Data Assimilation for the Geosciences. From Theory to Application

Description

Data Assimilation for the Geosciences: From Theory to Application brings together all of the mathematical,statistical, and probability background knowledge needed to formulate data assimilation systems in one place. It includes practical exercises for understanding theoretical formulation and presents some aspects of coding the theory with a toy problem. The book also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to the atmosphere, oceans, as well as the land surface and other geophysical situations. It offers a comprehensive presentation of the subject, from basic principles to advanced methods, such as Particle Filters and Markov-Chain Monte-Carlo methods. Additionally, Data Assimilation for the Geosciences: From Theory to Application covers the applications of data assimilation techniques in various disciplines of the geosciences, making the book useful to students, teachers, and research scientists. Content: Front Matter,CopyrightEntitled to full textChapter 1 - Introduction, Pages 1-4 Chapter 2 - Overview of Linear Algebra, Pages 5-27 Chapter 3 - Univariate Distribution Theory, Pages 29-124 Chapter 4 - Multivariate Distribution Theory, Pages 125-161 Chapter 5 - Introduction to Calculus of Variation, Pages 163-196 Chapter 6 - Introduction to Control Theory, Pages 197-234 Chapter 7 - Optimal Control Theory, Pages 235-272 Chapter 8 - Numerical Solutions to Initial Value Problems, Pages 273-315 Chapter 9 - Numerical Solutions to Boundary Value Problems, Pages 317-360 Chapter 10 - Introduction to Semi-Lagrangian Advection Methods, Pages 361-441 Chapter 11 - Introduction to Finite Element Modeling, Pages 443-482 Chapter 12 - Numerical Modeling on the Sphere, Pages 483-554 Chapter 13 - Tangent Linear Modeling and Adjoints, Pages 555-598 Chapter 14 - Observations, Pages 599-626 Chapter 15 - Non-variational Sequential Data Assimilation Methods, Pages 627-671 Chapter 16 - Variational Data Assimilation, Pages 673-703 Chapter 17 - Subcomponents of Variational Data Assimilation, Pages 705-751 Chapter 18 - Observation Space Variational Data Assimilation Methods, Pages 753-763 Chapter 19 - Kalman Filter and Smoother, Pages 765-782 Chapter 20 - Ensemble-Based Data Assimilation, Pages 783-821 Chapter 21 - Non-Gaussian Variational Data Assimilation, Pages 823-868 Chapter 22 - Markov Chain Monte Carlo and Particle Filter Methods, Pages 869-885 Chapter 23 - Applications of Data Assimilation in the Geosciences, Pages 887-916 Chapter 24 - Solutions to Select Exercise, Pages 917-922 Bibliography, Pages 923-939 Index, Pages 941-957