Data Assimilation Fundamentals : : A Unified Formulation of the State and Parameter Estimation Problem.
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Superior document: | Springer Textbooks in Earth Sciences, Geography and Environment Series |
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Place / Publishing House: | Cham : : Springer International Publishing AG,, 2022. Ã2022. |
Year of Publication: | 2022 |
Edition: | 1st ed. |
Language: | English |
Series: | Springer Textbooks in Earth Sciences, Geography and Environment Series
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Evensen, Geir. Data Assimilation Fundamentals : A Unified Formulation of the State and Parameter Estimation Problem. 1st ed. Cham : Springer International Publishing AG, 2022. Ã2022. 1 online resource (251 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Springer Textbooks in Earth Sciences, Geography and Environment Series Intro -- Preface -- Contents -- Symbols -- List of Approximations -- 1 Introduction -- 2 Problem Formulation -- 2.1 Bayesian Formulation -- 2.1.1 Assimilation Windows -- 2.1.2 Model with Uncertain Inputs -- 2.1.3 Model State -- 2.1.4 State Vector -- 2.1.5 Formulation Over Multiple Assimilation Windows -- 2.1.6 Measurements with Errors -- 2.1.7 Bayesian Inference -- 2.2 Recursive Bayesian Formulation -- 2.2.1 Markov Model -- 2.2.2 Independent Measurements -- 2.2.3 Recursive form of Bayes' -- 2.2.4 Marginal Bayes' for Filtering -- 2.3 Error Propagation -- 2.3.1 Fokker-Planck Equation -- 2.3.2 Covariance Evolution Equation -- 2.3.3 Ensemble Predictions -- 2.4 Various Problem Formulations -- 2.4.1 General Smoother Formulation -- 2.4.2 Filter Formulation -- 2.4.3 Recursive Smoother Formulation -- 2.4.4 A Smoother Formulation for Perfect Models -- 2.4.5 Parameter Estimation -- 2.4.6 Estimating Initial Conditions, Parameters, Controls, and Errors -- 2.5 Including the Predicted Measurements in Bayes Theorem -- 3 Maximum a Posteriori Solution -- 3.1 Maximum a Posteriori (MAP) Estimate -- 3.2 Gaussian Prior and Likelihood -- 3.3 Iterative Solutions -- 3.4 Gauss-Newton Iterations -- 3.5 Incremental Form of Gauss-Newton Iterations -- 4 Strong-Constraint 4DVar -- 4.1 Standard Strong-Constraint 4DVar Method -- 4.1.1 Data-Assimilation Problem -- 4.1.2 Lagrangian Formulation -- 4.1.3 Explaining the Measurement Operator -- 4.1.4 Euler-Lagrange Equations -- 4.2 Incremental Strong-Constraint 4DVar -- 4.2.1 Incremental Formulation -- 4.2.2 Lagrangian Formulation for the Inner Iterations -- 4.2.3 Euler-Lagrange Equations for the Inner Iterations -- 4.3 Preconditioning in Incremental SC-4DVar -- 4.4 Summary of SC-4DVar -- 5 Weak Constraint 4DVar -- 5.1 Forcing Formulation -- 5.2 State-Space Formulation -- 5.3 Incremental Form of the Generalized Inverse. 5.4 Minimizing the Cost Function for the Increment -- 5.5 Observation Space Formulation -- 5.5.1 Original Representer Method -- 5.5.2 Efficient Weak-Constraint Solution in Observation Space -- 6 Kalman Filters and 3DVar -- 6.1 Linear Update from Predicted Measurements -- 6.2 3DVar -- 6.3 Kalman Filter -- 6.4 Optimal Interpolation -- 6.5 Extended Kalman Filter -- 7 Randomized-Maximum-Likelihood Sampling -- 7.1 RML Sampling -- 7.2 Approximate EKF Sampling -- 7.3 Approximate Gauss-Newton Sampling -- 7.4 Least-Squares Best-Fit Model Sensitivity -- 8 Low-Rank Ensemble Methods -- 8.1 Ensemble Approximation -- 8.2 Definition of Ensemble Matrices -- 8.3 Cost Function in the Ensemble Subspace -- 8.4 Ensemble Subspace RML -- 8.5 Ensemble Kalman Filter (EnKF) Update -- 8.6 Ensemble DA with Multiple Updating (ESMDA) -- 8.7 Ensemble 4DVar with Consistent Error Statistics -- 8.8 Square-Root EnKF -- 8.9 Ensemble Subspace Inversion -- 8.10 A Note on the EnKF Analysis Equation -- 9 Fully Nonlinear Data Assimilation -- 9.1 Particle Approximation -- 9.2 Particle Filters -- 9.2.1 The Standard Particle Filter -- 9.2.2 Proposal Densities -- 9.2.3 The Optimal Proposal Density -- 9.2.4 Other Particle Filter Schemes -- 9.3 Particle-Flow Filters -- 9.3.1 Particle Flow Filters via Likelihood Factorization -- 9.3.2 Particle Flows via Distance Minimization -- 10 Localization and Inflation -- 10.1 Background -- 10.2 Various Forms of the EnKF Update -- 10.3 Impact of Sampling Errors in the EnKF Update -- 10.3.1 Spurious Correlations -- 10.3.2 Update Confined to Ensemble Subspace -- 10.3.3 Ensemble Representation of the Measurement Information -- 10.4 Localization in Ensemble Kalman Filters -- 10.4.1 Covariance Localization -- 10.4.2 Localization in Observation Space -- 10.4.3 Localization in Ensemble Space -- 10.4.4 Local Analysis -- 10.5 Adaptive Localization. 