simulations without assimilation.

Length Scale Analyses of Background Error Covariances for EnKF and EnSRF Data Assimilation

Data assimilation (DA) combines incomplete background values obtained via chemical transport model predictions with observational information. Several 3-Dimensional variational (3DVAR) and sequential methods (e.g., ensemble Kalman filter (EnKF)) are used to define model errors and build a background error covariance (BEC) and are important factors affecting the prediction performance of DA. The BEC determines the spatial range, where observation concentration is reflected in the model when DA is applied to an air pollution transport model. However, studies investigating the characteristics of BEC using air quality models remain lacking. In this study, horizontal length scale (HLS) and vertical length scale (VLS) analyses of a BEC were applied to EnKF and ensemble square root filter (EnSRF), respectively, and two ensemble-based DA methods were performed; the characteristics were compared with those of a BEC applied to 3DVAR. The results of 6 h PM2.5 predictions performed for 42 days were evaluated for a control run without DA (CTR), 3DVAR, EnKF, and EnSRF. HLS and VLS respectively exhibited a high correlation with the ground wind speed and with the planetary boundary layer height for diurnal and daily variations; EnKF and EnSRF exhibited superior performances among all the methods. The root mean square errors were 11.9 μg m−3 and 11.7 μg m−3 for EnKF and EnSRF, respectively, while those for 3DVAR and CTR were 12.6 μg m−3 and 18.3 μg m−3, respectively. Thus, we proposed a simple method to find a Gaussian function that best described the error correlation of the BEC based on the physical distance.

Uncertainty quantification in stochastic inversion with dimensionality reduction using variational autoencoder

Estimating rock and fluid properties in the subsurface from geophysical measurements is a computationally and memory-intensive inverse problem. For nonlinear problems with non-Gaussian variables, analytical solutions are generally not available, and the solutions of those inverse problems must be approximated using sampling and optimization methods. To reduce the computational cost, model and data can be reparameterized into low-dimensional spaces where the solution of the inverse problem can be computed more efficiently. Among the potential dimensionality reduction methods, deep-learning algorithms based on deep generative models provide an efficient approach to reduce the dimension of the model and data vectors. However, such dimension reduction might lead to information loss in the reconstructed model and data, reduction of the accuracy and resolution of the inverted models, and under- or overestimation of the uncertainty of the predicted models. To comprehensively investigate the impact of model and data dimension reduction with deep generative models on uncertainty quantification, we compare the prediction uncertainty in nonlinear inverse problem solutions obtained from Markov chain Monte Carlo and ensemble-based data assimilation methods implemented in lower dimensional data and model spaces using a deep variational autoencoder. Our workflow is applied to two geophysical inverse problems for the prediction of reservoir properties: prestack seismic inversion and seismic history matching. The inversion results consist of the most likely model and a set of realizations of the variables of interest. The application of dimensionality reduction methods makes the stochastic inversion more efficient.

A scalable model-independent iterative data assimilation tool for sequential and batch estimation of high dimensional model parameters and states

Ensemble-based data assimilation (DA) methods have displayed strong potential to improve model state and parameter estimation across several disciplines due to their computational efficiency, scalability, and ability to estimate uncertainty in the dynamic states and the parameters. However, a barrier to adoption of ensemble DA methods remains. Namely, there is currently a lack of available tools that enable efficient and scalable DA in a non-intrusive fashion and that support implementation flexibility. This paper presents an open-source software tool (PESTPP-DA) that implements a range of data assimilation methods—Ensemble Kalman filter, Ensemble Kalman Smoother and Ensemble Smoother—using the widely known PEST model-interface protocols, to interact with any model. Two iterative solutions can be used for nonlinear and/or non-Gaussian assimilation problems. To demonstrate the broad range of PESTPP-DA applications, two synthetic case studies are presented: (1) the Lorenz model and (2) a groundwater pumping test in the presence of a non-Gaussian hydraulic conductivity field.

