Titlebook: Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. IV); Seon Ki Park,Liang Xu Book 2022 The Editor(s) (if applic

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Filtering with One-Step-Ahead Smoothing for Efficient Data Assimilation,ate of the system based on available observations, the so-called filtering problem. Standard filtering solutions are computed recursively as successive cycles of alternating time-update (forecast) and observation-update (analysis) steps. This path is however not the only recursive way to compute the

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Sparsity-Based Kalman Filters for Data Assimilation,d engineering applications. However, traditional UKFs or EKFs cannot assimilate big data sets associated with models that have high dimensions, such as those in operational numerical weather prediction. In this chapter, we introduce two sparsity-based Kalman filters, namely the sparse-UKFand the pro

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Second-Order Methods in Variational Data Assimilation,d, the second-order adjoint method among them. General sensitivity analysis for the  optimality system is presented. Using the Hessian, the sensitivity of the optimal solution and its functionals is studied with respect to observations and uncertainties in model parameters. Numerical examples for jo

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Observability Gramian and Its Role in the Placement of Observations in Dynamic Data Assimilation,e efficiency with which it determines the cost function gradient with respect to control and available observations. Then through use of any of the gradient-based optimization algorithms, the minimum is iteratively found. The alternate methodology does not depend on available observations; rather, t

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Assimilation of In-Situ Observations, weather prediction, even in the current era when observations from satellites provide approximately 90% of the observations assimilated.In addition, these observations are widely used in verification for both model forecasts and satellite datasets, and radiosonde data serve as critical anchor obser