Data Assimilation

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.

Data Assimilation for the Geosciences: From Theory to Application, Second Edition brings together all of the mathematical and statistical background knowledge needed to formulate data assimilation systems into one place. It includes practical exercises enabling readers to apply theory in both a theoretical formulation as well as teach them how to code the theory with toy problems to verify their understanding. It also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to land surface, the atmosphere, ocean and other geophysical situations. The second edition of Data Assimilation for the Geosciences has been revised with up to date research that is going on in data assimilation, as well as how to apply the techniques. The new edition features an introduction of how machine learning and artificial intelligence are interfacing and aiding data assimilation. In addition to appealing to students and researchers across the geosciences, this now also appeals to new students and scientists in the field of data assimilation as it will now have even more information on the techniques, research, and applications, consolidated into one source. Includes practical exercises and solutions enabling readers to apply theory in both a theoretical formulation as well as enabling them to code theory Provides the mathematical and statistical background knowledge needed to formulate data assimilation systems into one place New to this edition: covers new topics such as Observing System Experiments (OSE) and Observing System Simulation Experiments; and expanded approaches for machine learning and artificial intelligence

Publisher description

Data assimilation is an approach that combines observations and model output, with the objective of improving the latter. This book places data assimilation into the broader context of inverse problems and the theory, methods, and algorithms that are used for their solution. It provides a framework for, and insight into, the inverse problem nature of data assimilation, emphasizing ?why? and not just ?how.? Methods and diagnostics are emphasized, enabling readers to readily apply them to their own field of study. Readers will find a comprehensive guide that is accessible to nonexperts; numerous examples and diverse applications from a broad range of domains, including geophysics and geophysical flows, environmental acoustics, medical imaging, mechanical and biomedical engineering, economics and finance, and traffic control and urban planning; and the latest methods for advanced data assimilation, combining variational and statistical approaches.

This book, first published in 2002, is a graduate-level text on numerical weather prediction, including atmospheric modeling, data assimilation and predictability.

This book reviews popular data-assimilation methods, such as weak and strong constraint variational methods, ensemble filters and smoothers. The author shows how different methods can be derived from a common theoretical basis, as well as how they differ or are related to each other, and which properties characterize them, using several examples. Readers will appreciate the included introductory material and detailed derivations in the text, and a supplemental web site.

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including targeting observation, sensitivity analysis, and parameter estimation. The book will be useful to individual researchers as well as graduate students for a reference in the field of data assimilation.

One of the main reasons we cannot tell what the weather will be tomorrow is that we do not know accurately enough what the weather is today. Mathematically speaking, numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear partial differential equations in which the necessary initial values are known only incompletely and inaccurately. Data at the initial time of a numerical forecast can be supplemented, however, by observations of the atmos phere over a time interval preceding it. New observing systems, in particular polar-orbiting and geostationary satellites, which are providing observations continuously in time, make is absolutely necess ary to find new and more satisfactory methods of assimilating meteorological observations - for the dual purpose of defining atmospheric states and of issuing forecasts from the states thus defined. FUndamental progress in this area has been made in recent years and this book attempts to give a review and some suggestions for further improvements in the field of meteorological data assimila tion methods. The European Centre for Medium Range Weather Forecasts (ECMWF) every year organises seminars for the benefit of meteorologists and geophysicists of the ECMWF Member states. The 1980 Seminar was devoted to data assimilation methods, and this book contains selected lectures from that seminar. The purpose of the seminar was twofold: it was intended to give a basic introduction to the subject, as well as an overview of the latest developments in the field.