Assimilation Problem Research Articles

A component-based data assimilation strategy with applications to vascular flows

We present a parameterized-background data-weak (PBDW) approach [Y Maday, AT Patera, JD Penn, M Yano, Int J Numer Meth Eng, 102(5), 933–965] to the steady-state variational data assimilation (DA) problem for systems modeled by partial differential equations (PDEs) and characterized by multiple interconnected components, with emphasis on vascular flows. We focus on the problem of reconstructing the state of the system in one specific component, based on local measurements. The PBDW approach does not require the solution of any PDE model at prediction stage (projection-by-data) and, as such, enables local state estimates on single components, as long as good background and update spaces for the estimation can be constructed. We discuss the application of PBDW to a two-dimensional steady Navier-Stokes problem for a family of parameterized geometries, and investigate instead the effects of enforcing no-slip boundary conditions and incompressibility constraints on the background and update spaces to enhance the state estimation. Furthermore, we show an actionable strategy to train local reduced-order bases (ROBs) for the background space that can later be used for DA tasks.

Problems in Assimilation of English Words for Undergraduate Level Students in Hazara University

This present study has focused on the problems in the assimilation of English words for undergraduates in Hazara University. A survey descriptive design was used to collect data from fifty undergraduates selected through convenient-non probability sampling technique who were asked to comprehend the assimilation process in certain words in the selected clips from English movies. To measure the problems in assimilation for the students, the students were asked to reproduce the same speech. The statistical analysis of the data shows that undergraduates did not have any major issues in the comprehension of the assimilated sounds in English words as they identified the assimilated sounds from the available lexical items and the speech context itself. The findings of the study show that students had fewer issues regarding the comprehension of the assimilated speech by native speakers than the issues they had while reproducing the same speech in spoken form themselves. In light of the findings of the study, it is suggested that due attention should be given to speaking skills in order to eliminate issues of assimilation in connected speech.

Sensitivity of functionals of the solution to a variational data assimilation problem with heat flux reconstruction for the sea thermodynamics model

Abstract The problem of variational observation data assimilation is considered for the mathematical thermodynamics model developed at the Marchuk Institute of Numerical Mathematics of RAS with the aim to reconstruct the sea surface heat flux. The sensitivity of functionals of solutions to observation data is studied for the considered variational assimilation problem and the results of numerical experiments for the Black Sea dynamics problem are presented.

Particle network EnKF for large-scale data assimilation

The Ensemble Kalman filter (EnKF) is a classic method of data assimilation. For distributed sampling, the conventional EnKF usually requires a centralized server to integrate the predictions of all particles or a fully-connected communication network, causing traffic jams and low bandwidth utilization in high-performance computing. In this paper, we propose a novel distributed scheme of EnKF based on network setting of sampling, called Particle Network EnKF. Without a central server, every sampling particle communicates with its neighbors over a sparsely connected network. Unlike the existing work, this method focuses on the distribution of sampling particles instead of sensors and has been proved effective and robust on numerous tasks. The numerical experiments on the Lorenz-63 and Lorenz-96 systems indicate that, with proper communication rounds, even on a sparse particle network, this method achieves a comparable performance to the standard EnKF. A detailed analysis of effects of the network topology and communication rounds is performed. Another experiment demonstrating a trade-off between the particle homogeneity and performance is also provided. The experiments on the whole-brain neuronal network model show promises for applications in large-scale assimilation problems.

MIGRATION POLICY OF EUROPEAN UNION AND IMMIGRANTS IN EUROPEAN UNION

In this study, European Union’s general migration policy is studied. Also, immigrants in European Union and their problem are mentioned. This study is studied by explanatory approach and literature review method. The problem during the research is that there is not much source about problems of immigrants in European Union. European Union’s policy on immigrants in European Union is based on controlling and integration. Controlling is possible via legal migration. Integration is possible via fill the gaps between cultures. As a brief, common problems of immigrants (asylum seeker, refugee, kids of refugees) in European Union are these: problems because illegal entrance, problem of reaching to education, reaching to health service problem and assimilation problem.

The Morozov’s principle applied to data assimilation problems

This paper is focused on the Morozov’s principle applied to an abstract data assimilation framework, with particular attention to three simple examples: the data assimilation problem for the Laplace equation, the Cauchy problem for the Laplace equation and the data assimilation problem for the heat equation. Those ill-posed problems are regularized with the help of a mixed type formulation which is proved to be equivalent to a Tikhonov regularization applied to a well-chosen operator. The main issue is that such operator may not have a dense range, which makes it necessary to extend well-known results related to the Morozov’s choice of the regularization parameter to that unusual situation. The solution which satisfies the Morozov’s principle is computed with the help of the duality in optimization, possibly by forcing the solution to satisfy given a priori constraints. Some numerical results in two dimensions are proposed in the case of the data assimilation problem for the Laplace equation.

