Asch M., Bocquet M., Nodet M. Data Assimilation: Methods, Algorithms, and Applications

Philadelphia: Society for Industrial and Applied Mathematics, 2016. — 310 p.This book places data assimilation (DA) into the broader context of inverse problems and the theory, methods, and algorithms that are used for their solution. It strives to provide a framework and new insight into the inverse problem nature of DA — the book emphasizes “why” and not just “how.” We cover both statistical and variational approaches to DA (see Figure 1) and give an important place to the latest hybrid methods that combine the two. Since the methods and diagnostics are emphasized, readers will readily be able to apply them to their own, precise field of study. This will be greatly facilitated by numerous examples and diverse applications. The applications are taken from the following fields: geophysics and geophysical flows, environmental acoustics, medical imaging, mechanical and biomedical engineering, urban planning, economics, and finance.
In fact, this book is about building bridges — bridges between inverse problems and DA, bridges between variational and statistical approaches, bridges between statistics and inverse problems. These bridges will enable you to cross valleys and moats, thus avoiding the dangers that are most likely/possibly lurking down there. These bridges will allow you to fetch/go and get/retrieve different approaches and better understanding of the vast, and sometimes insular, domains of DA and inverse problems, stochastic and deterministic approaches, and direct and inverse problems. We claim that by assembling these, by reconciling these, we will be better armed to confront and tackle the grand societal challenges of today, broadly defined as “global change” issues — such as climate change, disaster prediction and mitigation, and nondestructive and noninvasive testing and imaging.
The aim of the book is thus to provide a comprehensive guide for advanced undergraduate and early graduate students and for practicing researchers and engineers engaged in (partial) differential equation–based DA, inverse problems, optimization, and optimal control — we will emphasize the close relationships among all of these. The reader will be presented with a statistical approach and a variational approach and will find pointers to all the numerical methods needed for either. Of course, the applications will furnish many case studies