A Multiscale Local Gain Form Ensemble Transform Kalman Filter (MLGETKF)

AbstractA new multiscale, ensemble-based data assimilation (DA) method, multiscale local gain form ensemble transform Kalman filter (MLGETKF), is introduced. MLGETKF allows simultaneous update of multiple scales for both the ensemble mean and perturbations through assimilating all observations at once. MLGETKF performs DA in independent local volumes, which lends the algorithm a high degree of computational scalability. The multiscale analysis is enabled through the rapid creation of many pseudoensemble perturbations via a multiscale ensemble modulation procedure. The Kalman gain that is used to update the raw background ensemble mean and perturbations is based on this modulated ensemble, which intrinsically includes multiscale model space localization. Experiments with a noncycled statistical model show that the full background covariance estimated by MLGETKF more accurately resembles the shape of the true covariance than a scale-unaware localization. The mean analysis from the best-performing MLGETKF is statistically significantly more accurate than the best-performing scale-unaware LGETKF. The accuracy of the MLGETKF analysis is more sensitive to small-scale band localization radius than large-scale band. MLGETKF is further examined in a cycling DA context with a surface quasigeostrophic model. The root-mean-square potential temperature analysis error of the best-performing MLGETKF is 17.2% lower than that of the best-performing LGETKF. MLGETKF reduces analysis errors measured in kinetic energy spectra space by 30%–80% relative to LGETKF with the largest improvement at large scales. MLGETKF deterministic and ensemble mean forecasts are more accurate than LGETKF for full and large scales up to 5–6-day lead time and for small scales up to 3–4-day lead time, gaining ~12 h–1 day of predictability.

Reservoir history matching by ensemble smoother with principle component and sensitivity analysis for heterogeneous formations

Ensemble-based data assimilation methods have been widely investigated and applied for inverse problems of fluid flow in porous media during the past decades. Among these methods, the ensemble Kalman filter and the ensemble smoother are probably the most popular in history-matching applications. For large-scale problems, the ensemble size is limited to the computational resources in running the forward simulation, and is usually much smaller than the total number of gridblocks. In this case, the ensemble forms a reduced-order subspace, and principle component analysis is suggested by retaining the leading eigenvectors after truncation.In this paper, we propose to improve the ensemble smoother by proper orthogonal decomposition with optimal parameter selection. The motivation behind this method is that the estimation would be more accurate if the subspace spanned by the ensemble favors the dominant components. Specifically, the principle component analysis is first applied to obtain the eigenvalues and orthogonal eigenvectors. Then, a number of eigenvectors are selected according to importance from sensitivity analysis, rather than the eigenvalues. Finally, the ensemble smoother is implemented using these eigenvectors.The proposed method is illustrated by a simple mathematical example, and tested in a 2D single-phase and a 3D multiphase flow problem. The numerical results show that the traditional ensemble smoother may provide poor results in some ill-posed inverse problems, because some important features are lost in the randomly generated realizations. The principle component analysis alleviates this issue by sorting the eigenvectors based on energy, but it may still produce unsatisfactory results. The combination of sensitivity analysis and principle component analysis provides more accurate matching and prediction than those obtained from the previous two methods. The local sensitivity analysis is preferred since it is much more efficient than the global sensitivity analysis, and its accuracy is validated in the case studies.

Indicator-based data assimilation with multiple-point statistics for updating an ensemble of models with non-Gaussian parameter distributions

Ground-water flow and the transport of contaminants in groundwater systems are strongly controlled by geologic heterogeneities. Because, the data available to model these subsurface heterogeneities are generally sparse, the observed groundwater flow, piezometric head at well locations, or the concentration profile of solutes provide valuable additional information about these complex subsurface systems. Regardless, there is likely to be considerable uncertainty associated with the predictions of the subsurface heterogeneities. This has motivated the development of several ensemble-based schemes for assimilating flow response data into predictions of subsurface heterogeneities. Most ensemble-based data assimilation methods including ensemble Kalman filter (EnKF) or indicator-based data assimilation (InDA), used for assimilation of dynamic data into geologic models, utilize statistics in the form of covariances calculated using the ensemble of models to perform model updates. These covariance based updates do not preserve the complex spatial characteristics of geologic structures that are better represented using multiple-point statistics. Additionally, in EnKF, the mismatch between the observed and the simulated values are assumed to be linearly related to the parameter updates, and the distribution of the state variable is assumed to be multi-Gaussian. The spatial distribution of the primary variables like facies can be non-Gaussian because of the spatial continuity exhibited by channel facies (sands) and non-channel facies (clay), that have distinctly different properties. Also, the relationship between the mismatch and the parameter updates can be strongly non-linear. In indicator-based data assimilation (InDA) method the indicator transforms of parameter and mismatch variables are used, which affords the treatment of these variables as bi-variate non-Gaussian. Furthermore, in the indicator transformed space, restrictive linear assumption can also be lifted as the indicator transform is invariant under non-linear transformations. However, the updates are still governed by the bivariate interactions between the state variables. A multiple-point extension of InDA is proposed in this paper which utilizes existing multiple-point simulation algorithms like single normal equation simulation (SNESIM) in combination with InDA, to preserve the spatial characteristics of the geologic model while at the same time honor the observed flow or transport response. The proposed method is applied to a synthetic groundwater system with complex channel distributions. The channel features of the final updated ensemble of models is shown to converge towards the reference model and the ensemble flow responses are also shown to match the reference flow response.

