Assimilation Problem Research Articles

Toward Utilizing Similarity in Hydrologic Data Assimilation

Similarity to reality is a necessary property of models in earth sciences. Similarity information can thus possess a large potential in advancing geophysical modeling and data assimilation. We present a formalism for utilizing similarity within the existing theoretical data assimilation framework. Two examples illustrate the usefulness of utilizing similarity in data assimilation. The first, theoretical example shows changes in the accuracy of the amplitude estimate in the presence of a phase error in a sine function, where correcting the phase error prior to the assimilation reduces the degree of ill-posedness of the assimilation problem. This signifies the importance of accounting for the phase error in order to reduce the error in the amplitude estimate of the sine function. The second, real-world example illustrates that timing errors in simulated flow degrade the data assimilation performance, and that the flow gradient-informed shifting of rainfall time series improved the assimilation results with less adjusting model states. This demonstrates the benefit of utilizing streamflow gradients in shifting rainfall time series in a way to improve streamflow timing—vital information for flood early warning and preparedness planning. Finally, we discuss the implications, potential issues, and future challenges associated with utilizing similarity in hydrologic data assimilation.

Bayesian Ensemble Kalman Filter for Gaussian Mixture Models

AbstractInverse theory and data assimilation methods are commonly used in earth and environmental science studies to predict unknown variables, such as the physical properties of underground rocks, from a set of measured geophysical data, like geophysical seismic or electromagnetic data. A new Bayesian approach based on the ensemble Kalman filter using Gaussian mixture models is presented to overcome the assumption of Gaussian distribution of the unknown variables commonly used in the data assimilation literature and to generalize the algorithm to inverse problems with multimodal probability distributions. In applications of subsurface characterization, the multimodality of the unknown variables is generally due to the presence of different rock types, also known as geological facies. In the proposed method, the weights of the Gaussian mixture model represent the facies proportions, and they follow a Markov chain model. The proposed Bayesian model generates the unknown model parameters conditioned on measured data using a Markov chain Monte Carlo sampler. The validity of the method is demonstrated on a data assimilation problem where the goal is to estimate the posterior distribution of the unknown rock density from a set of repeated measurements of acoustic wave velocity measured at different times. The proposed method provides accurate estimates with efficient computational times.

Data Assimilation and Parameter Identification for Water Waves Using the Nonlinear Schrödinger Equation and Physics-Informed Neural Networks

The measurement of deep water gravity wave elevations using in situ devices, such as wave gauges, typically yields spatially sparse data due to the deployment of a limited number of costly devices. This sparsity complicates the reconstruction of the spatio-temporal extent of surface elevation and presents an ill-posed data assimilation problem, which is challenging to solve with conventional numerical techniques. To address this issue, we propose the application of a physics-informed neural network (PINN) to reconstruct physically consistent wave fields between two elevation time series measured at distinct locations within a numerical wave tank. Our method ensures this physical consistency by integrating residuals of the hydrodynamic nonlinear Schrödinger equation (NLSE) into the PINN’s loss function. We first showcase a data assimilation task by employing constant NLSE coefficients predetermined from spectral wave properties. However, due to the relatively short duration of these measurements and their possible deviation from the narrow-band assumptions inherent in the NLSE, using constant coefficients occasionally leads to poor reconstructions. To enhance this reconstruction quality, we introduce the base variables of frequency and wavenumber, from which the NLSE coefficients are determined, as additional neural network parameters that are fine tuned during PINN training. Overall, the results demonstrate the potential for real-world applications of the PINN method and represent a step toward improving the initialization of deterministic wave prediction methods.

A latent space method with maximum entropy deep reinforcement learning for data assimilation

Data assimilation aims to calibrate the uncertain state or parameter vectors of a system by matching simulation results with observations, which is crucial for uncertainty quantification and optimization. Although traditional methods of data assimilation have shown promising results in practical applications, they need well-designed iteration rules (i.e., gradient, covariance, search strategies). Deep reinforcement learning (DRL) can solve data assimilation problems by trial and error, which does not require convoluted iteration rules. However, previous DRL methods cannot tackle high-dimensional data assimilation problems efficiently. In this work, we propose a latent space method with maximum entropy DRL for data assimilation to extend DRL to complicated systems with lots of parameters. Solutions can be found in a reduced space, through the interaction between the agent represented by artificial neural networks and the environment of numerical simulation. The proposed method contains two key points. First, to make the method applicable to high-dimensional problems, we construct a latent space method by integrating a dimensionality reduction method with the state, action, and reward settings for the agent. Second, a maximum entropy DRL algorithm, Soft Actor–Critic (SAC), was employed to efficiently explore the parameter space. The proposed method overcomes the limitation that previous DRL algorithms are only suitable for small-scale cases, and enables DRL to deal with medium-scale or even large-scale data assimilation problems. The performance of the proposed method was validated by comparison with a deep reinforcement learning algorithm and traditional data assimilation algorithms on 2D synthetic and 3D reservoir cases.

