Titlebook: Data Assimilation Fundamentals; A Unified Formulatio Geir Evensen,Femke C. Vossepoel,Peter Jan van Leeu Textbook‘‘‘‘‘‘‘‘ 2022 The Editor(s)

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Kalman Filters and 3DVaror a closed-form solution that minimizes the cost function, and then we continue discussing how specific cases lead to several well-known methods. The first case assumes that the measurements are all located at the initial time of the assimilation window. Thus, there is no need for any model integra

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Localization and Inflationases the effective rank of the ensemble covariance matrix and allows it to fit a large number of independent observations. Thus, we use localization to reduce sampling errors, in combination with inflation, to reduce the underestimation of the ensemble variance caused by the low-rank approximation.

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3Dvar and SC-4DVar for the Lorenz 63 Modelapply both 3DVar and SC-4DVar sequentially over multiple data-assimilation windows, and we will demonstrate the difference between the filter solution obtained by 3DVar and the recursive SC-4DVar smoother solution. We will also dive deeper into the behavior of the SC-4DVar with highly nonlinear- and

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Textbook‘‘‘‘‘‘‘‘ 2022 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 fo

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3Dvar and SC-4DVar for the Lorenz 63 Model chaotic dynamics and try to understand more of the method’s properties and possible limitations in these cases. After studying the 3DVar and 4DVar methods, we compare them with the ensemble methods used in Chap.?..

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