10.6 Localization in Time -- 10.7 Inflation -- 10.8 Localization in Particle Filters -- 10.9 Summary -- 11 Methods' Summary -- 11.1 Discussion of Methods -- 11.2 So Which Method to Use? -- blackPart II Examples and Applications-1pt -- 12 A Kalman Filter with the Roessler Model -- 12.1 Roessler Model System -- 12.2 Kalman Filter with the Roessler System -- 12.3 Extended Kalman Filter with the Roessler System -- 13 Linear EnKF Update -- 13.1 EnKF Update Example -- 13.2 Solution Methods -- 13.3 Example 1 (Large Ensemble Size) -- 13.4 Example 2 (Ensemble Size of 100) -- 13.5 Example 3 (Augmenting the Measurement Perturbations) -- 13.6 Example 4 (Large Number of Measurements) -- 14 EnKF for an Advection Equation -- 14.1 Experiment Description -- 14.2 Assimilation Experiment -- 15 EnKF with the Lorenz Equations -- 15.1 The Lorenz'63 Model -- 15.2 Ensemble Smoother Solution -- 15.3 Ensemble Kalman Filter Solution -- 15.4 Ensemble Kalman Smoother Solution -- 16 3Dvar and SC-4DVar for the Lorenz 63 Model -- 16.1 Data Assimilation Set up -- 16.2 Comparing 3DVar and SC-4DVar -- 16.3 Sensitivity to Observation Density in SC-4DVar -- 16.4 3DVar and SC-4DVar with Partial Observations -- 16.5 Sensitivity to the Length of Assimilation Window -- 16.6 SC-4DVar with Multiple Assimilation Windows -- 16.7 A Comparison with Ensemble Methods -- 17 Representer Method with an Ekman-Flow Model -- 17.1 Ekman-Flow Model -- 17.2 Example Experiment -- 17.3 Assimilation of Real Measurements -- 18 Comparison of Methods on a Scalar Model -- 18.1 Scalar Model and Inverse Problem -- 18.2 Discussion of Data-Assimilation Examples -- 18.3 Summary -- 19 Particle Filter for Seismic-Cycle Estimation -- 19.1 Particle Filter for State and Parameter Estimation -- 19.2 Seismic Cycle Model -- 19.3 Data-Assimilation Experiments -- 19.4 Case A: State Estimation. 19.5 Case B: State Estimation with Increased Model Error -- 19.6 Case C: State- and Parameter Estimation -- 19.7 Summary -- 20 Particle Flow for a Quasi-Geostrophic Model -- 20.1 Introduction -- 20.2 Application to the QG Model -- 20.3 Data-Assimilation Experiment -- 20.4 Results -- 21 EnRML for History Matching Petroleum Models -- 21.1 Reservoir Modeling -- 21.2 History Matching Reservoir Models -- 21.3 Example -- 22 ESMDA with a SARS-COV-2 Pandemic Model -- 22.1 An Extended SEIR Model -- 22.2 Example -- 22.3 Sensitivity to Ensemble Size -- 22.4 Sensitivity to MDA Steps -- 22.5 Summary -- 23 Final Summary -- 23.1 Classification of the Nonlinearity -- 23.1.1 Linear to Weakly-Nonlinear Systems with Gaussian Priors -- 23.1.2 Weakly Nonlinear Systems with Gaussian Priors -- 23.1.3 Strongly Nonlinear Systems -- 23.2 Purpose of the Data Assimilation -- 23.2.1 Hindcasts and Re-analyses -- 23.2.2 Prediction Systems -- 23.2.3 Uncertainty Quantification and Risk Assessment -- 23.2.4 Model Improvement and Parameter Estimation -- 23.2.5 Scenario Forecasts and Optimal Controls -- 23.3 How to Reduce Computational Costs -- 23.4 What Will the Future Hold? -- References -- Author Index -- Author Index -- Index -- Index. Description based on publisher supplied metadata and other sources. Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. Electronic books. Vossepoel, Femke C. van Leeuwen, Peter Jan. Print version: Evensen, Geir Data Assimilation Fundamentals Cham : Springer International Publishing AG,c2022 9783030967086 ProQuest (Firm) https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6961341 Click to View |
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Evensen, Geir. |
