Data Assimilation: A Mathematical Introduction - Kody Law
Data Assimilation: A Mathematical Introduction - Table of Contents
- PART I: PRELIMINARIES & FOUNDATIONS
- 1. Introduction to Data Assimilation
- 2. Probability and Bayesian Inverse Problems
- 3. Dynamical Systems and Observational Models
- PART II: DISCRETE-TIME FILTERING
- 4. The Linear Gaussian Case: Kalman Filter Analysis
- 5. The Extended Kalman Filter
- 6. Ensemble Kalman Filter (EnKF) Methods
- 7. Particle Filters and Sequential Monte Carlo
- PART III: CONTINUOUS-TIME FILTERING & VARIATIONAL METHODS
- 8. Continuous-Time Limit and Stochastic Filtering
- 9. Variational Data Assimilation (3DVar)
- 10. 4DVar Variational Assimilation Algorithms
- 11. Asymptotic Behavior and Filter Stability
- 12. Advanced Topics in High-Dimensional State Estimation
What You Will Learn in Data Assimilation: A Mathematical Introduction
Data Assimilation: A Mathematical Introduction by Kody Law, Andrew Stuart, and Konstantinos Zygalakis bridges the gap between probability theory, dynamical systems, and real-world state estimation. Addressing the critical challenge of combining noisy observational data with complex physical models, this text breaks down core methodologies including discrete and continuous time Kalman filters, Ensemble Kalman Filters (EnKF), variational methods (3DVar and 4DVar), particle filtering, and Markov chain Monte Carlo (MCMC) algorithms into clear, structured chapters.
Designed for applied mathematicians, theoretical meteorologists, computational engineers, and data science researchers, this book presents data assimilation from a unified Bayesian perspective. The authors rigorously analyze asymptotic convergence, stability bounds, and algorithmic performance in high-dimensional contexts. Whether formulating variational cost functions or evaluating sequential Monte Carlo filtering techniques, practitioners will find this systematic mathematical exposition invaluable.
Globally praised for its precision, analytical depth, and clear connection to geophysical and physical applications, it remains one of the best data assimilation mathematical textbooks pdf available for academic research. It equips learners with essential computational tools for mastering state estimation and uncertainty quantification with confidence.
Book Details & Specifications
Title:
Data Assimilation: A Mathematical Introduction - Kody Law
Publisher:
Springer
Year:
2015
Pages:
158
Type:
PDF
Language:
English
ISBN-10 #:
331920324X
ISBN-13 #:
978-3319203249
License:
arXiv License (Non-Exclusive Distribution)
Amazon:
Amazon
About the Author: Kody Law
The author Kody Law
is a Professor of Applied Mathematics at the University of Manchester. His research spans Bayesian inverse problems, data assimilation, uncertainty quantification, and numerical analysis of stochastic differential equations.
Andrew Stuart is a David Howarth Professor of Computing and Mathematical Sciences at Caltech, globally renowned for his pioneering contributions to Bayesian inverse problems and data assimilation. Konstantinos Zygalakis is a Professor of Applied Mathematics at the University of Edinburgh, specializing in stochastic computation and data-driven modeling.
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