Evaluation of ensemble methods for quantifying uncertainties in steady-state CFD applications with small ensemble sizes

Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high computational costs, for instance, the computational fluid dynamics (CFD) problem, the conventional, exact Bayesian approach such as Markov chain Monte Carlo is intractable. To this end, the ensemble-based Bayesian methods have been used for CFD applications. However, their applicability for UQ has not been fully analyzed and understood thus far. Here, we evaluate the performance of three widely used iterative ensemble-based data assimilation methods, namely ensemble Kalman filter, ensemble randomized maximum likelihood method, and ensemble Kalman filter with multiple data assimilation for UQ problems. We present the derivations of the three ensemble methods from an optimization viewpoint. Further, a scalar case is used to demonstrate the performance of the three different approaches with emphasis on the effects of small ensemble sizes. Finally, we assess the three ensemble methods for quantifying uncertainties in steady-state CFD problems involving turbulent mean flows. Specifically, the Reynolds averaged Navier–Stokes (RANS) equation is considered the forward model, and the uncertainties in the propagated velocity are quantified and reduced by incorporating observation data. The results show that the ensemble methods cannot accurately capture the true posterior distribution, but they can provide a good estimation of the uncertainties even when very limited ensemble sizes are used. Based on the overall performance and efficiency from the comparison, the ensemble randomized maximum likelihood method is identified as the best choice of approximate Bayesian UQ approach among the three ensemble methods evaluated here.

Comparison of regularized ensemble Kalman filter and tempered ensemble transform particle filter for an elliptic inverse problem with uncertain boundary conditions

In this paper, we focus on parameter estimation for an elliptic inverse problem. We consider a 2D steady-state single-phase Darcy flow model, where permeability and boundary conditions are uncertain. Permeability is parameterized by the Karhunen-Loeve expansion and thus assumed to be Gaussian distributed. We employ two ensemble-based data assimilation methods: ensemble Kalman filter and ensemble transform particle filter. The formal one approximates mean and variance of a Gaussian probability function by means of an ensemble. The latter one transforms ensemble members to approximate any posterior probability function. Ensemble Kalman filter considered here is employed with regularization and localization—R(L)EnKF. Ensemble transform particle filter is also employed with a form of regularization called tempering and localization—T(L)ETPF. Regularization is required for highly non-linear problems, where prior is updated to posterior via a sequence of intermediate probability measures. Localization is required for small ensemble sizes to remove spurious correlations. We have shown that REnKF outperforms TETPF. We have shown that localization improves estimations of both REnKF and TETPF. In numerical experiments when uncertainty is only in permeability, TLETPF outperforms RLEnKF. When uncertainty is both in permeability and in boundary conditions, TLETPF outperforms RLEnKF only for a large ensemble size 1000. Furthermore, when uncertainty is both in permeability and in boundary conditions but we do not account for error in boundary conditions in data assimilation, RLEnKF outperforms TLETPF.

Efficient Assimilation of Crosswell Electromagnetic Data Using an Ensemble-Based History-Matching Framework

SummaryAn ensemble-based history-matching framework is proposed to enhance the characterization of petroleum reservoirs through the assimilation of crosswell electromagnetic (EM) data. As an advanced technology in reservoir surveillance, crosswell EM tomography can be used to estimate a cross-sectional conductivity map and associated saturation profile at an interwell scale by exploiting the sharp contrast in conductivity between hydrocarbons and saline water. Incorporating this information into reservoir simulation in combination with other available observations is expected to enhance the forecasting capability of reservoir models and to lead to better quantification of uncertainty.The proposed approach applies ensemble-based data-assimilation methods to build a robust and flexible framework in which various sources of available measurements can be integrated. A comparative study evaluates two different implementations of the assimilation of crosswell EM data. The first approach integrates the crosswell EM field components in their original form, which entails forward simulation of the observed EM responses from the simulated reservoir state. In the second approach, formation conductivity is derived from the EM data through inversion and is subsequently assimilated into the reservoir model. An image-oriented distance parameterization of the fluid front assimilates the conductivity field in an efficient and robust manner and overcomes issues with data size, errors, and their correlation. Numerical experiments for different test cases with increasing complexity provide insight into the performance of the two proposed integration schemes. The results demonstrate the efficiency of the developed history-matching workflow and the added value of crosswell EM data in enhancing the reservoir characterization and reliability of dynamic reservoir forecasts.