Turkisms in the Russian language: The problem of assimilation and functioning in the concept of P. U. Bakirov

Turkisms in the Russian language: The problem of assimilation and functioning in the concept of P. U. Bakirov

Structure of an Information and Computing System for Solving the Problem of Data Assimilation in Environmental Modeling

Structure of an Information and Computing System for Solving the Problem of Data Assimilation in Environmental Modeling

Simultaneous Inference of Sea Ice State and Surface Emissivity Model Using Machine Learning and Data Assimilation

AbstractSatellite microwave radiance observations are strongly sensitive to sea ice, but physical descriptions of the radiative transfer of sea ice and snow are incomplete. Further, the radiative transfer is controlled by poorly‐known microstructural properties that vary strongly in time and space. A consequence is that surface‐sensitive microwave observations are not assimilated over sea ice areas, and sea ice retrievals use heuristic rather than physical methods. An empirical model for sea ice radiative transfer would be helpful but it cannot be trained using standard machine learning techniques because the inputs are mostly unknown. The solution is to simultaneously train the empirical model and a set of empirical inputs: an “empirical state” method, which draws on both generative machine learning and physical data assimilation methodology. A hybrid physical‐empirical network describes the known and unknown physics of sea ice and atmospheric radiative transfer. The network is then trained to fit a year of radiance observations from Advanced Microwave Scanning Radiometer 2, using the atmospheric profiles, skin temperature and ocean water emissivity taken from a weather forecasting system. This process estimates maps of the daily sea ice concentration while also learning an empirical model for the sea ice emissivity. The model learns to define its own empirical input space along with daily maps of these empirical inputs. These maps represent the otherwise unknown microstructural properties of the sea ice and snow that affect the radiative transfer. This “empirical state” approach could be used to solve many other problems of earth system data assimilation.

Acculturation and adjustment among international college students: The moderating role of perceived second language proficiency

Objectives: This study was aimed at examining the relationship between acculturation strategies and both psychological and socio-cultural adjustment, while concurrently assessing the moderating role of perceived second language proficiency. The premise was that proficiency in the host country’s language could potentially facilitate successful acculturative outcomes. Method: We used self-report measures to collect data on a sample of 237 international students in Los Angeles. A General Linear Model was applied for data analyses. Results: Overall, integration emerged as the most adaptive acculturation strategy, whereas marginalization was identified as the least adaptive. Noteworthy, moderating effects were observed in the relationships between marginalization and life satisfaction, integration and socio-cultural adjustment, assimilation and psychological problems, as well as socio-cultural adjustment. Conclusions: Our findings lend support to the Integration Hypothesis, highlighting that adopting integration is associated with superior adaptive outcomes, also pointing out that the pattern of associations between acculturation strategies and both psychological and socio-cultural adjustment could fluctuate depending on the level of perceived second language proficiency.

A Novel Localized Fast Multipole Method for Computations With Spatially Correlated Observation Error Statistics in Data Assimilation

AbstractSeveral observation types (e.g., geostationary satellite and Doppler radar observations) have recently been found to exhibit strong spatial error correlations. Including these error statistics in data assimilation for numerical weather prediction can improve analysis quality and forecast skill. Moreover, it allows for increases in the spatial density of observations assimilated, which is needed for the provision of information on appropriate scales for high‐resolution forecasting. However, introducing correlated error statistics may increase the computational complexity and parallel communication costs of matrix‐vector products involving observation precision matrices (inverse observation error covariance matrices). Without new approaches, we cannot take full advantage of new observation uncertainty estimates. We develop a new numerical approximation method based on a particular type of fast multipole method and a domain localization approach. The basic idea is to divide the observation domain into boxes and then separate calculations of matrix‐vector products according to the partition. These calculations can be done in parallel with very low communication overheads. The new method is easy to implement and parallelize, and it is applicable to a wide variety of observation precision matrices. We applied the new method to a simple variational data assimilation problem and found that the computational cost of the variational minimization was dramatically reduced while preserving analysis accuracy across a range of scales. The new method has the potential to be used as an efficient technique for practical applications where a large number of observations with mutual error correlations need to be assimilated quickly.

