The mathematical foundations of work in data assimilation are treated methodically in this book, which covers both theoretical and computational methods. The many examples used in the text, along with the algorithms that are introduced and discussed, are all illustrated by the MATLAB software that is described in the book and made freely available online.
More specifically, the authors develop an integrated mathematical framework in which a Bayesian formulation of the problem serves as the foundation for the derivation, development, and analysis of algorithms.
The book is divided into nine chapters. The first chapter provides a brief overview of the mathematical concepts and tools that serve as the framework for the remaining eight chapters, which deal with discrete time dynamical systems and discrete time data respectively. The remaining four chapters, which deal with continuous time dynamical systems and continuous time data, are organized similarly to the discrete-time chapters' discrete-time counterparts.
Researchers from the geosciences and a number of other scientific fields who use tools from data assimilation to combine data with time-dependent models are the target audience for this book, as well as mathematical researchers who are interested in the systematic development of this interdisciplinary field. The many examples and illustrations make it easy to comprehend the theoretical foundations of data assimilation. Additionally, the book is appropriate for practical mathematics students, whether they are taking a lecture course or doing their own independent study because of the examples, exercises, and MATLAB software.