Including parameterized error covariance in local ensemble solvers: Experiments in a 1D model with balance constraints

AbstractLack of efficient ways to include parameterized error covariance in ensemble‐based local volume solvers (e.g. the local ensemble‐transform Kalman filter – the LETKF) remains an outstanding problem in data assimilation. Here, we describe two new algorithms: GETKF‐OI and LETKF‐OI. These algorithms are similar to the traditional optimal interpolation (OI) algorithm in that they use parameterized error covariance to update each of the local volume solutions. However, unlike the traditional OI that scales poorly as the number of observations increases, the new algorithms achieve linear scalability by using either the observational‐space localization strategy of the traditional LETKF algorithm or the modulated ensembles of the gain‐form (GETKF) algorithm. In our testing with a simple one‐dimensional univariate system, we find that the GETKF‐OI algorithm can recover the exact solution within the truncation bounds of the modulated ensemble and the LETKF‐OI algorithm achieves a close approximation to the exact solution. We also demonstrate how to extend GETKF‐OI algorithm to a toy multivariate system with balance constraints.

Where did the Tobolsk and Tyumen Bukharans “disappear” to (historical and demographic characteristic of the ethno-estate group at the end of the 19th — first third of the 20th c.)

One of the significant ethnic components that became part of the Siberian-Tatar community at the later stages of ethnogenesis were Bukharans / Siberian Bukharans. This ethnic group emerged in Western Siberia during the 16th–19th centuries from migrants from Central Asia. Despite the considerable amount of research on the Siberian Bukharans, transformation of this ethno-estate group in the twentieth century and the process of its inclusion into the group of Siberian Tatars remain an underexplored question. The aim of this work is to study the ethno-demographic processes that took place among the Siberian Bukharians at the end of the 19th — first third of the 20th century. Based on the materials of the First General Census of 1897, the All-Union Census of 1926, and other statistical sources, historical and demographic characteristics of the Bukharan population of Western Siberia at the end of the 19th — first third of the 20th century are given. The dynamics of changes in their numbers, settling and composition that had occurred since the end of the 19th century is considered. Special attention is paid to the problem of assimilation of the Bukharans by the Siberian Tatars in the aspect of the question of their “disappearance” in the districts of the Ural Region according to the Census of 1926. It has been revealed that, as a result of the zoning carried out in the 1920s by the Soviet state, the accounting system of the Bukharans and Tatars changed. The problem of the specifics of the tax relations of different estates of the Turkic-Tatar popula-tion, which existed earlier, disappeared with the arrival of the new government and the change in realities. The former settlements of the Tatars and Bukharans were distributed according to the territorial principle, since the state no longer saw any differences between the indigenous Siberian Tatars and Bukharans. In this connection, there appeared a “distribution” of the Bukharans and Tatars by districts, which did not coincide with the actual places of their traditional residence. As a result, there was an increase in the Bukharans in the Tarsky district due to the Tatar population of the district, whereas the former Bukharan population of the Tobolsk and Tyumen dis-tricts was counted as Tatars in the Census of 1926.

Variational data assimilation for a sea dynamics model

Abstract The 4D variational data assimilation technique is presented for modelling the sea dynamics problems, developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The approach is based on the splitting method for the mathematical model of sea dynamics and the minimization of cost functionals related to the observation data by solving an optimality system that involves the adjoint equations and observation and background error covariances. Efficient algorithms for solving the variational data assimilation problems are presented based on iterative processes with a special choice of iterative parameters. The technique is illustrated for the Black Sea dynamics model with variational data assimilation to restore the sea surface heat fluxes.

Randomized Tensor Decomposition for Large-Scale Data Assimilation Problems for Carbon Dioxide Sequestration

Randomized Tensor Decomposition for Large-Scale Data Assimilation Problems for Carbon Dioxide Sequestration

