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, emphasising 'why' and not just 'how'. Methods and diagnostics are emphasised, enabling readers to readily apply them to their own field of study. This comprehensive guide is accessible to non-experts and contains numerous examples and diverse applications from a broad range of domains, including geophysics, environmental acoustics, medical imaging, mechanical and biomedical engineering, economics and finance, and traffic control and urban planning. Readers will also find included the latest methods for advanced data assimilation, combining variational and statistical approaches.
List of figures; List of algorithms; Notation; Preface; Part I. Basic Methods and Algorithms for Data Assimilation: 1. Introduction to data assimilation and inverse problems; 2. Optimal control and variational data assimilation; 3. Statistical estimation and sequential data assimilation; Part II. Advanced Methods and Algorithms for Data Assimilation: 4. Nudging methods; 5. Reduced methods; 6. The ensemble Kalman filter; 7. Ensemble variational methods; Part III. Applications and Case Studies: 8. Applications in environmental sciences; 9. Applications in atmospheric sciences; 10. Applications in geosciences; 11. Applications in medicine, biology, chemistry, and physical sciences; 12. Applications in human and social sciences; Bibliography; Index.
