Data Assimilation for the Geosciences: From Theory to Application

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.

Includes practical exercises, enabling readers to apply concepts in a theoretical formulationOffers explanations for how to code certain parts of the theoryPresents a step-by-step guide on how, and why, data assimilation works and can be used

1: Introduction 2: Overview of Linear Algebra 3: Univariate Distribution Theory 4: Multivariate Distribution Theory 5: Introduction to Calculus of Variation 6: Introduction to Control Theory 7: Optimal Control Theory 8: Numerical Solutions to Initial Value Problems 9: Numerical Solutions to Boundary Value Problems 10: Introduction to Semi-Lagrangian Advection Methods 11: Introduction to Finite Element Modeling 12: Numerical Modeling on the Sphere 13: Tangent Linear Modeling and Adjoints 14: Observations 15: Non-variational Sequential Data Assimilation Methods 16: Variational Data Assimilation 17: Subcomponents of Variational Data Assimilation 18: Observation Space Variational Data Assimilation Methods 19: Kalman Filter and Smoother 20: Ensemble-Based Data Assimilation 21: Non-Gaussian Variational Data Assimilation 22: Markov Chain Monte Carlo and Particle Filter Methods 23: Applications of Data Assimilation in the Geosciences 24: Solutions to Select Exercise