Data Assimilation Fundamentals: A Unified Formulation of the State and Parameter Estimation Problem

This open-access textbook provides a unified derivation of data-assimilation techniques from Bayes' theorem, offering a top-down approach that categorizes methods based on approximations. It is suitable for graduate students, post-docs, scientists, and practitioners working in data assimilation.

Format: Hardback
Length: 245 pages
Publication date: 23 April 2022
Publisher: Springer Nature Switzerland AG

This open-access textbook makes a significant contribution by deriving data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. What sets this book apart is its unique top-down derivation of the assimilation methods. It begins with Bayes' theorem and gradually introduces the assumptions and approximations necessary to arrive at today's popular data-assimilation methods. This approach stands in contrast to most textbooks and reviews on data assimilation, which typically take a bottom-up approach to derive a particular assimilation method. For instance, the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter. The bottom-up approach derives the assimilation methods from different mathematical principles, making it challenging to compare them. Consequently, it becomes unclear which assumptions are made to derive an assimilation method and, at times, even which problem it aims to solve.

The book's top-down approach offers a solution to this problem. It allows categorizing data-assimilation methods based on the approximations used. This approach empowers users to select the most suitable method for a particular problem or application. For example, would you like to know the differences between the ensemble 4DVar and the ensemble randomized likelihood (EnRML) methods? Do you know the distinctions between the ensemble smoother and the ensemble-Kalman smoother? Would you like to understand how a particle flow is related to a particle filter? In this book, we will provide clear answers?answers to several such questions.

The book serves as a foundation for an advanced course in data assimilation. It focuses on the unified derivation of the methods and illustrates their properties on multiple examples. The book is suitable for researchers, graduate students, and practitioners interested in data assimilation and its applications in various fields, such as meteorology, oceanography, and climate science.

In conclusion, this open-access textbook offers a valuable resource for anyone seeking to understand the unified derivation of data-assimilation techniques from Bayes' theorem. Its top-down approach, combined with detailed explanations and examples, makes it an essential tool for researchers, graduate students, and practitioners in the field of data assimilation.

Weight: 578g
Dimension: 242 x 161 x 21 (mm)
ISBN-13: 9783030967086
Edition number: 1st ed. 2022