Data Assimilation Fundamentals: A Unified Formulation of the State and Parameter Estimation Problem

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.

Geir Evensen gained his PhD in Mathematics at the University of Bergen, Norway. His extensive experiences include data assimilation in ocean and weather models, as well as ensemble-based history matching within petroleum-reservoir models. He has initiated and led several international research projects from an initial idea to operational implementation in various disciplines. Since 2016, he has worked as a Chief scientist at the International Research Institute of Stavanger (IRIS), which from 2018, merged into NORCE. He teaches data assimilation and its applications in various courses and summer schools. He also holds a secondary position at the Nansen Environmental and Remote Sensing Center in Bergen, Norway.

Femke Vossepoel gained her PhD in Aerospace Engineering at Delft University of Technology, The Netherlands. Her research focuses on the use of data assimilation in numerical models of subsurface flow and mechanics to estimate the effects of subsurface activities and their uncertainties and associated risks. Applications of her current research include subsidence and induced seismicity, slope stability, and flooding risk. She works as an Associate Professor, Department of Geoscience and Engineering, Delft University of Technology, The Netherlands. She teaches on statistics and data assimilation in various international summer schools and courses.

Peter Jan van Leeuwen gained his PhD from the Delft University of Technology, The Netherlands. His research focuses on the development of advanced data-assimilation methods and causal discovery methods for high-dimensional highly nonlinear systems, and applying these methods for a better understanding of geophysical fluids, especially atmosphere and ocean. He joined the University of Reading,UK, as Professor in Data Assimilation in 2009, and is also a Professor in Data Assimilation and Oceanography at Colorado State University, USA, since 2018. In 2016 we won the prestigious Advanced Investigator grant from the European Research Council, the largest personal award in the EU. The teaches many courses at universities and summerschools on Data Assimilation, Causal Discovery, Physical Oceanography, Statistical mechanics for the Geosciences, and Remote Sensing.