Data assimilation : methods, algorithms, and applications

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. The core audience is advanced undergraduate and early graduate students in applied mathematics, environmental sciences, and any domain (engineering, social science, biology, etc.) that deals with inverse problems related to physical measurements. A strong potential audience is practicing researchers and engineers engaged in (partial) differential equation based data assimilation, inverse problems, optimization, and optimal control. Part Basic Methods and Algorithms for Data Assimilation; Chapter 1: Introduction to Data Assimilation and Inverse Problems; Chapter 2: Optimal Control and Variational Data Assimilation; Chapter 3: Statistical Estimation and Sequential Data Assimilation; Part Advanced Methods and Algorithms for Data Assimilation; Chapter 4: Nudging Methods; Chapter 5: Reduced Methods; Chapter 6: The Ensemble Kalman Filter; Chapter 7: Ensemble Variational Methods; Part Applications and Case Studies; Chapter 8: Applications in Environmental Sciences; Chapter 9: Applications in Atmospheric Sciences; Chapter 10: Applications in Geosciences; Chapter 11: Applications in Medicine, Biology, Chemistry, and Physical Sciences; Chapter 12: Applications in Human and Social Sciences.