LEADER 03470nam 2200553Ia 450 001 9910786161003321 005 20200520144314.0 010 $a1-283-94037-X 010 $a1-4422-0489-3 035 $a(CKB)2670000000329164 035 $a(EBL)1043754 035 $a(SSID)ssj0000804486 035 $a(PQKBManifestationID)12380803 035 $a(PQKBTitleCode)TC0000804486 035 $a(PQKBWorkID)10814466 035 $a(PQKB)11280351 035 $a(MiAaPQ)EBC1043754 035 $a(Au-PeEL)EBL1043754 035 $a(CaPaEBR)ebr10643311 035 $a(CaONFJC)MIL425287 035 $a(OCoLC)747306219 035 $a(EXLCZ)992670000000329164 100 $a20100709d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAmerica's beginnings$b[electronic resource] $ethe dramatic events that shaped a nation's character /$fTony Williams 210 $aLanham, MD $cRowman & Littlefield Publishers ;$aWilliamsburg, VA $cin association with The Colonial Williamsburg Foundation$dc2010 215 $a1 online resource (209 p.) 300 $aDescription based upon print version of record. 311 $a1-4422-0488-5 311 $a1-4422-0487-7 320 $aIncludes bibliographical references (p. 175-187) and index. 327 $aAmerica'a Beginnings; Contents; Preface and Acknowledgments; Part I. Settlement; 1. Lost Colony; 2. Jamestown; 3. Starving Time; 4. First Representative Legislature in Britain's New World; 5. First Africans; 6. Mayflower Compact; 7. City Upon a Hill; 8. Indian Uprising of 1622; 9. Dissents of Anne Hutchinson and Roger Williams; 10. Pequot War; Part II. Colonies; 11. King Philip's War; 12. Bacon's Rebellion; 13. Glorious Revolution in America; 14. Salem Witch Trials; 15. Boston Smallpox Epidemic of 1721; 16. Great Awakening; 17. Benjamin Franklin and the Lightning Rod; 18. Albany Plan of Union 327 $a19. Great Meadows20. Braddock's March; 21. Royal Proclamation of 1763; Part III. Resistance; 22. Stamp Act; 23. Townshend Acts; 24. Boston Massacre; 25. Boston Tea Party; 26. Continental Congress; 27. Give Me Liberty or Give Me Death; Part IV. War; 28. Lexington and Concord; 29. Bunker Hill; 30. Fort Ticonderoga; 31. Common Sense; 32. Declaration of Rights; 33. Declaration of Independence; 34. Crossing the Delaware; 35. Saratoga; 36. French Alliance; 37. Valley Forge; 38. Guilford Courthouse; 39. Yorktown; 40. Newburgh Conspiracy; 41. Peace Treaty of 1783 327 $a42. Washington Surrenders His CommissionPart V. Nationhood; 43. Virginia Statute for Religious Freedom; 44. Annapolis Convention; 45. Shays' Rebellion; 46. Constitutional Convention; 47. Ratifying Conventions; 48. The Federalist; 49. Inauguration of George Washington; 50. Bill of Rights; Bibliography; Index 330 $aAt a time when surveys reveal that Americans know less and less about our past, Tony Williams provides entertaining and informative descriptions of 50 key events-some known and some forgotten-that shaped colonial and revolutionary America, from the Mayflower Compact to the Annapolis Convention. 607 $aUnited States$xHistory$yColonial period, ca. 1600-1775 676 $a973.2 700 $aWilliams$b Tony$f1970-$01531757 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786161003321 996 $aAmerica's beginnings$93777647 997 $aUNINA LEADER 10816nam 22006973u 450 001 9910564680903321 005 20250606212713.0 010 $a3-030-96709-3 035 $a(CKB)5700000000081231 035 $aEBL6961341 035 $a(OCoLC)1312727657 035 $a(AU-PeEL)EBL6961341 035 $a(MiAaPQ)EBC6961341 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/81696 035 $a(PPN)262170469 035 $a(Au-PeEL)EBL6961341 035 $a(oapen)doab81696 035 $a(EXLCZ)995700000000081231 100 $a20250630d2022 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aData Assimilation Fundamentals $eA Unified Formulation of the State and Parameter Estimation Problem 205 $a1st ed. 210 $aCham $cSpringer International Publishing AG$d2022 215 $a1 online resource (251 p.) 225 1 $aSpringer Textbooks in Earth Sciences, Geography and Environment 300 $aDescription based upon print version of record. 311 08$a3-030-96708-5 327 $aIntro -- 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. 327 $a5.4 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. 327 $a10.6 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. 327 $a19.5 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. 330 $aThis open-access textbook's significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. Unique for this book is the "top-down" derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today's popular data-assimilation methods. This strategy is the opposite of most textbooks and reviews on data assimilation that typically take a bottom-up approach to derive a particular assimilation method. E.g., the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter. The bottom-up approach derives the assimilation methods from different mathematical principles, making it difficult to compare them. Thus, it is unclear which assumptions are made to derive an assimilation method and sometimes even which problem it aspires to solve. The book's top-down approach allows categorizing data-assimilation methods based on the approximations used. This approach enables the user to choose the most suitable method for a particular problem or application. Have you ever wondered about the difference between the ensemble 4DVar and the "ensemble randomized likelihood" (EnRML) methods? Do you know the differences between the ensemble smoother and the ensemble-Kalman smoother? Would you like to understand how a particle flow is related to a particle filter? In this book, we will provide clear answers to several such questions. The book provides the basis for an advanced course in data assimilation. It focuses on the unified derivation of the methods and illustrates their properties on multiple examples. It is suitable for graduate students, post-docs, scientists, and practitioners working in data assimilation. 410 0$aSpringer Textbooks in Earth Sciences, Geography and Environment 606 $aEarth sciences$2bicssc 606 $aProbability & statistics$2bicssc 606 $aBayesian inference$2bicssc 610 $aData Assimilation 610 $aParameter Estimation 610 $aEnsemble Kalman Filter 610 $a4DVar 610 $aRepresenter Method 610 $aEnsemble Methods 610 $aParticle Filter 610 $aParticle Flow 615 7$aEarth sciences 615 7$aProbability & statistics 615 7$aBayesian inference 700 $aEvensen$b Geir$01239450 701 $aVossepoel$b Femke C$01239451 701 $aLeeuwen$b Peter Jan van$0755603 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9910564680903321 996 $aData Assimilation Fundamentals$93008730 997 $aUNINA