Data Assimilation (eBook)

Making Sense of Observations

William Lahoz, Boris Khattatov, Richard Menard (Herausgeber)

eBook Download: PDF

2010 | 2010
XIV, 718 Seiten
Springer Berlin (Verlag)
978-3-540-74703-1 (ISBN)

Infos

Data assimilation methods were largely developed for operational weather forecasting, but in recent years have been applied to an increasing range of earth science disciplines. This book will set out the theoretical basis of data assimilation with contributions by top international experts in the field. Various aspects of data assimilation are discussed including: theory; observations; models; numerical weather prediction; evaluation of observations and models; assessment of future satellite missions; application to components of the Earth System. References are made to recent developments in data assimilation theory (e.g. Ensemble Kalman filter), and to novel applications of the data assimilation method (e.g. ionosphere, Mars data assimilation).

William Lahoz's main interests are data assimilation and Earth Observation. He has numerous publications in leading scientific journals and book chapters. He has organized international symposia, conferences and Summer Schools, and been an invited speaker. William is an ACP editor. He contributed to the 1998 WMO Ozone Assessment. He has been on several international scientific committees. William currently leads NILU land data assimilation activities. He co-funded the UK-DARC, of which he was Deputy Director, and led the prestigious European project on Envisat data assimilation, ASSET.

Boris Khattatov' primary area of expertise involves applications of optimal control, estimation, and inverse problem theory to problems in the numerical modelling of the Earth's atmosphere and satellite data analysis. Boris led a US Air Force sponsored effort on advancing modelling capabilities for nowcasting and forecasting ionospheric 'weather'. He has numerous publications in leading scientific journals, and has contributed to books and patents.

Richard Ménard has been involved in data assimilation for nearly 20 years. Thereafter, he joined the NASA Global Modeling and Assimilation Office and then joined Environment Canada in 2000. He was awarded his Ph.D. on Kalman filtering of Burgers' equation (Roger Daley, advisor). He has made several contributions in the field of Kalman filtering, chemical data assimilation, covariance modelling, validation of assimilation systems, and chemical-dynamical coupling.

 

 

