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

Data assimilation aims at determining as accurately as possible the state of a dynamical system by combining heterogeneous sources of information in an optimal way. Generally speaking, the mathematical methods of data assimilation describe algorithms for forming optimal combinations of observations of a system, a numerical model that describes its evolution, and appropriate prior information. Data assimilation has a long history of application to high-dimensional geophysical systems dating back to the 1960s, with application to the estimation of initial conditions for weather forecasts. It has become a major component of numerical forecasting systems in geophysics, and an intensive field of research, with numerous additional applications in oceanography, atmospheric chemistry, and extensions to other geophysical sciences. The physical complexity and the high dimensionality of geophysical systems have led the community of geophysics to make significant contributions to the fundamental theory of data assimilation. This book gathers notes from lectures and seminars given by internationally recognized scientists during a three-week school held in the Les Houches School of physics in 2012, on theoretical and applied data assimilation. It is composed of (i) a series of main lectures, presenting the fundamentals of the most commonly used methods, and the information theory background required to understand and evaluate the role of observations; (ii) a series of specialized lectures, addressing various aspects of data assimilation in detail, from the most recent developments of the theory to the specificities of various thematic applications.

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.

Data assimilation is the combination of information from observations and models of a particular physical system in order to get the best possible estimate of the state of that system. The technique has wide applications across a range of earth sciences, a major application being the production of operational weather forecasts. Others include oceanography, atmospheric chemistry, climate studies, and hydrology. Data Assimilation for the Earth System is a comprehensive survey of both the theory of data assimilation and its application in a range of earth system sciences. Data assimilation is a key technique in the analysis of remote sensing observations and is thus particularly useful for those analysing the wealth of measurements from recent research satellites. This book is suitable for postgraduate students and those working on the application of data assimilation in meteorology, oceanography and other earth sciences.

This open-access textbook's significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. Unique for this book is the "top-down" derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today's popular data-assimilation methods. This strategy is the opposite of most textbooks and reviews on data assimilation that typically take a bottom-up approach to derive a particular assimilation method. E.g., the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter. The bottom-up approach derives the assimilation methods from different mathematical principles, making it difficult to compare them. Thus, it is unclear which assumptions are made to derive an assimilation method and sometimes even which problem it aspires to solve. The book's top-down approach allows categorizing data-assimilation methods based on the approximations used. This approach enables the user to choose the most suitable method for a particular problem or application. Have you ever wondered about the difference between the ensemble 4DVar and the "ensemble randomized likelihood" (EnRML) methods? Do you know the differences between the ensemble smoother and the ensemble-Kalman smoother? Would you like to understand how a particle flow is related to a particle filter? In this book, we will provide clear answers to several such questions. The book provides the basis for an advanced course in data assimilation. It focuses on the unified derivation of the methods and illustrates their properties on multiple examples. It is suitable for graduate students, post-docs, scientists, and practitioners working in data assimilation.

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.