## Abstract

A central research challenge for the mathematical sciences in the twenty-first century is the development of principled methodologies for the seamless integration of (often vast) data sets with sophisticated mathematical models. Such data sets are becoming routinely available in almost all areas of engineering, science, and technology, while mathematical models describing

phenomena of interest are often built on decades, or even centuries, of human knowledge. Ignoring either the data or the models is clearly unwise, and so the issue of combining them is of paramount importance. When the underlying mathematical model is a (possibly stochastic) dynamical system and the data may be time-ordered, combining model and data is referred to as data assimilation.

The research area of data assimilation has been driven, to a large extent, by practitioners working in the atmospheric and oceanographic sciences and in other areas of the geosciences, such as oil recovery. The resulting research has led to a host of algorithmic approaches and a number of significant algorithmic innovations. However, there has been no systematic treatment of the mathematical underpinnings of the subject. The goal of this book is to provide such a treatment. Specifically, we develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation and development of algorithms; furthermore, the examples used in the text, together with the algorithms that are introduced and discussed, are all illustrated by MATLAB software detailed in the book and freely available online via the Springer website, the authors’ personal web pages, and at the

following link: http://tiny.cc/damat.

phenomena of interest are often built on decades, or even centuries, of human knowledge. Ignoring either the data or the models is clearly unwise, and so the issue of combining them is of paramount importance. When the underlying mathematical model is a (possibly stochastic) dynamical system and the data may be time-ordered, combining model and data is referred to as data assimilation.

The research area of data assimilation has been driven, to a large extent, by practitioners working in the atmospheric and oceanographic sciences and in other areas of the geosciences, such as oil recovery. The resulting research has led to a host of algorithmic approaches and a number of significant algorithmic innovations. However, there has been no systematic treatment of the mathematical underpinnings of the subject. The goal of this book is to provide such a treatment. Specifically, we develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation and development of algorithms; furthermore, the examples used in the text, together with the algorithms that are introduced and discussed, are all illustrated by MATLAB software detailed in the book and freely available online via the Springer website, the authors’ personal web pages, and at the

following link: http://tiny.cc/damat.

Original language | English |
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Publisher | Springer, Cham |

Number of pages | 256 |

Volume | 62 |

ISBN (Print) | 978-3-319-20324-9; 978-3-319-20325-6 |

DOIs | |

Publication status | Published - 2015 |

### Publication series

Name | Texts in Applied Mathematics |
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Publisher | Springer, Cham |