Inhalt

Contents 5
Contributors 8
Introduction 11
Part I Theory 13
Data Assimilation and Information 14
1 Introduction 14
2 Need for Information 14
3 Sources of Information 15
4 Characteristics of Information 16
5 Objective Ways of Filling in Information Gaps 17
6 Simple Examples of Data Assimilation 18
7 Benefits of Combining Information 22
8 What This Book Is About 23
References 23
Mathematical Concepts of Data Assimilation 24
1 Introduction 24
2 Data Assimilation for Non-linear Dynamical Systems 25
2.1 Basic Least-Squares Formulation for Perfect Models 25
2.2 Properties of the Basic Least-Squares Formulation 27
2.3 Best Linear Least-Squares Estimate 28
2.4 Statistical Interpretation 29
3 Sequential Data Assimilation Schemes 31
3.1 Optimal Sequential Assimilation Scheme 32
3.2 Practical Implementation 34
3.3 Ensemble Filters and Sampling Methods 35
4 Four-Dimensional Variational Assimilation Schemes 36
4.1 4D-Var and the Adjoint Method 36
4.2 Incremental Variational Methods 38
4.3 Control Variable Transforms 39
4.4 Model Reduction 40
5 Data Assimilation for Dynamical Systems with Model Errors 41
5.1 Least-Squares Formulation for Models with Errors 41
5.2 Optimal Solution of the Assimilation Problem 43
5.3 Systematic Model Error and State Augmentation 44
5.4 Data Assimilation for Parameter Estimation 46
6 Conclusions 47
References 47
Variational Assimilation 51
1 Introduction 51
2 Variational Assimilation in the Context of Statistical Linear Estimation 52
3 Minimization Methods: The Adjoint Approach 59
3.1 Gradient Methods for Minimization 59
3.2 The Adjoint Method 60
4 Practical Implementation 64
4.1 The Incremental Approach 65
4.2 First-Guess-At-the-Right-Time 3D-Var 66
5 Further Considerations on Variational Assimilation 67
6 More on the Adjoint Method 71
7 Conclusion 73
References 74
Ensemble Kalman Filter: Current Status and Potential 78
1 Introduction 78
2 Brief Review of Ensemble Kalman Filtering 79
LETKF Algorithm 83
3 Adaptation of 4D-Var Techniques into EnKF 84
3.1 4D-LETKF and No-Cost Smoother 85
3.2 Application of the No-Cost Smoother to the Acceleration of the Spin-Up 86
3.3 ''Outer Loop'' and Dealing with Non-linear Ensemble Perturbations 89
3.4 Adjoint Forecast Sensitivity to Observations Without Adjoint Model 91
3.5 Use of a Lower Resolution Analysis 93
3.6 Model and Observational Error 95
4 Summary and Discussion 96
References 98
Error Statistics in Data Assimilation: Estimation and Modelling 102
1 Introduction 102
1.1 Source of Statistical Information 103
1.2 Importance of Background and Observation Error Statistics in Data Assimilation 103
2 Estimation of Background and Observation Error Statistics 104
2.1 Estimation of Background and Observation Error Statistics from Innovations 104
2.2 Estimation of Background Error Covariances with the Lagged-Forecast (NMC) Method 106
2.3 Estimation of Background Error Covariances with Monte Carlo Approaches 106
2.4 Other Approaches for the Estimation of Background Error Covariances 107
2.5 Estimation of Observation-Error Correlations 108
3 Modelling Error Covariances 110
3.1 Spectral Representation: Homogeneous and Isotropic Error Correlations 110
3.2 Physical-Space Representation 111
3.3 Spectral/Physical-Space Representation 112
3.4 Theoretically-Based Correlation Modelling 112
4 Illustrative Examples 114
4.1 Estimated Error Variances 114
4.2 Single Observation Experiments 115
5 Summary 118
References 119
Bias Estimation 122
1 Introduction 122
2 Detection of Bias 123
2.1 Bias Detection Using Innovations 123
2.2 Bias Detection Using Analysis Increments 124
3 Bias Analysis 126
3.1 Variational Formulation 127
3.2 Sequential Formulation 129
4 Observation Bias Correction Schemes 131
4.1 Static Bias Correction Scheme 131
4.2 Adaptive Off-Line Bias Correction Scheme 133
4.3 Adaptive On-Line Bias Correction Scheme or Variational Correction Scheme 133
5 Model Bias Correction Schemes 134
5.1 Static Schemes 134
5.2 Dynamical Schemes 136
6 Conclusions 141
References 142
The Principle of Energetic Consistency in Data Assimilation 145
1 Introduction 145
1.1 Applications 146
1.2 Theory 149
2 The Principle of Energetic Consistency: Some Applications 150
2.1 The Principle of Energetic Consistency 150
2.2 Minimum Variance State Estimation 153
2.3 Discretization 158
2.4 Application to Ensemble Kalman Filter Methods 161
2.4.1 General Formulation 161
2.4.2 Ensemble Behaviour Between Observation Times 163