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Evensen, Geir. Data Assimilation Fundamentals : A Unified Formulation of the State and Parameter Estimation Problem. Springer Textbooks in Earth Sciences, Geography and Environment Series Intro -- Preface -- Contents -- Symbols -- List of Approximations -- 1 Introduction -- 2 Problem Formulation -- 2.1 Bayesian Formulation -- 2.1.1 Assimilation Windows -- 2.1.2 Model with Uncertain Inputs -- 2.1.3 Model State -- 2.1.4 State Vector -- 2.1.5 Formulation Over Multiple Assimilation Windows -- 2.1.6 Measurements with Errors -- 2.1.7 Bayesian Inference -- 2.2 Recursive Bayesian Formulation -- 2.2.1 Markov Model -- 2.2.2 Independent Measurements -- 2.2.3 Recursive form of Bayes' -- 2.2.4 Marginal Bayes' for Filtering -- 2.3 Error Propagation -- 2.3.1 Fokker-Planck Equation -- 2.3.2 Covariance Evolution Equation -- 2.3.3 Ensemble Predictions -- 2.4 Various Problem Formulations -- 2.4.1 General Smoother Formulation -- 2.4.2 Filter Formulation -- 2.4.3 Recursive Smoother Formulation -- 2.4.4 A Smoother Formulation for Perfect Models -- 2.4.5 Parameter Estimation -- 2.4.6 Estimating Initial Conditions, Parameters, Controls, and Errors -- 2.5 Including the Predicted Measurements in Bayes Theorem -- 3 Maximum a Posteriori Solution -- 3.1 Maximum a Posteriori (MAP) Estimate -- 3.2 Gaussian Prior and Likelihood -- 3.3 Iterative Solutions -- 3.4 Gauss-Newton Iterations -- 3.5 Incremental Form of Gauss-Newton Iterations -- 4 Strong-Constraint 4DVar -- 4.1 Standard Strong-Constraint 4DVar Method -- 4.1.1 Data-Assimilation Problem -- 4.1.2 Lagrangian Formulation -- 4.1.3 Explaining the Measurement Operator -- 4.1.4 Euler-Lagrange Equations -- 4.2 Incremental Strong-Constraint 4DVar -- 4.2.1 Incremental Formulation -- 4.2.2 Lagrangian Formulation for the Inner Iterations -- 4.2.3 Euler-Lagrange Equations for the Inner Iterations -- 4.3 Preconditioning in Incremental SC-4DVar -- 4.4 Summary of SC-4DVar -- 5 Weak Constraint 4DVar -- 5.1 Forcing Formulation -- 5.2 State-Space Formulation -- 5.3 Incremental Form of the Generalized Inverse. 5.4 Minimizing the Cost Function for the Increment -- 5.5 Observation Space Formulation -- 5.5.1 Original Representer Method -- 5.5.2 Efficient Weak-Constraint Solution in Observation Space -- 6 Kalman Filters and 3DVar -- 6.1 Linear Update from Predicted Measurements -- 6.2 3DVar -- 6.3 Kalman Filter -- 6.4 Optimal Interpolation -- 6.5 Extended Kalman Filter -- 7 Randomized-Maximum-Likelihood Sampling -- 7.1 RML Sampling -- 7.2 Approximate EKF Sampling -- 7.3 Approximate Gauss-Newton Sampling -- 7.4 Least-Squares Best-Fit Model Sensitivity -- 8 Low-Rank Ensemble Methods -- 8.1 Ensemble Approximation -- 8.2 Definition of Ensemble Matrices -- 8.3 Cost Function in the Ensemble Subspace -- 8.4 Ensemble Subspace RML -- 8.5 Ensemble Kalman Filter (EnKF) Update -- 8.6 Ensemble DA with Multiple Updating (ESMDA) -- 8.7 Ensemble 4DVar with Consistent Error Statistics -- 8.8 Square-Root EnKF -- 8.9 Ensemble Subspace Inversion -- 8.10 A Note on the EnKF Analysis Equation -- 9 Fully Nonlinear Data Assimilation -- 9.1 Particle Approximation -- 9.2 Particle Filters -- 9.2.1 The Standard Particle Filter -- 9.2.2 Proposal Densities -- 9.2.3 The Optimal Proposal Density -- 9.2.4 Other Particle Filter Schemes -- 9.3 Particle-Flow Filters -- 9.3.1 Particle Flow Filters via Likelihood Factorization -- 9.3.2 Particle Flows via Distance Minimization -- 10 Localization and Inflation -- 10.1 Background -- 10.2 Various Forms of the EnKF Update -- 10.3 Impact of Sampling Errors in the EnKF Update -- 10.3.1 Spurious Correlations -- 10.3.2 Update Confined to Ensemble Subspace -- 10.3.3 Ensemble Representation of the Measurement Information -- 10.4 Localization in Ensemble Kalman Filters -- 10.4.1 Covariance Localization -- 10.4.2 Localization in Observation Space -- 10.4.3 Localization in Ensemble Space -- 10.4.4 Local Analysis -- 10.5 Adaptive Localization. 