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Browsing by Author "Jardak, Mohamed"

Now showing 1 - 5 of 5
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    Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation
    Singh, Kumaresh; Jardak, Mohamed; Sandu, Adrian; Bowman, Kevin; Lee, Meemong (Department of Computer Science, Virginia Polytechnic Institute & State University, 2011-11-01)
    Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. In the companion paper [Sandu et al.(2011)] we derived an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. Here we apply this methodology to quantify two information metrics (the signal and degrees of freedom for signal) for satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical transport model. The assimilation of a subset of data points characterized by the highest information content, gives analyses that are comparable in quality with the one obtained using the entire data set.
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    A Hybrid Approach to Estimating Error Covariances in Variational Data Assimilation
    Cheng, Haiyan; Jardak, Mohamed; Alexe, Mihai; Sandu, Adrian (Department of Computer Science, Virginia Polytechnic Institute & State University, 2009-03-01)
    Data Assimilation (DA) involves the combination of observational data with the underlying dynamical principles governing the system under observation. In this work we combine the advantages of the two prominent advanced data assimilation systems, the 4D-Var and the ensemble methods. The proposed method consists of identifying the subspace spanned by the major 4D-Var error reduction directions. These directions are then removed from the background covariance through a Galerkin-type projection. This generates an updated error covariance information at both end points of an assimilation window. The error covariance information is updated between assimilation windows to capture the ``error of the day''. Numerical results using our new hybrid approach on a nonlinear model demonstrate how the background covariance matrix leads to an error covariance update that improves the 4D-Var DA results.
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    A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. I: Methodology
    Sandu, Adrian; Singh, Kumaresh; Jardak, Mohamed; Bowman, Kevin; Lee, Meemong (Department of Computer Science, Virginia Polytechnic Institute & State University, 2011-11-01)
    Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. This paper focuses on the four dimensional variational (4D-Var) data assimilation framework. Metrics from information theory are used to quantify the contribution of observations to decreasing the uncertainty with which the system state is known. We establish an interesting relationship between different information-theoretic metrics and the variational cost function/gradient under Gaussian linear assumptions. Based on this insight we derive an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. The approach is illustrated on linear and nonlinear test problems. In the companion paper [Singh et al.(2011)] the methodology is applied to a global chemical data assimilation problem.
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    A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. I: Methodology
    Sandu, Adrian; Singh, Kumaresh; Jardak, Mohamed; Bowman, Kevin; Lee, Meemong (Department of Computer Science, Virginia Polytechnic Institute & State University, 2012-03-01)
    Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. This paper focuses on the four dimensional variational (4D-Var) data assimilation framework. Metrics from information theory are used to quantify the contribution of observations to decreasing the uncertainty with which the system state is known. We establish an interesting relationship between different information-theoretic metrics and the variational cost function/gradient under Gaussian linear assumptions. Based on this insight we derive an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. The approach is illustrated on a nonlinear test problem. In the companion paper (Singh et al., 2012a) the methodology is applied to a global chemical data assimilation experiment.
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    A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation
    Singh, Kumaresh; Jardak, Mohamed; Sandu, Adrian; Bowman, Kevin; Lee, Meemong (Department of Computer Science, Virginia Polytechnic Institute & State University, 2012-03-01)
    Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. In the companion paper (Sandu et al., 2012) we derive an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. Here we apply this methodology to quantify the signal and degrees of freedom for signal information metrics of satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical transport model. The assimilation of a subset of data points characterized by the highest information content yields an analysis comparable in quality with the one obtained using the entire data set.