Proper Noun Pronunciation Inaccuracies in English by Educated Arabic Speakers

Analysis of a corpus of errors in pronouncing Proper Nouns used in English collected from the spontaneous speech of a sample of Arab informants showed that Arabic speakers have the following problems: (i) mispronouncing English vowels in Google, Moodle, Uber, Nixon, London; (ii) replacing consonants absent in L1 (p v) by their equivalents (bebsi, jafa); (iii) geminating consonants in city and country names (Peking; Venezuela, Minnesota); (iv); inserting a vowel in consonant clusters in Proper Nouns and acronyms (Zelinsky, Logansk, SNAS, GMC, ); (v) breaking words into two sub-words (Kasper+sky, Sky+pe); (vi) pronouncing words the way they are spelled (Nazi, Nike, Huawei, Hyundai, Wednesday); and (vii) transferring Arabic stress rules to English words (McDonald, Mayflower). Pronunciation errors made by Arab students are attributed to transfer from the native language, i.e., Modern Standard Arabic (MSA) or the local dialect, insufficient mastery of English pronunciation rules, phonics and phone-grapheme correspondences and lack of knowledge of the differences between English and Arabic phonology. To correct pronunciation problems, the study recommends that students watch pronunciation practice videos that focus on a single error or rule at a time; raising students’ awareness of English pronunciation rules, phonics, phoneme-grapheme correspondences and comparing English and Arabic vowels, consonants, syllable structure, pause, juncture and stress rules; providing direct pronunciation instruction, graded lessons and remedial exercises. Future research needs to investigate Arab students’ pronunciation problems in assimilation, elision, and others.

Physics‐Informed Machine Learning Method for Large‐Scale Data Assimilation Problems

AbstractWe develop a physics‐informed machine learning approach for large‐scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two‐dimensional steady‐state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics‐informed conditional Karhunen‐Loéve expansion (PICKLE) method to modeling subsurface flow with unknown flux (Neumann) and varying head (time‐dependent Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large‐scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen‐Loéve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as N1.15) with the number of grid nodes N, while that of MAP increases much faster (as N3.28). We also show that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).

Inverse modeling of atmospheric chemistry with a differential evolution solver: Inverse problem and Data assimilation

In this paper, we numerically compare an inverse problem for an atmospheric chemistry model, when all the measurement data is available a priory, to a corresponding data assimilation problem when the data are obtained in some portions during the simulation. In both cases, we reconstruct the unobservable parts of the model state function by the observable ones (i.e., solve a continuation problem). This is done by identifying the model reaction rate parameters with the available measurement data by solving an optimization problem with a derivative-free differential evolution solver. In our numerical experiments, the inverse problem formulation of the continuation problem has not necessarily provided better results than the data assimilation formulation despite the latter being more limited in the measurement data.

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

Data assimilation with soft constraints (DASC) through a generalized iterative ensemble smoother

This work investigates an ensemble-based workflow to simultaneously handle generic, nonlinear equality and inequality constraints in reservoir data assimilation problems. The proposed workflow is built upon a recently proposed umbrella algorithm, called the generalized iterative ensemble smoother (GIES), and inherits the benefits of ensemble-based data assimilation algorithms in geoscience applications. Unlike the traditional ensemble assimilation algorithms, the proposed workflow admits cost functions beyond the form of nonlinear-least-squares, and has the potential to develop an infinite number of constrained assimilation algorithms. In the proposed workflow, we treat data assimilation with constraints as a constrained optimization problem. Instead of relying on a general-purpose numerical optimization algorithm to solve the constrained optimization problem, we derive an (approximate) closed form to iteratively update model variables, but without the need to explicitly linearize the constraint systems. The established model update formula bears similarities to that of an iterative ensemble smoother (IES). Therefore, in terms of theoretical analysis, it becomes relatively easy to transit from an ordinary IES to the proposed constrained assimilation algorithms, and in terms of practical implementation, it is also relatively straightforward to implement the proposed workflow for users who are familiar with the IES, or other conventional ensemble data assimilation algorithms like the ensemble Kalman filter (EnKF). Apart from the aforementioned features, we also develop efficient methods to handle two noticed issues that would be of practical importance for ensemble-based constrained assimilation algorithms. These issues include localization in the presence of constraints, and the (possible) high dimensionality induced by the constraint systems. We use one 2D and one 3D case studies to demonstrate the performance of the proposed workflow. In particular, the 3D example contains experiment settings close to those of real field case studies. In both case studies, the proposed workflow achieves better data assimilation performance in comparison to the choice of using an original IES algorithm. As such, the proposed workflow has the potential to further improve the efficacy of ensemble-based data assimilation in practical reservoir data assimilation problems.

4D Technology of Variational Data Assimilation for Sea Dynamics Problems

The technology aimed at high-performance computing is presented for modeling the sea dynamics problems based on 4D variational data assimilation technique developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS). The technology is based on the multicomponent splitting method for the mathematical model of sea dynamics and the minimization of cost functionals related to the observation data by solving an optimality system that involves the adjoint equations with observation data and observation error covariances. Efficient algorithms for solving the variational data assimilation problems are presented based on modern iterative processes with a special choice of iterative parameters. The technology is illustrated for the Baltic Sea dynamics model with variational data assimilation to restore the initial states and the heat fluxes on the sea surface.

