Browsing by Author "Singh, Kumaresh"
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- Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone AssimilationSingh, 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.
- Efficient Computational Tools for Variational Data Assimilation and Information Content EstimationSingh, Kumaresh (Virginia Tech, 2010-08-10)The overall goals of this dissertation are to advance the field of chemical data assimilation, and to develop efficient computational tools that allow the atmospheric science community benefit from state of the art assimilation methodologies. Data assimilation is the procedure to combine data from observations with model predictions to obtain a more accurate representation of the state of the atmosphere. As models become more complex, determining the relationships between pollutants and their sources and sinks becomes computationally more challenging. The construction of an adjoint model ( capable of efficiently computing sensitivities of a few model outputs with respect to many input parameters ) is a difficult, labor intensive, and error prone task. This work develops adjoint systems for two of the most widely used chemical transport models: Harvard's GEOS-Chem global model and for Environmental Protection Agency's regional CMAQ regional air quality model. Both GEOS-Chem and CMAQ adjoint models are now used by the atmospheric science community to perform sensitivity analysis and data assimilation studies. Despite the continuous increase in capabilities, models remain imperfect and models alone cannot provide accurate long term forecasts. Observations of the atmospheric composition are now routinely taken from sondes, ground stations, aircraft, and satellites, etc. This work develops three and four dimensional variational data assimilation capabilities for GEOS-Chem and CMAQ which allow to estimate chemical states that best fit the observed reality. Most data assimilation systems to date use diagonal approximations of the background covariance matrix which ignore error correlations and may lead to inaccurate estimates. This dissertation develops computationally efficient representations of covariance matrices that allow to capture spatial error correlations in data assimilation. Not all observations used in data assimilation are of equal importance. Erroneous and redundant observations not only affect the quality of an estimate but also add unnecessary computational expense to the assimilation system. This work proposes techniques to quantify the information content of observations used in assimilation; information-theoretic metrics are used. The four dimensional variational approach to data assimilation provides accurate estimates but requires an adjoint construction, and uses considerable computational resources. This work studies versions of the four dimensional variational methods (Quasi 4D-Var) that use approximate gradients and are less expensive to develop and run. Variational and Kalman filter approaches are both used in data assimilation, but their relative merits and disadvantages in the context of chemical data assimilation have not been assessed. This work provides a careful comparison on a chemical assimilation problem with real data sets. The assimilation experiments performed here demonstrate for the first time the benefit of using satellite data to improve estimates of tropospheric ozone.
- A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. I: MethodologySandu, 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.
- A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. I: MethodologySandu, 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.
- A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone AssimilationSingh, 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.