Comparison of NMC and Ensemble-Based Climatological Background-Error Covariances in an Operational Limited-Area Data Assimilation System

The evaluation of several climatological background-error covariance matrix (defined as the B matrix) estimation methods was performed using the ALADIN limited-area modeling data-assimilation system at a 4 km horizontal grid spacing. The B matrices compared were derived using the standard National Meteorological Center (NMC) and ensemble-based estimation methods. To test the influence of lateral boundary condition (LBC) perturbations on the characteristics of ensemble-based B matrix, two ensemble prediction systems were established: one used unperturbed lateral boundary conditions (ENS) and another used perturbed lateral boundary conditions (ENSLBC). The characteristics of the three B matrices were compared through a diagnostic comparison, while the influence of the different B matrices on the analysis and quality of the forecast were evaluated for the ENSLBC and NMC matrices. The results showed that the lateral boundary condition perturbations affected all the control variables, while the smallest influence was found for the specific humidity. The diagnostic comparison showed that the ensemble-based estimation method shifted the correlations toward the smaller spatial scales, while the LBC perturbations gave rise to larger spatial scales. The influence on the analysis showed a smaller spatial correlation for the ensemble B matrix compared to that of the NMC, with the most pronounced differences for the specific humidity. The verification of the forecast showed modest improvement for the experiment with the ensemble B matrix. Among the methods tested, the results suggest that the ensemble-based data-assimilation method is the favorable approach for background-error covariance calculation in high-resolution limited-area data assimilation systems.

Dysregulated mitochondrial dynamics and apoptosis in Bipolar Disorder

Hydrological hazards such as storm surges, tsunamis, and rainfall-induced flooding are physically complex events that are costly in loss of human life and economic productivity. Many such disasters could be mitigated through improved emergency evacuation in real-time and through the development of resilient infrastructure based on knowledge of how systems respond to extreme events. Data-driven computational modeling is a critical technology underpinning these efforts. This investigation focuses on the novel combination of methodologies in forward simulation and data assimilation. The forward geophysical model utilizes adaptive mesh refinement (AMR), a process by which a computational mesh can adapt in time and space based on the current state of a simulation. The forward solution is combined with ensemble based data assimilation methods, whereby observations from an event are assimilated into the forward simulation to improve the veracity of the solution, or used to invert for uncertain physical parameters. The novelty in our approach is the tight two-way coupling of AMR and ensemble filtering techniques. The technology is tested using actual data from the Chile tsunami event of February 27, 2010. These advances offer the promise of significantly transforming data-driven, real-time modeling of hydrological hazards, with potentially broader applications in other science domains.

A novel localization scheme for scalar uncertainties in ensemble-based data assimilation methods

History matching, also known as data assimilation, is an inverse problem with multiple solutions responsible for generating more reliable models for use in decision-making processes. An iterative ensemble-based method (Ensemble Smoother with Multiple Data Assimilation—ES-MDA) has been used to improve the solution of history-matching processes with a technique called distance-dependent localization. In conjunction, ES-MDA and localization can obtain consistent petrophysical images (permeability and porosity). However, the distance-dependent localization technique is not used to update scalar uncertainties, such as relative permeability; therefore, the variability for these properties is excessively reduced, potentially excluding plausible answers. This work presents three approaches to update scalar parameters while increasing the final variability of these uncertainties to better scan the search space. The three approaches that were developed and compared using a benchmark case are: binary correlation coefficient (BCC), based on correlation calculated by ES-MDA through cross-covariance matrix C_{text{MD}}^{text{f}} (BCC-CMD); BCC, based on a correlation coefficient between the objective functions and scalar uncertainties (R) (BCC–R); and full correlation coefficient (FCC). We used the work of Soares et al. (J Pet Sci Eng 169:110–125, 2018) as a base case to compare the approaches because although it showed good matches with geologically consistent petrophysical images, it generated an excessive reduction in the scalar parameters. BCC-CMD presented similar results to the base case, excessively reducing the variability of the scalar uncertainties. BCC–R increased the variability in the scalar parameters, especially for BCC with a higher threshold value. Finally, FCC found many more potential answers in the search space without impairing data matches and production forecast quality.