10.6 Localization in Time -- 10.7 Inflation -- 10.8 Localization in Particle Filters -- 10.9 Summary -- 11 Methods' Summary -- 11.1 Discussion of Methods -- 11.2 So Which Method to Use? -- blackPart II Examples and Applications-1pt -- 12 A Kalman Filter with the Roessler Model -- 12.1 Roessler Model System -- 12.2 Kalman Filter with the Roessler System -- 12.3 Extended Kalman Filter with the Roessler System -- 13 Linear EnKF Update -- 13.1 EnKF Update Example -- 13.2 Solution Methods -- 13.3 Example 1 (Large Ensemble Size) -- 13.4 Example 2 (Ensemble Size of 100) -- 13.5 Example 3 (Augmenting the Measurement Perturbations) -- 13.6 Example 4 (Large Number of Measurements) -- 14 EnKF for an Advection Equation -- 14.1 Experiment Description -- 14.2 Assimilation Experiment -- 15 EnKF with the Lorenz Equations -- 15.1 The Lorenz'63 Model -- 15.2 Ensemble Smoother Solution -- 15.3 Ensemble Kalman Filter Solution -- 15.4 Ensemble Kalman Smoother Solution -- 16 3Dvar and SC-4DVar for the Lorenz 63 Model -- 16.1 Data Assimilation Set up -- 16.2 Comparing 3DVar and SC-4DVar -- 16.3 Sensitivity to Observation Density in SC-4DVar -- 16.4 3DVar and SC-4DVar with Partial Observations -- 16.5 Sensitivity to the Length of Assimilation Window -- 16.6 SC-4DVar with Multiple Assimilation Windows -- 16.7 A Comparison with Ensemble Methods -- 17 Representer Method with an Ekman-Flow Model -- 17.1 Ekman-Flow Model -- 17.2 Example Experiment -- 17.3 Assimilation of Real Measurements -- 18 Comparison of Methods on a Scalar Model -- 18.1 Scalar Model and Inverse Problem -- 18.2 Discussion of Data-Assimilation Examples -- 18.3 Summary -- 19 Particle Filter for Seismic-Cycle Estimation -- 19.1 Particle Filter for State and Parameter Estimation -- 19.2 Seismic Cycle Model -- 19.3 Data-Assimilation Experiments -- 19.4 Case A: State Estimation. 19.5 Case B: State Estimation with Increased Model Error -- 19.6 Case C: State- and Parameter Estimation -- 19.7 Summary -- 20 Particle Flow for a Quasi-Geostrophic Model -- 20.1 Introduction -- 20.2 Application to the QG Model -- 20.3 Data-Assimilation Experiment -- 20.4 Results -- 21 EnRML for History Matching Petroleum Models -- 21.1 Reservoir Modeling -- 21.2 History Matching Reservoir Models -- 21.3 Example -- 22 ESMDA with a SARS-COV-2 Pandemic Model -- 22.1 An Extended SEIR Model -- 22.2 Example -- 22.3 Sensitivity to Ensemble Size -- 22.4 Sensitivity to MDA Steps -- 22.5 Summary -- 23 Final Summary -- 23.1 Classification of the Nonlinearity -- 23.1.1 Linear to Weakly-Nonlinear Systems with Gaussian Priors -- 23.1.2 Weakly Nonlinear Systems with Gaussian Priors -- 23.1.3 Strongly Nonlinear Systems -- 23.2 Purpose of the Data Assimilation -- 23.2.1 Hindcasts and Re-analyses -- 23.2.2 Prediction Systems -- 23.2.3 Uncertainty Quantification and Risk Assessment -- 23.2.4 Model Improvement and Parameter Estimation -- 23.2.5 Scenario Forecasts and Optimal Controls -- 23.3 How to Reduce Computational Costs -- 23.4 What Will the Future Hold? -- References -- Author Index -- Author Index -- Index -- Index. |
author_facet |
Evensen, Geir. Vossepoel, Femke C. van Leeuwen, Peter Jan. |
author_variant |
g e ge |
author2 |
Vossepoel, Femke C. van Leeuwen, Peter Jan. |
author2_variant |
f c v fc fcv l p j v lpj lpjv |
author2_role |
TeilnehmendeR TeilnehmendeR |
author_sort |
Evensen, Geir. |
title |
Data Assimilation Fundamentals : A Unified Formulation of the State and Parameter Estimation Problem. |
title_sub |
A Unified Formulation of the State and Parameter Estimation Problem. |
title_full |
Data Assimilation Fundamentals : A Unified Formulation of the State and Parameter Estimation Problem. |
title_fullStr |
Data Assimilation Fundamentals : A Unified Formulation of the State and Parameter Estimation Problem. |
title_full_unstemmed |
Data Assimilation Fundamentals : A Unified Formulation of the State and Parameter Estimation Problem. |
title_auth |
Data Assimilation Fundamentals : A Unified Formulation of the State and Parameter Estimation Problem. |
title_new |
Data Assimilation Fundamentals : |
title_sort |
data assimilation fundamentals : a unified formulation of the state and parameter estimation problem. |
series |
Springer Textbooks in Earth Sciences, Geography and Environment Series |
series2 |
Springer Textbooks in Earth Sciences, Geography and Environment Series |
publisher |
Springer International Publishing AG, |
publishDate |