A stabilized finite element method for inverse problems subject to the convection\u2013diffusion equation. II: convection-dominated regime

We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection–diffusion equations and extend our previous analysis in Burman et al. (Numer. Math. 144:451–477, 2020) to the convection-dominated regime. Slightly adjusting the stabilized finite element method proposed for dominant diffusion, we draw upon a local error analysis to obtain quasi-optimal convergence along the characteristics of the convective field through the data set. The weight function multiplying the discrete solution is taken to be Lipschitz continuous and a corresponding super approximation result (discrete commutator property) is proven. The effect of data perturbations is included in the analysis and we conclude the paper with some numerical experiments.

On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems

Abstract Prediction of pollution in water flow is a very important task. To this end, it is imperative to be able to define the uncertainty in a model prediction. This is the purpose of sensitivity analysis whose role is to identify what uncertainty in the model outputs is attributable to the model inputs (parameters in this case). Traditionally, this is achieved by running the model perturbed by many random samples in the parameter space to determine their impact on the model outputs. It provides information on how much of the output variance is controlled by each parameter of the inputs. The theoretical results related to the procedure based adjoint approach for computing a sensitivity of the response function (RF) to changes in the input source are presented in the paper. It is shown that this approach allows to compute, by one single integration of the adjoint equation over a given time interval, a sensitivity of the RF to any source located in the domain of interest. The proposed approach is applied to the 2D Saint-Venant flow equations for modelling the water pollution problem. A numerical experiment is formulated and implemented for the Thanh Nhan Lake in Hanoi for studying a sensitivity of some RF to observations. The numerical model is constructed by applying the well-known finite-volume method. Two appropriate optimization problems are introduced and solved on the basis of the BFGS algorithm. The numerical results show the efficiency of the proposed method and confirm the theoretical findings.

The influence of the use of lignohumate on the yield and quality parameters of tomato in vegetable crop rotation

The results of the development of regulations for the use of humic growth stimulants on tomatoes in the vegetable crop rotation fertilizer system are represented in this article. The problem of effective assimilation of mineral fertilizers is central in crop production. The combination of humates with mineral fertilizers is a guarantee of their effective assimilation by the plant. The intensity of growth of tomato plants is considered one of the main indicators of the impact of agricultural practices on plants. Treatment of tomato plants with preparations Lignohumate AM and Humate +7 promotes a more intensive increase in growth rate. Recalculation of tomato yield showed that the use of growth stimulants gives a significant increase. The most effective was Lignohumate AM, the increase was 23.9%. The effectiveness of Humat +7 and Argolan Aqua were at the same level and amounted to 21.8 and 20.3%, respectively. The use of humic preparations stimulated the accumulation of dry matter in tomato fruits from 4.6-4.7% in the control to 4.9-5.1% in the experimental variants. The studied preparations had a positive effect on the productivity and quality indicators of tomato. The economic efficiency of the use of growth stimulants in tomato is high. The net profit from the application of Lignohumate AM amounted to 1,038 thousand rubles, which is 198 thousand rubles higher than the control variant. The profitability is higher than when using Humat +7 and Argolan Aqua by 30 and 42%, respectively. Based on the results of the research, it is recommended to use the humic preparation Lignohumate AM on tomatoes to increase productivity and quality indicators in the conditions of the Central part of the North Caucasian region.

Formuvannia mihratsiinoi polityky Yevropeiskoho Soiuzu ta yii zviazok z politykoiu bezpeky

The problem of international migration, especially illegal migration, is a much politicized problem in most EU member states. Countries such as Italy, France or Spain have a strong interest in reducing the influx of illegal workers into national labour markets. This anti-immigration pressure has a profound effect on the EU’s common migration policy. Immigration has become a real challenge for the countries of the European Union. Some member states, unable to cope with the problem of assimilation and integration of their immigrants, have become hostages of populist slogans in the fight against illegal migration and crime. Under the threat of an increase in the number of migrants in the EU, the question of the impossibility of gradual integration is becoming increasingly apparent. Ukraine has declared its membership in the European Union as its normative goal. In the course of strengthening Ukraine’s cooperation with the EU and Ukraine’s integration into the European community, the stability of migration legislation is necessary. Therefore, based on the experience of the European Union, Ukraine must create and implement its own legal norms and principles of the domestic legal system in accordance with the standards and principles of European law. The aim of the article is to present the evolution of European migration management policy. The article shows that migration has been inextricably linked to security issues since the beginning of European integration. However, such policies do not take into account important demographic challenges for the EU economy, especially the problem of population aging. The historical preconditions of the legal regulation of migration processes in the law of the European Union are considered, the analysis of normative documents of the EU law and in this sphere is carried out. It is concluded that the existence of a sufficiently extensive system of protection of migrants’ rights in the EU and determining their status does not guarantee a solution to the problems of such persons. Overcoming migration crises is a matter of joint efforts of the entire international community. Solving the problems of migrants must depend on the coordination of the political will of states.