2.4.3 Ensemble Behaviour at Observation Times 164
2.4.4 Ensemble Behaviour for Dissipative Models 166
3 The Principle of Energetic Consistency 171
3.1 Problem Setting 171
3.2 Scalar and Hilbert Space-Valued Random Variables 172
3.3 The Principle of Energetic Consistency in Hilbert Space 175
3.4 A Natural Restriction on S 176
4 The Principle of Energetic Consistency for Differential Equations 178
4.1 Ordinary Differential Equations 178
4.2 Symmetric Hyperbolic Partial Differential Equations 181
4.2.1 The Deterministic Initial-Value Problem 181
4.2.2 The Solution Operator 185
4.2.3 The Stochastic Initial-Value Problem 186
5 The Shallow-Water Equations 189
6 Concluding Remarks 192
Appendix 1: Random Variables Taking Values in Hilbert Space 194
1a H-Valued Random Variables 194
1b Second-Order H-Valued Random Variables 196
1c Properties of Second-Order H-Valued Random Variables 197
1d Construction of Second-Order H-Valued Random Variables 201
Appendix 2: The Hilbert Spaces 206
2a Construction of the Hilbert Spaces 206
2b The Case 209
Appendix 3: Some Basic Concepts and Definitions 214
3a Measure Spaces 214
3b Integration 215
3c Probability 218
3d Hilbert Space 220
References 223
Evaluation of Assimilation Algorithms 225
1 Introduction 225
2 Reminder on Statistical Linear Estimation 226
3 Objective Evaluation of Assimilation Algorithms 230
4 Estimation of the Statistics of Data Errors 232
5 Diagnostics of Internal Consistency 233
6 Diagnostics of Optimality of Assimilation Algorithms 245
7 Conclusions 246
References 247
Initialization 249
1 Introduction 249
2 Early Initialization Methods 251
2.1 The Filtered Equations 251
2.2 Static Initialization 251
2.3 Dynamic Initialization 252
2.4 Variational Initialization 252
3 Atmospheric Normal Mode Oscillations 253
3.1 The Laplace Tidal Equations 253
3.2 Vorticity and Divergence 254
3.3 Rossby-Haurwitz Modes 255
3.4 Gravity Wave Modes 256
4 Normal Mode Initialization 257
5 Digital Filter Initialization 258
5.1 Design of Non-recursive Filters 259
5.2 Application of a Non-recursive Digital Filter to Initialization 261
5.3 Initialization Example 262
5.4 Benefits for the Data Assimilation Cycle 264
6 Constraints in 4D-Var 264
7 Conclusion 266
References 267
Part II Observations 269
The Global Observing System 270
1 Introduction 270
2 In Situ Observations 270
2.1 Surface and Marine Observations 271
2.2 Radiosondes 272
2.3 Aircraft Observations 274
2.4 Targeted Observing 275
3 Remote Sensing Observations 276
3.1 Passive Technologies 278
3.1.1 Atmospheric Sounding Channels from Passive Instruments 279
3.1.2 Surface Sensing Channels from Passive Instruments 280
3.2 Active Technologies 281
3.2.1 Surface Instruments 281
3.2.2 Atmospheric Sensing Instruments 282
3.3 Limb Technologies 282
3.3.1 Limb Passive Sounders 283
3.3.2 GPS Technologies 283
4 Evolution of the Global Observing System 284
4.1 Development of the In Situ Component of the GOS 284
4.2 Development of the Space Component of the GOS 285
5 Concluding Remarks 286
References 287
Assimilation of Operational Data 289
1 Introduction 289
2 Assimilation of Radiance Observations 289
2.1 Constraints on the Inversion of Radiance Data 290
2.2 Non-linear Dependence on the Background Humidity Field 291
2.3 Temperature/Humidity Partitioning of Radiance Increments 292
2.4 Passive Tracer Analysis 294
3 Assimilation of Hourly Surface Pressure Measurements 294
3.1 Synoptic Analysis of Rapidly Developing Storm Using Surface-Pressure Data from a Single Station 295
3.2 Background Errors in Observable Quantities 296
4 Variational Quality Control of Observations with Non-Gaussian Errors 297
4.1 Probability Density Function of Observation Error 297
4.2 Variational Quality Control 298
4.3 The Need for Realistic Background Error Specification 300
5 Impact of Observations on the Quality of Numerical Forecasts 300
6 Final Remarks 302
References 303
Research Satellites 306
1 Introduction 306
2 Observations 306
3 Research Satellite Data 307
3.1 General Considerations 307
3.2 Research Satellites 309
3.3 Benefits of Research Satellites 316
3.4 Research Satellites and the Global Climate Observing System 317
3.5 Capacity Report for Satellite Missions 318
3.5.1 Capabilities 319
3.5.2 Limitations 320
3.5.3 Conclusions 321
4 Data Assimilation of Research Satellites 321
5 Future Prospects 324
References 324
Part III Meteorology and Atmospheric Dynamics 327
General Concepts in Meteorology and Dynamics 328