2022 |
physical |
1 online resource (251 pages) |
edition |
1st ed. |
contents |
Intro -- Preface -- Contents -- Symbols -- List of Approximations -- 1 Introduction -- 2 Problem Formulation -- 2.1 Bayesian Formulation -- 2.1.1 Assimilation Windows -- 2.1.2 Model with Uncertain Inputs -- 2.1.3 Model State -- 2.1.4 State Vector -- 2.1.5 Formulation Over Multiple Assimilation Windows -- 2.1.6 Measurements with Errors -- 2.1.7 Bayesian Inference -- 2.2 Recursive Bayesian Formulation -- 2.2.1 Markov Model -- 2.2.2 Independent Measurements -- 2.2.3 Recursive form of Bayes' -- 2.2.4 Marginal Bayes' for Filtering -- 2.3 Error Propagation -- 2.3.1 Fokker-Planck Equation -- 2.3.2 Covariance Evolution Equation -- 2.3.3 Ensemble Predictions -- 2.4 Various Problem Formulations -- 2.4.1 General Smoother Formulation -- 2.4.2 Filter Formulation -- 2.4.3 Recursive Smoother Formulation -- 2.4.4 A Smoother Formulation for Perfect Models -- 2.4.5 Parameter Estimation -- 2.4.6 Estimating Initial Conditions, Parameters, Controls, and Errors -- 2.5 Including the Predicted Measurements in Bayes Theorem -- 3 Maximum a Posteriori Solution -- 3.1 Maximum a Posteriori (MAP) Estimate -- 3.2 Gaussian Prior and Likelihood -- 3.3 Iterative Solutions -- 3.4 Gauss-Newton Iterations -- 3.5 Incremental Form of Gauss-Newton Iterations -- 4 Strong-Constraint 4DVar -- 4.1 Standard Strong-Constraint 4DVar Method -- 4.1.1 Data-Assimilation Problem -- 4.1.2 Lagrangian Formulation -- 4.1.3 Explaining the Measurement Operator -- 4.1.4 Euler-Lagrange Equations -- 4.2 Incremental Strong-Constraint 4DVar -- 4.2.1 Incremental Formulation -- 4.2.2 Lagrangian Formulation for the Inner Iterations -- 4.2.3 Euler-Lagrange Equations for the Inner Iterations -- 4.3 Preconditioning in Incremental SC-4DVar -- 4.4 Summary of SC-4DVar -- 5 Weak Constraint 4DVar -- 5.1 Forcing Formulation -- 5.2 State-Space Formulation -- 5.3 Incremental Form of the Generalized Inverse. 5.4 Minimizing the Cost Function for the Increment -- 5.5 Observation Space Formulation -- 5.5.1 Original Representer Method -- 5.5.2 Efficient Weak-Constraint Solution in Observation Space -- 6 Kalman Filters and 3DVar -- 6.1 Linear Update from Predicted Measurements -- 6.2 3DVar -- 6.3 Kalman Filter -- 6.4 Optimal Interpolation -- 6.5 Extended Kalman Filter -- 7 Randomized-Maximum-Likelihood Sampling -- 7.1 RML Sampling -- 7.2 Approximate EKF Sampling -- 7.3 Approximate Gauss-Newton Sampling -- 7.4 Least-Squares Best-Fit Model Sensitivity -- 8 Low-Rank Ensemble Methods -- 8.1 Ensemble Approximation -- 8.2 Definition of Ensemble Matrices -- 8.3 Cost Function in the Ensemble Subspace -- 8.4 Ensemble Subspace RML -- 8.5 Ensemble Kalman Filter (EnKF) Update -- 8.6 Ensemble DA with Multiple Updating (ESMDA) -- 8.7 Ensemble 4DVar with Consistent Error Statistics -- 8.8 Square-Root EnKF -- 8.9 Ensemble Subspace Inversion -- 8.10 A Note on the EnKF Analysis Equation -- 9 Fully Nonlinear Data Assimilation -- 9.1 Particle Approximation -- 9.2 Particle Filters -- 9.2.1 The Standard Particle Filter -- 9.2.2 Proposal Densities -- 9.2.3 The Optimal Proposal Density -- 9.2.4 Other Particle Filter Schemes -- 9.3 Particle-Flow Filters -- 9.3.1 Particle Flow Filters via Likelihood Factorization -- 9.3.2 Particle Flows via Distance Minimization -- 10 Localization and Inflation -- 10.1 Background -- 10.2 Various Forms of the EnKF Update -- 10.3 Impact of Sampling Errors in the EnKF Update -- 10.3.1 Spurious Correlations -- 10.3.2 Update Confined to Ensemble Subspace -- 10.3.3 Ensemble Representation of the Measurement Information -- 10.4 Localization in Ensemble Kalman Filters -- 10.4.1 Covariance Localization -- 10.4.2 Localization in Observation Space -- 10.4.3 Localization in Ensemble Space -- 10.4.4 Local Analysis -- 10.5 Adaptive Localization. 