Data Assimilation for the Geosciences: From Theory to Application, Second Edition brings together all of the mathematical and statistical background knowledge needed to formulate data assimilation systems into one place. It includes practical exercises enabling readers to apply theory in both a theoretical formulation as well as teach them how to code the theory with toy problems to verify their understanding. It also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to land surface, the atmosphere, ocean and other geophysical situations. The second edition of Data Assimilation for the Geosciences has been revised with up to date research that is going on in data assimilation, as well as how to apply the techniques. The new edition features an introduction of how machine learning and artificial intelligence are interfacing and aiding data assimilation. In addition to appealing to students and researchers across the geosciences, this now also appeals to new students and scientists in the field of data assimilation as it will now have even more information on the techniques, research, and applications, consolidated into one source.
1. Chapter 1 : Introduction - p. Page vii 2. Chapter 2 : Overview of Linear Algebra - p. Page 6 3. Chapter 3 : Univariate Distribution Theory - p. Page 29 4. Chapter 4 : Multivariate Distribution Theory - p. Page 132 5. Chapter 5 : Introduction to Calculus of Variation - p. Page 173 6. Chapter 6 : Introduction to Control Theory - p. Page 208 7. Chapter 7 : Optimal Control Theory - p. Page 246 8. Chapter 8 : Numerical Solutions to Initial Value Problems - p. Page 284 9. Chapter 9 : Numerical Solutions to Boundary Value Problems - p. Page 326 10. Chapter 10 : Introduction to Semi-Lagrangian Advection Methods - p. Page 370 11. Chapter 11 : Introduction to Finite Element Modeling - p. Page 443 12. Chapter 12 : Numerical Modeling on the Sphere - p. Page 484 13. Chapter 13 : Tangent Linear Modeling and Adjoints - p. Page 555 14. Chapter 14 : Observations - p. Page 599 15. Chapter 15 : Non-Variational Sequential Data Assimilation Methods - p. Page 629 16. Chapter 16 : Variational Data Assimilation - p. Page 675 17. Chapter 17 : Subcomponents of Variational Data Assimilation - p. Page 733 18. Chapter 18 : Observation Space Variational Data Assimilation Methods - p. Page 784 19. Chapter 19 : Kalman Filter and Smoother - p. Page 795 20. Chapter 20 : Ensemble-Based Data Assimilation - p. Page 813 21. Chapter 21 : Non-Gaussian Based Data Assimilation - p. Page 863 22. Chapter 22 : Markov Chain Monte Carlo, Particle Filters, Particle Smoothers, and Sigma Point Filters - p. Page 929 23. Chapter 23 : Lagrangian Data Assimilation - p. Page 963 24. Chapter 24 : Artificial Intelligence and Data Assimilation - p. Page 983 25. Chapter 25 : Applications of Data Assimilation in the Geosciences - p. Page 1017 26. Chapter 26 : Solutions to Select Exercise - p. Page 1065 27. Bibliography - p. Page 1071 28. Index - p. Page 1071
Data Assimilation for the Geosciences: From Theory to Application, Second Edition brings together all of the mathematical and statistical background knowledge needed to formulate data assimilation systems into one place. It includes practical exercises enabling readers to apply theory in both a theoretical formulation as well as teach them how to code the theory with toy problems to verify their understanding. It also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to land surface, the atmosphere, ocean and other geophysical situations. The second edition of Data Assimilation for the Geosciences has been revised with up to date research that is going on in data assimilation, as well as how to apply the techniques. The new edition features an introduction of how machine learning and artificial intelligence are interfacing and aiding data assimilation. In addition to appealing to students and researchers across the geosciences, this now also appeals to new students and scientists in the field of data assimilation as it will now have even more information on the techniques, research, and applications, consolidated into one source.
1. Chapter 1 : Introduction - p. Page vii 2. Chapter 2 : Overview of Linear Algebra - p. Page 6 3. Chapter 3 : Univariate Distribution Theory - p. Page 29 4. Chapter 4 : Multivariate Distribution Theory - p. Page 132 5. Chapter 5 : Introduction to Calculus of Variation - p. Page 173 6. Chapter 6 : Introduction to Control Theory - p. Page 208 7. Chapter 7 : Optimal Control Theory - p. Page 246 8. Chapter 8 : Numerical Solutions to Initial Value Problems - p. Page 284 9. Chapter 9 : Numerical Solutions to Boundary Value Problems - p. Page 326 10. Chapter 10 : Introduction to Semi-Lagrangian Advection Methods - p. Page 370 11. Chapter 11 : Introduction to Finite Element Modeling - p. Page 443 12. Chapter 12 : Numerical Modeling on the Sphere - p. Page 484 13. Chapter 13 : Tangent Linear Modeling and Adjoints - p. Page 555 14. Chapter 14 : Observations - p. Page 599 15. Chapter 15 : Non-Variational Sequential Data Assimilation Methods - p. Page 629 16. Chapter 16 : Variational Data Assimilation - p. Page 675 17. Chapter 17 : Subcomponents of Variational Data Assimilation - p. Page 733 18. Chapter 18 : Observation Space Variational Data Assimilation Methods - p. Page 784 19. Chapter 19 : Kalman Filter and Smoother - p. Page 795 20. Chapter 20 : Ensemble-Based Data Assimilation - p. Page 813 21. Chapter 21 : Non-Gaussian Based Data Assimilation - p. Page 863 22. Chapter 22 : Markov Chain Monte Carlo, Particle Filters, Particle Smoothers, and Sigma Point Filters - p. Page 929 23. Chapter 23 : Lagrangian Data Assimilation - p. Page 963 24. Chapter 24 : Artificial Intelligence and Data Assimilation - p. Page 983 25. Chapter 25 : Applications of Data Assimilation in the Geosciences - p. Page 1017 26. Chapter 26 : Solutions to Select Exercise - p. Page 1065 27. Bibliography - p. Page 1071 28. Index - p. Page 1071