Continuous data assimilation for the three dimensional primitive equations with magnetic field

In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the H 2 -strong solution of the assimilation system converges exponentially to the reference solution in the sense of L 2 as t → ∞. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity equation.

Variational data assimilation with finite-element discretization for second-order parabolic interface equation

Abstract In this paper, we propose and analyze a finite-element method of variational data assimilation for a second-order parabolic interface equation on a two-dimensional bounded domain. The Tikhonov regularization plays a key role in translating the data assimilation problem into an optimization problem. Then the existence, uniqueness and stability are analyzed for the solution of the optimization problem. We utilize the finite-element method for spatial discretization and backward Euler method for the temporal discretization. Then based on the Lagrange multiplier idea, we derive the optimality systems for both the continuous and the discrete data assimilation problems for the second-order parabolic interface equation. The convergence and the optimal error estimate are proved with the recovery of Galerkin orthogonality. Moreover, three iterative methods, which decouple the optimality system and significantly save computational cost, are developed to solve the discrete time evolution optimality system. Finally, numerical results are provided to validate the proposed method.

A Data Assimilation Methodology to Analyze the Unsaturated Seepage of an Earth–Rockfill Dam Using Physics-Informed Neural Networks Based on Hybrid Constraints

Data assimilation for unconfined seepage analysis has faced significant challenges due to hybrid causes, such as sparse measurements, heterogeneity of porous media, and computationally expensive forward models. To address these bottlenecks, this paper introduces a physics-informed neural network (PINN) model to resolve the data assimilation problem for seepage analysis of unsaturated earth–rockfill dams. This strategy offers a solution that decreases the reliance on numerical models and enables an accurate and efficient prediction of seepage parameters for complex models in the case of sparse observational data. For the first attempt in this study, the observed values are obtained by random sampling of numerical solutions, which are then contributed to the synchronous constraints in the loss function by informing both the seepage control equations and boundary conditions. To minimize the effects of sharp gradient shifts in seepage parameters within the research domain, a residual adaptive refinement (RAR) constraint is introduced to strategically allocate training points around positions with significant residuals in partial differential equations (PDEs), which could facilitate enhancing the prediction accuracy. The model’s effectiveness and precision are evaluated by analyzing the proposed strategy against the numerical solutions. The results indicate that even with limited sparse data, the PINN model has great potential to predict seepage data and identify complex structures and anomalies inside the dam. By incorporating coupling constraints, the validity of our PINN model could lead to theoretically viable applications of hydrogeophysical inversion or multi-parameter seepage inversion. The results show that the proposed framework can predict the seepage parameters for the entire research domain with only a small amount of observation data. Furthermore, with a small amount of observation data, PINNs are able to obtain more accurate results than purely data-driven DNNs.

On the growth of localised perturbations in isotropic turbulence

Assessing the impact of localised perturbations is staple for the problems of data assimilation and control of turbulent flows. In the present work we exploit the public database of [1] that contains the growth and location of about 105 perturbations of approximately thirty Kolmogorov units in isotropic turbulence at moderate Reynolds numbers. All the terms in the evolution equation for the perturbation kinetic energy are analysed statistically, disregarding in the process the effect of viscosity. Of the relevant terms, only the stretching of the perturbation by the mean flow can result in production of kinetic energy, whereas every other term must only transport the perturbation across the flow field. However, it is shown that if the problem of interest is the coarse-grained propagation of the perturbation, i.e. its radius, the dynamical terms related to incompressibility are of equal importance for the growth. A simplified model based on the balance between these terms is proposed to explain the quasi-linear growth of the radius with time.

Sensitivity of Functionals to Input Data in a Variational Assimilation Problem for a Sea Thermodynamics Model

Sensitivity of Functionals to Input Data in a Variational Assimilation Problem for a Sea Thermodynamics Model

Large-eddy simulation-based reconstruction of turbulence in a neutral boundary layer using spectral-tensor regularization