10.6 Localization in Time -- 10.7 Inflation -- 10.8 Localization in Particle Filters -- 10.9 Summary -- 11 Methods' Summary -- 11.1 Discussion of Methods -- 11.2 So Which Method to Use? -- blackPart II Examples and Applications-1pt -- 12 A Kalman Filter with the Roessler Model -- 12.1 Roessler Model System -- 12.2 Kalman Filter with the Roessler System -- 12.3 Extended Kalman Filter with the Roessler System -- 13 Linear EnKF Update -- 13.1 EnKF Update Example -- 13.2 Solution Methods -- 13.3 Example 1 (Large Ensemble Size) -- 13.4 Example 2 (Ensemble Size of 100) -- 13.5 Example 3 (Augmenting the Measurement Perturbations) -- 13.6 Example 4 (Large Number of Measurements) -- 14 EnKF for an Advection Equation -- 14.1 Experiment Description -- 14.2 Assimilation Experiment -- 15 EnKF with the Lorenz Equations -- 15.1 The Lorenz'63 Model -- 15.2 Ensemble Smoother Solution -- 15.3 Ensemble Kalman Filter Solution -- 15.4 Ensemble Kalman Smoother Solution -- 16 3Dvar and SC-4DVar for the Lorenz 63 Model -- 16.1 Data Assimilation Set up -- 16.2 Comparing 3DVar and SC-4DVar -- 16.3 Sensitivity to Observation Density in SC-4DVar -- 16.4 3DVar and SC-4DVar with Partial Observations -- 16.5 Sensitivity to the Length of Assimilation Window -- 16.6 SC-4DVar with Multiple Assimilation Windows -- 16.7 A Comparison with Ensemble Methods -- 17 Representer Method with an Ekman-Flow Model -- 17.1 Ekman-Flow Model -- 17.2 Example Experiment -- 17.3 Assimilation of Real Measurements -- 18 Comparison of Methods on a Scalar Model -- 18.1 Scalar Model and Inverse Problem -- 18.2 Discussion of Data-Assimilation Examples -- 18.3 Summary -- 19 Particle Filter for Seismic-Cycle Estimation -- 19.1 Particle Filter for State and Parameter Estimation -- 19.2 Seismic Cycle Model -- 19.3 Data-Assimilation Experiments -- 19.4 Case A: State Estimation. 19.5 Case B: State Estimation with Increased Model Error -- 19.6 Case C: State- and Parameter Estimation -- 19.7 Summary -- 20 Particle Flow for a Quasi-Geostrophic Model -- 20.1 Introduction -- 20.2 Application to the QG Model -- 20.3 Data-Assimilation Experiment -- 20.4 Results -- 21 EnRML for History Matching Petroleum Models -- 21.1 Reservoir Modeling -- 21.2 History Matching Reservoir Models -- 21.3 Example -- 22 ESMDA with a SARS-COV-2 Pandemic Model -- 22.1 An Extended SEIR Model -- 22.2 Example -- 22.3 Sensitivity to Ensemble Size -- 22.4 Sensitivity to MDA Steps -- 22.5 Summary -- 23 Final Summary -- 23.1 Classification of the Nonlinearity -- 23.1.1 Linear to Weakly-Nonlinear Systems with Gaussian Priors -- 23.1.2 Weakly Nonlinear Systems with Gaussian Priors -- 23.1.3 Strongly Nonlinear Systems -- 23.2 Purpose of the Data Assimilation -- 23.2.1 Hindcasts and Re-analyses -- 23.2.2 Prediction Systems -- 23.2.3 Uncertainty Quantification and Risk Assessment -- 23.2.4 Model Improvement and Parameter Estimation -- 23.2.5 Scenario Forecasts and Optimal Controls -- 23.3 How to Reduce Computational Costs -- 23.4 What Will the Future Hold? -- References -- Author Index -- Author Index -- Index -- Index. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>08609nam a22004573i 4500</leader><controlfield tag="001">5006961341</controlfield><controlfield tag="003">MiAaPQ</controlfield><controlfield tag="005">20240229073846.0</controlfield><controlfield tag="006">m o d | </controlfield><controlfield tag="007">cr cnu||||||||</controlfield><controlfield tag="008">240229s2022 xx o ||||0 eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783030967093</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9783030967086</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(MiAaPQ)5006961341</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(Au-PeEL)EBL6961341</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1312727657</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">MiAaPQ</subfield><subfield code="b">eng</subfield><subfield code="e">rda</subfield><subfield code="e">pn</subfield><subfield code="c">MiAaPQ</subfield><subfield code="d">MiAaPQ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">GB3-5030</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Evensen, Geir.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Data Assimilation Fundamentals :</subfield><subfield code="b">A Unified Formulation of the State and Parameter Estimation Problem.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1st ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham :</subfield><subfield code="b">Springer International Publishing AG,</subfield><subfield code="c">2022.