Data Assimilation for the Geosciences: From Theory to Application brings together all of the mathematical,statistical, and probability background knowledge needed to formulate data assimilation systems in one place. It includes practical exercises for understanding theoretical formulation and presents some aspects of coding the theory with a toy problem. The book also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to the atmosphere, oceans, as well as the land surface and other geophysical situations. It offers a comprehensive presentation of the subject, from basic principles to advanced methods, such as Particle Filters and Markov-Chain Monte-Carlo methods. Additionally, Data Assimilation for the Geosciences: From Theory to Application covers the applications of data assimilation techniques in various disciplines of the geosciences, making the book useful to students, teachers, and research scientists. Includes practical exercises, enabling readers to apply concepts in a theoretical formulation Offers explanations for how to code certain parts of the theory Presents a step-by-step guide on how, and why, data assimilation works and can be used

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.

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.

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

This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.

Grid-based Nonlinear Estimation and its Applications presents new Bayesian nonlinear estimation techniques developed in the last two decades. Grid-based estimation techniques are based on efficient and precise numerical integration rules to improve performance of the traditional Kalman filtering based estimation for nonlinear and uncertainty dynamic systems. The unscented Kalman filter, Gauss-Hermite quadrature filter, cubature Kalman filter, sparse-grid quadrature filter, and many other numerical grid-based filtering techniques have been introduced and compared in this book. Theoretical analysis and numerical simulations are provided to show the relationships and distinct features of different estimation techniques. To assist the exposition of the filtering concept, preliminary mathematical review is provided. In addition, rather than merely considering the single sensor estimation, multiple sensor estimation, including the centralized and decentralized estimation, is included. Different decentralized estimation strategies, including consensus, diffusion, and covariance intersection, are investigated. Diverse engineering applications, such as uncertainty propagation, target tracking, guidance, navigation, and control, are presented to illustrate the performance of different grid-based estimation techniques.

Data assimilation is theoretically founded on probability, statistics, control theory, information theory, linear algebra, and functional analysis. At the same time, data assimilation is a very practical subject, given its goal of estimating the posterior probability density function in realistic high-dimensional applications. This puts data assimilation at the intersection between the contrasting requirements of theory and practice. Based on over twenty years of teaching courses in data assimilation, Principles of Data Assimilation introduces a unique perspective that is firmly based on mathematical theories, but also acknowledges practical limitations of the theory. With the inclusion of numerous examples and practical case studies throughout, this new perspective will help students and researchers to competently interpret data assimilation results and to identify critical challenges of developing data assimilation algorithms. The benefit of information theory also introduces new pathways for further development, understanding, and improvement of data assimilation methods.