Data Assimilation: A Mathematical Introduction

By Kody J. H. Law, Andrew M. Stuart, Konstantinos C. Zygalakis. 2015

319 citations recorded by the source corpus.

This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/efba02752d17002182c12aefe57edae317740441

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In Atmospheric Science

In Global and Planetary Change

Citations in the corpus

Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High‐Resolution Simulations (2017, methodology): “…can be developed further in several ways: • Minimization of the objective functions Jo and Js may be performed by online filtering algorithms, akin to those used in the initialization of weather forecasts, which sequentially update parameters as information becomes available [Law et al., 2015].”
Model Reduction and Neural Networks for Parametric PDEs (2020, methodology): “on of PDEs, motivated by small-data scenarios; see the paper [12] which relates, in part, to earlier work focused on the small-data setting [7,37]. These approaches are more akin to data assimilation [45,33] where the data is incorporated into a model. 1.2. Our Contribution. The primary contribution”
Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, background): “The topic has recently reached the rank of a discipline per se, as testified by the appearance of books such as van Leeuwen, Cheng, and Reich (2015), Reich and Cotter (2015), Law, Stuart, and Zygalakis (2015), Asch, Bocquet, and Nodet (2016), or Fletcher (2017).”