</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">Ã2022.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (251 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Springer Textbooks in Earth Sciences, Geography and Environment Series</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Intro -- Preface -- Contents -- Symbols -- List of Approximations -- 1 Introduction -- 2 Problem Formulation -- 2.1 Bayesian Formulation -- 2.1.1 Assimilation Windows -- 2.1.2 Model with Uncertain Inputs -- 2.1.3 Model State -- 2.1.4 State Vector -- 2.1.5 Formulation Over Multiple Assimilation Windows -- 2.1.6 Measurements with Errors -- 2.1.7 Bayesian Inference -- 2.2 Recursive Bayesian Formulation -- 2.2.1 Markov Model -- 2.2.2 Independent Measurements -- 2.2.3 Recursive form of Bayes' -- 2.2.4 Marginal Bayes' for Filtering -- 2.3 Error Propagation -- 2.3.1 Fokker-Planck Equation -- 2.3.2 Covariance Evolution Equation -- 2.3.3 Ensemble Predictions -- 2.4 Various Problem Formulations -- 2.4.1 General Smoother Formulation -- 2.4.2 Filter Formulation -- 2.4.3 Recursive Smoother Formulation -- 2.4.4 A Smoother Formulation for Perfect Models -- 2.4.5 Parameter Estimation -- 2.4.6 Estimating Initial Conditions, Parameters, Controls, and Errors -- 2.5 Including the Predicted Measurements in Bayes Theorem -- 3 Maximum a Posteriori Solution -- 3.1 Maximum a Posteriori (MAP) Estimate -- 3.2 Gaussian Prior and Likelihood -- 3.3 Iterative Solutions -- 3.4 Gauss-Newton Iterations -- 3.5 Incremental Form of Gauss-Newton Iterations -- 4 Strong-Constraint 4DVar -- 4.1 Standard Strong-Constraint 4DVar Method -- 4.1.1 Data-Assimilation Problem -- 4.1.2 Lagrangian Formulation -- 4.1.3 Explaining the Measurement Operator -- 4.1.4 Euler-Lagrange Equations -- 4.2 Incremental Strong-Constraint 4DVar -- 4.2.1 Incremental Formulation -- 4.2.2 Lagrangian Formulation for the Inner Iterations -- 4.2.3 Euler-Lagrange Equations for the Inner Iterations -- 4.3 Preconditioning in Incremental SC-4DVar -- 4.4 Summary of SC-4DVar -- 5 Weak Constraint 4DVar -- 5.1 Forcing Formulation -- 5.2 State-Space Formulation -- 5.3 Incremental Form of the Generalized Inverse.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5.4 Minimizing the Cost Function for the Increment -- 5.5 Observation Space Formulation -- 5.5.1 Original Representer Method -- 5.5.2 Efficient Weak-Constraint Solution in Observation Space -- 6 Kalman Filters and 3DVar -- 6.1 Linear Update from Predicted Measurements -- 6.2 3DVar -- 6.3 Kalman Filter -- 6.4 Optimal Interpolation -- 6.5 Extended Kalman Filter -- 7 Randomized-Maximum-Likelihood Sampling -- 7.1 RML Sampling -- 7.2 Approximate EKF Sampling -- 7.3 Approximate Gauss-Newton Sampling -- 7.4 Least-Squares Best-Fit Model Sensitivity -- 8 Low-Rank Ensemble Methods -- 8.1 Ensemble Approximation -- 8.2 Definition of Ensemble Matrices -- 8.3 Cost Function in the Ensemble Subspace -- 8.4 Ensemble Subspace RML -- 8.5 Ensemble Kalman Filter (EnKF) Update -- 8.6 Ensemble DA with Multiple Updating (ESMDA) -- 8.7 Ensemble 4DVar with Consistent Error Statistics -- 8.8 Square-Root EnKF -- 8.9 Ensemble Subspace Inversion -- 8.10 A Note on the EnKF Analysis Equation -- 9 Fully Nonlinear Data Assimilation -- 9.1 Particle Approximation -- 9.2 Particle Filters -- 9.2.1 The Standard Particle Filter -- 9.2.2 Proposal Densities -- 9.2.3 The Optimal Proposal Density -- 9.2.4 Other Particle Filter Schemes -- 9.3 Particle-Flow Filters -- 9.3.1 Particle Flow Filters via Likelihood Factorization -- 9.3.2 Particle Flows via Distance Minimization -- 10 Localization and Inflation -- 10.1 Background -- 10.2 Various Forms of the EnKF Update -- 10.3 Impact of Sampling Errors in the EnKF Update -- 10.3.1 Spurious Correlations -- 10.3.2 Update Confined to Ensemble Subspace -- 10.3.3 Ensemble Representation of the Measurement Information -- 10.4 Localization in Ensemble Kalman Filters -- 10.4.1 Covariance Localization -- 10.4.2 Localization in Observation Space -- 10.4.3 Localization in Ensemble Space -- 10.4.4 Local Analysis -- 10.5 Adaptive Localization.