1 Introduction 328
2 The Atmospheric Circulation 328
2.1 General Details 328
2.2 Influence of Rotation 331
3 General Circulation in the Troposphere 335
3.1 The Thermally-Driven Circulation in the Tropics 335
3.2 Angular Momentum Balance 336
3.3 Rossby Waves and Mid Latitude Systems 337
3.4 The Extra-Tropical Meridional Circulation 340
3.5 Other Tropical Circulations 341
4 General Circulation in the Middle Atmosphere: The BrewerDobson Circulation 343
4.1 Introduction to the Middle Atmosphere 343
4.2 Winter and Summer Stratosphere 344
4.3 Humidity 347
4.4 Ozone 349
4.5 Interaction Between Dynamics, Radiation and Chemistry 350
5 Conclusions 350
References 351
The Role of the Model in the Data Assimilation System 353
1 Introduction 353
2 Definition and Description of the Model 353
3 The Role of the Model in Data Assimilation 357
4 Component Structure of an Atmospheric Model 362
5 Consideration of the Observation-Model Interface 369
6 Physical Consistency and Data Assimilation 372
Example 1: Observational Correction to the Thermodynamic Equation 374
Example 2: Horizontal Divergence and the Vertical Wind 376
7 Summary 379
References 380
Numerical Weather Prediction 382
1 Introduction 382
2 Observations 383
2.1 Operational Observing System 383
2.2 Quality Control 384
3 Data Assimilation 386
3.1 Introduction 386
3.2 Variational Methods 387
3.3 Assimilation of Satellite Soundings 390
3.4 Ensemble Assimilation Methods 391
4 Numerical Modelling 393
4.1 Development of Numerical Models 393
4.2 Model Configurations 394
5 Ensemble Forecasting 395
5.1 Benefits of Ensemble Forecasts 395
5.2 Initial Condition Perturbations 396
5.3 Accounting for Model Errors 397
6 Forecast Products 399
6.1 Weather Forecasts 399
6.2 Site-Specific Information 400
6.3 Probabilistic Forecasts 401
6.4 Warnings of High-Impact Weather 402
6.5 Improving the Prediction of High-Impact Weather 404
7 Conclusions 405
References 405
Part IV Atmospheric Chemistry 408
Introduction to Atmospheric Chemistry and Constituent Transport 409
1 Importance of Chemistry 409
2 Atmospheric Processes Affecting the Composition 410
2.1 Elementary Chemical Processes 411
2.2 Stratospheric Chemistry 413
2.3 Tropospheric Chemistry 414
2.4 Surface Emissions 417
2.5 Transport of Chemicals from Sources in the PBL and Convection 420
2.6 Circulation and Transport 421
2.6.1 Tropospheric Circulation and Mixing 422
2.6.2 Stratospheric Circulation and Mixing 424
2.6.3 Transport and Chemistry Across the Tropopause 426
3 Summary 429
References 429
Representation and Modelling of Uncertainties in Chemistry and Transport Models 431
1 Introduction 431
2 Linear Formalism for Error Evolution in Box Chemical Models 432
3 Variance Evolution and Applications to Measurement Information Content 437
4 Error Representation in 3-D Chemistry-Transport Models 442
5 Discussion 445
References 447
Constituent Assimilation 449
1 Introduction 449
2 GCM-Based Approaches 454
2.1 Introduction 454
2.2 Assimilation of Humidity 455
2.3 Assimilation of Ozone 456
3 Chemical Model Approaches 462
4 Evaluation of Models, Observations and Analyses 467
5 Applications 472
5.1 Tropospheric Pollution 472
5.2 Analyses of Constituents 473
5.3 Stratospheric Ozone Monitoring 478
5.4 Ozone Forecasting 480
6 Future Directions 481
References 483
Inverse Modelling and Combined State-Source Estimation for Chemical Weather 491
1 Introduction 491
1.1 General Remarks 491
1.2 Features of Tropospheric Chemical Data Assimilation 492
1.3 Observations 494
2 Spatio-Temporal Data Assimilation Studies 495
2.1 Tropospheric Gas Phase Data Assimilation 495
2.2 Tropospheric Aerosol Data Assimilation 498
3 Advanced Methods in Tropospheric Chemistry Data Assimilation 499
3.1 Kalman Filter Equations 499
3.2 Ensemble Kalman Filter 500
3.3 Reduced Rank Square Root Kalman Filter 501
3.4 4D Variational Data Assimilation 502
3.5 Implementation of a Chemical 4D-Var System 504
4 Examples 504
4.1 Nested Application of 4D-Var 505
4.2 Emission Rate Estimates 506
4.3 Tropospheric Satellite Data Assimilation 508
4.4 Aerosol Assimilation 509
5 Outlook 510
References 511
Part V Wider Applications 514
Ocean Data Assimilation 515
1 Introduction to the Ocean Circulation 515
2 Ocean Modelling Methods 517
3 Observational Ocean Data 520
4 Ocean Data Assimilation: Applications and Current Issues 526
5 Altimeter Data Assimilation 529
5.1 General Considerations 529
5.2 Physical Relationships Between Variables 531