We propose an efficient method to reconstruct the turbulent flow field in a neutrally stratified atmospheric boundary layer using large-eddy simulation (LES) and a series of lidar measurements. The reconstruction is formulated as a strong four-dimensional variational data assimilation problem, which involves optimizing two competing terms that contribute in the objective functional. The first term is a likelihood term, while the second contains the initial background distribution of turbulent velocity fluctuations and works as a regularization term. However, computing and storing the full background covariance tensor in turbulent flows is time consuming and resource intensive. In the current work, we investigate the possibility of replacing the complex background tensor by simple analytical approximations based on spectral tensors such as the Hunt–Graham–Wilson (HGW) model (Boundary-Layer Meteorol., vol. 85, 1997, pp. 35–52) or the Mann model (J. Fluid Mech., vol. 273, 1994, pp. 141–168). Afterwards, the problem is solved using a quasi-Newton algorithm and preconditioned to enhance the convergence rate. We test the method using virtual lidar measurements collected on a fine reference LES. Results show a super-linear convergence rate of the optimization algorithm to a local minimum and very good agreement between virtual lidar measurements and reconstruction in the scanning region. Furthermore, we demonstrate that incorporating the Saffman energy spectrum ( $E(k) \sim k^2$ where E is the energy spectrum and k is the magnitude of the wavenumber vector) at low wavenumbers into the Mann spectral tensor yields a longer streamwise correlation length, resulting in reduced reconstruction error when compared with the Batchelor spectrum ( $E(k) \sim k^4$ ). Finally, we observe that using the HGW model or Mann model with a Saffman spectrum yields similar results.

A unified Bayesian inversion approach for a class of tumor growth models with different pressure laws

Abstract. In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a physical parameter m, which characterizes the constitutive relation between density and pressure. Based on these models, we employ the Bayesian inversion framework to infer parametric and nonparametric unknowns that affect tumor growth from noisy observations of tumor cell density. We establish the well-posedness and the stability theories for the Bayesian inversion problem and further prove the convergence of the posterior distribution in the so-called incompressible limit, m →∞. Since the posterior distribution across the index regime m ∈ [2,∞) can thus be treated in a unified manner, such theoretical results also guide the design of the numerical inference for the unknown. We propose a generic computational framework for such inverse problems, which consists of a typical sampling algorithm and an asymptotic preserving solver for the forward problem. With extensive numerical tests, we demonstrate that the proposed method achieves satisfactory accuracy in the Bayesian inference of the tumor growth models, which is uniform with respect to the constitutive relation.

Sensitivity of the Functionals of the Variational Data Assimilation Problem when Reconstructing the Initial State and Heat Flux for a Model of Sea Thermodynamics

Sensitivity of the Functionals of the Variational Data Assimilation Problem when Reconstructing the Initial State and Heat Flux for a Model of Sea Thermodynamics

Problems of Assimilation of Borrowings Belonging to Different Language Families

Problems of Assimilation of Borrowings Belonging to Different Language Families

The study of the local sensitivity of functionals of the optimal solution to observational data and the heat flux input data in a variational assimilation problem for the sea thermodynamics model

Abstract The problem of variational assimilation of observational data for the sea thermodynamics model is considered with the aim to reconstruct heat fluxes on the sea surface. The local sensitivity of functionals of the solution to the observational data and input data for heat fluxes is studied in the considered problem and the results of numerical experiments are presented for the Black Sea dynamics model.

Казаки-эмигранты в Чехословакии в 1921–1939 годах

Introduction. The purpose of this study is to analyze key aspects of the lives and details of Cossack emigrants in the Czechoslovak Republic (ČSR). Methods and materials. Within the research process, the author relied mainly on the following methods: narrative, historical-genetic, comparative-historical, and the method of analogies. The sources used were regulatory legal acts and office documents of the government and several ministries of the Czechoslovak Republic, speeches by individual representatives of the Czechoslovak ruling circles, documents of various organizations and societies, orders and decrees of army atamans, periodical press materials, and sources of private origin. Analysis. Most Cossacks moved to Czechoslovakia from Turkey and Greece, where they ended up after the evacuation from Crimea. The organization of the Cossacks’ move to Czechoslovakia was carried out mainly by public associations and societies. The first part of the Cossacks arrived in Czechoslovakia in June 1921. By the beginning of 1922, about 3,000 Cossacks were stationed on the territory of Czechoslovakia. The Cossacks received great support as part of the campaign to help Russian refugees. Within Czechoslovakia, the Cossacks formed public associations in the form of villages and khutors, as well as workers’ artels, in order to obtain and perform various jobs. Most Cossacks living in Czechoslovakia were involved in agriculture. Atamans of Cossack troops tried in every possible way to counteract the assimilation of Cossacks. Many Cossacks, after getting an education, were trying to leave Czechoslovakia for other states, mainly for France. Results. A comparative analysis showed that the Cossacks generally adapted more easily to the conditions of life in the position of an emigrant than most representatives of other parts of the Russian emigration. At the same time, the problem of assimilation among the Cossacks was sometimes quite acute and required the adoption of effective measures by their leaders. One of these measures was the popularization among the Cossacks of facts from their historical past and the preservation of historical memory. Not least, it was contributed by the Cossack historical commissions and archives.