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">10.6 Localization in Time -- 10.7 Inflation -- 10.8 Localization in Particle Filters -- 10.9 Summary -- 11 Methods' Summary -- 11.1 Discussion of Methods -- 11.2 So Which Method to Use? -- blackPart II Examples and Applications-1pt -- 12 A Kalman Filter with the Roessler Model -- 12.1 Roessler Model System -- 12.2 Kalman Filter with the Roessler System -- 12.3 Extended Kalman Filter with the Roessler System -- 13 Linear EnKF Update -- 13.1 EnKF Update Example -- 13.2 Solution Methods -- 13.3 Example 1 (Large Ensemble Size) -- 13.4 Example 2 (Ensemble Size of 100) -- 13.5 Example 3 (Augmenting the Measurement Perturbations) -- 13.6 Example 4 (Large Number of Measurements) -- 14 EnKF for an Advection Equation -- 14.1 Experiment Description -- 14.2 Assimilation Experiment -- 15 EnKF with the Lorenz Equations -- 15.1 The Lorenz'63 Model -- 15.2 Ensemble Smoother Solution -- 15.3 Ensemble Kalman Filter Solution -- 15.4 Ensemble Kalman Smoother Solution -- 16 3Dvar and SC-4DVar for the Lorenz 63 Model -- 16.1 Data Assimilation Set up -- 16.2 Comparing 3DVar and SC-4DVar -- 16.3 Sensitivity to Observation Density in SC-4DVar -- 16.4 3DVar and SC-4DVar with Partial Observations -- 16.5 Sensitivity to the Length of Assimilation Window -- 16.6 SC-4DVar with Multiple Assimilation Windows -- 16.7 A Comparison with Ensemble Methods -- 17 Representer Method with an Ekman-Flow Model -- 17.1 Ekman-Flow Model -- 17.2 Example Experiment -- 17.3 Assimilation of Real Measurements -- 18 Comparison of Methods on a Scalar Model -- 18.1 Scalar Model and Inverse Problem -- 18.2 Discussion of Data-Assimilation Examples -- 18.3 Summary -- 19 Particle Filter for Seismic-Cycle Estimation -- 19.1 Particle Filter for State and Parameter Estimation -- 19.2 Seismic Cycle Model -- 19.3 Data-Assimilation Experiments -- 19.4 Case A: State Estimation.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">19.5 Case B: State Estimation with Increased Model Error -- 19.6 Case C: State- and Parameter Estimation -- 19.7 Summary -- 20 Particle Flow for a Quasi-Geostrophic Model -- 20.1 Introduction -- 20.2 Application to the QG Model -- 20.3 Data-Assimilation Experiment -- 20.4 Results -- 21 EnRML for History Matching Petroleum Models -- 21.1 Reservoir Modeling -- 21.2 History Matching Reservoir Models -- 21.3 Example -- 22 ESMDA with a SARS-COV-2 Pandemic Model -- 22.1 An Extended SEIR Model -- 22.2 Example -- 22.3 Sensitivity to Ensemble Size -- 22.4 Sensitivity to MDA Steps -- 22.5 Summary -- 23 Final Summary -- 23.1 Classification of the Nonlinearity -- 23.1.1 Linear to Weakly-Nonlinear Systems with Gaussian Priors -- 23.1.2 Weakly Nonlinear Systems with Gaussian Priors -- 23.1.3 Strongly Nonlinear Systems -- 23.2 Purpose of the Data Assimilation -- 23.2.1 Hindcasts and Re-analyses -- 23.2.2 Prediction Systems -- 23.2.3 Uncertainty Quantification and Risk Assessment -- 23.2.4 Model Improvement and Parameter Estimation -- 23.2.5 Scenario Forecasts and Optimal Controls -- 23.3 How to Reduce Computational Costs -- 23.4 What Will the Future Hold? -- References -- Author Index -- Author Index -- Index -- Index.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources.</subfield></datafield><datafield tag="590" ind1=" " ind2=" "><subfield code="a">Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. </subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vossepoel, Femke C.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">van Leeuwen, Peter Jan.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Evensen, Geir</subfield><subfield code="t">Data Assimilation Fundamentals</subfield><subfield code="d">Cham : Springer International Publishing AG,c2022</subfield><subfield code="z">9783030967086</subfield></datafield><datafield tag="797" ind1="2" ind2=" "><subfield code="a">ProQuest (Firm)</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Springer Textbooks in Earth Sciences, Geography and Environment Series</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6961341</subfield><subfield code="z">Click to View</subfield></datafield></record></collection> |