6 In Situ Temperature and Salinity Assimilation 538
7 Future Prospects for Ocean Data Assimilation 541
References 541
Land Surface Data Assimilation 546
1 Introduction 546
2 Background: Land Surface Observations 547
3 Background: Land Surface Modelling 549
4 History of Land Surface Data Assimilation 550
4.1 Early Land Surface State Estimation Studies 552
4.2 Data Assimilation Beyond State Estimation 553
5 General Concept of Land Surface Data Assimilation 554
5.1 Direct Observer Assimilation 555
5.2 Dynamic Observer Assimilation 556
5.3 Features of Data Assimilation 557
5.4 Quality Control for Data Assimilation 558
5.5 Validation Using Data Assimilation 559
6 Land Surface Data Assimilation Techniques 560
6.1 Land Surface System 560
6.2 Direct Observer Data Assimilation 562
6.3 Dynamic Observer Assimilation Methods 568
6.4 Challenges in Land Surface Data Assimilation 569
7 Assimilation of Land Surface Observations 569
7.1 Soil Moisture Observations 570
7.1.1 Direct Insertion 570
7.1.2 Statistical Correction, Nudging, Optimal Interpolation 570
7.1.3 Kalman Filter 571
7.1.4 3D/4D-Var 575
7.2 Soil Temperature Observations 576
7.3 Low-Level Atmospheric Observations 577
7.4 Land Surface Flux Observations 577
7.5 Vegetation-Based Observations 578
7.6 Discharge Observations 578
7.7 Snow Water Equivalent/Snow Cover Observations 578
7.8 Ground Water Storage Observations 579
8 Case Studies 580
8.1 Case Study 1: Soil Moisture Assimilation 580
8.2 Case Study 2: Streamflow Assimilation 581
8.3 Case Study 3: Snow Assimilation 583
8.4 Case Study 4: Skin Temperature Assimilation 585
9 Summary 586
References 587
Assimilation of GPS Soundings in Ionospheric Models 595
1 Introduction 595
2 Background 596
3 Overview of Ionospheric Processes 597
3.1 Elementary Processes 597
3.2 Transport and Solar Effects 600
4 Modelling the Ionosphere 602
5 GPS Data 605
6 Ionospheric Data Assimilation 606
7 Impact of Ionosphere on Telecommunications, Scintillations 608
8 Application to Single-Frequency GPS Positioning 610
9 Future Directions 613
References 614
Part VI The Longer View 616
Reanalysis: Data Assimilation for Scientific Investigation of Climate 617
1 Introduction 617
2 Special Aspects of the Reanalysis Problem 619
3 Lessons from Applications 627
4 Summary 636
5 Web Resources 637
References 637
Observing System Simulation Experiments 641
1 Definition and Motivation of OSSEs 641
2 Historical Summary of OSSEs 644
3 The Nature Run 647
3.1 Characteristics of the Nature Run 647
3.2 Evaluation and Potential Adjustment of the Nature Run 648
3.3 Requirements for a Future Nature Run 650
4 Assignment of Realistic Observation Errors 651
5 Simulation of Observations 654
5.1 Basic Guidelines 654
5.2 Specific Issues Related to Different Observational Types 656
5.2.1 Simulation of Conventional Observations 657
5.2.2 Simulation of Radiance Data 658
5.2.3 Simulation of Doppler Wind Lidar (DWL) Data 659
6 Initial Conditions and Spin-Up Period 660
6.1 Initial Conditions 660
6.2 Spin-Up Period 661
7 Evaluation of OSSE Results 662
7.1 Data Denial (or Adding) Experiments (DDEs) 662
7.2 Adjoint--Based Techniques 663
8 Calibration of OSSEs 664
9 Experiences from the NCEP OSSE 665
9.1 Background of the NCEP OSSE 665
9.2 Calibration Performed for NCEP OSSE 665
9.3 Evaluation of DWL Impact Using the NCEP OSSE 667
10 Summary and Concluding Remarks for OSSEs 668
References 670
Data Assimilation for Other Planets 674
1 Introduction 674
2 Motivation for the Assimilation of Extra-Terrestrial Data 675
3 Data Assimilation for the Atmosphere of Mars 676
3.1 Data Assimilation Schemes for Mars 679
3.2 Results from Martian Data Assimilation 681
4 Future Prospects for Other Planets 687
5 Implications for Terrestrial Data Assimilation 688
References 689
Appendix 693
List of Acronyms 693
Index 697

Produkt-Details

• Erscheint lt. Verlag: 23.7.2010
• Zusatzinfo: XIV, 718 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geografie / Kartografie
• Themenwelt: Technik
• Schlagworte: air pollution and air quality • algorithm • algorithms • atmospheric chemistry • Chemistry • Climate • Data Assimilation • earth system • Ensemble Kalman Filter • meteorology • Model • Modeling • Numerical weather prediction • ocean • Operational weather forcecasting • Remote Sensing/Photogrammetry • Satellite • Simulation • Statistics • Weather • Weather forecasting
• ISBN-10: 3-540-74703-6 / 3540747036
• ISBN-13: 978-3-540-74703-1 / 9783540747031