数据同化基础：状态和参数估计问题的统一表述

这本教科书的重要贡献是从一个共同的基本和最佳出发点，即贝叶斯定理，统一推导了数据同化技术。这本书的独特之处在于同化方法的“自上而下”推导。它从贝叶斯定理开始，逐步引入了获得当今流行的数据同化方法所需的假设和近似。
这种策略与大多数关于数据同化的教科书和评论相反，它们通常采用自下而上的方法来推导特定的同化方法。例如，从控制理论推导卡尔曼滤波器，并将集合卡尔曼滤波器作为标准卡尔曼滤波器的低阶近似值进行推导。自下而上的方法从不同的数学原理中推导出同化方法，因此很难对它们进行比较。因此，目前尚不清楚采用何种假设来推导同化方法，有时甚至不清楚该方法希望解决什么问题。本书自上而下的方法允许根据使用的近似值对数据同化方法进行分类。这种方法使用户能够为特定问题或应用选择最合适的方法。你有没有想过集合4DVar和“集合随机可能性”（EnRML）方法之间的区别？你知道集合平滑器和集合卡尔曼平滑器的区别吗？您想了解粒子流与粒子过滤器的关系吗？在这本书中，我们将为几个这样的问题提供明确的答案。这本书为数据同化高级课程提供了基础。它着重于这些方法的统一推导，并在多个例子中说明了它们的性质。它适用于研究生、博士后、科学家和从事数据同化工作的从业者。
Data Assimilation Fundamentals: A Unified Formulation of the State and Parameter Estimation Problem
This 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.

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