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52
Observation Bias Correction with an Ensemble Kalman Filter
, 2007
"... This paper considers the use of an ensemble Kalman filter to correct satellite radiance observations for state dependent biases relative to the observation operator in use. Our approach is to use statespace augmentation to estimate satellite biases as part of the ensemble data assimilation procedu ..."
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This paper considers the use of an ensemble Kalman filter to correct satellite radiance observations for state dependent biases relative to the observation operator in use. Our approach is to use statespace augmentation to estimate satellite biases as part of the ensemble data assimilation procedure. We illustrate our approach by applying it to a particular ensemble scheme, the Local Ensemble Transform Kalman Filter (LETKF), to assimilate simulated biased AIRS brightness temperature observations on the Simplified Parameterizations, primitivEEquation DYnamics (SPEEDY) model. The bias parameters estimated by LETKF successfully reduce both the observation bias and analysis error. 1
Nonglobal parameter estimation using local ensemble kalman filtering. Monthly Weather Review, forthcoming
, 2014
"... Abstract. We study parameter estimation for nonglobal parameters in a lowdimensional chaotic model using the local ensemble transform Kalman filter (LETKF). By modifying existing techniques for using observational data to estimate global parameters, we present a methodology whereby spatiallyvaryi ..."
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Abstract. We study parameter estimation for nonglobal parameters in a lowdimensional chaotic model using the local ensemble transform Kalman filter (LETKF). By modifying existing techniques for using observational data to estimate global parameters, we present a methodology whereby spatiallyvarying parameters can be estimated using observations only within a localized region of space. Taking a lowdimensional nonlinear chaotic conceptual model for atmospheric dynamics as our numerical testbed, we show that this parameter estimation methodology accurately estimates parameters which vary in both space and time, as well as parameters representing physics absent from the model. 1.
Data Assimilation in Brain Tumor Models
"... A typical problem in applied mathematics and science is to estimate the future state of a dynamical system given its current state. One approach aimed at understanding one or more aspects determining the behavior of the system is mathematical modeling. This method frequently entails formulation of a ..."
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A typical problem in applied mathematics and science is to estimate the future state of a dynamical system given its current state. One approach aimed at understanding one or more aspects determining the behavior of the system is mathematical modeling. This method frequently entails formulation of a set of equations, usually
© Author(s) 2013. CC Attribution 3.0 License. Nonlinear Processes in Geophysics
"... pen A ccess A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks ..."
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pen A ccess A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks
Implementation of the Constrained Runs Scheme for Initializing on a Slow Manifold
, 2007
"... The longterm dynamics of many dynamical systems evolves on a lowdimensional, attracting, invariant slow manifold, which can be parameterized by only a few variables (“observables”). The explicit derivation of such a slow manifold (and thus, the reduction of the longterm system dynamics) can be ex ..."
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The longterm dynamics of many dynamical systems evolves on a lowdimensional, attracting, invariant slow manifold, which can be parameterized by only a few variables (“observables”). The explicit derivation of such a slow manifold (and thus, the reduction of the longterm system dynamics) can be extremely difficult, or practically impossible. For this class of problems, the equationfree computational approach has been developed to perform numerical tasks with the unavailable reduced (coarsegrained) model based on short full model simulations. Each full model simulation should be initialized consistent with the values of the observables and close to the slow manifold. For this purpose, a class of constrained runs functional iterations was recently proposed. The schemes in this class only use the full model simulator and converge, under certain conditions, to an approximation of the desired state on the slow
Assimilating Nonlocal Observations using a Local Ensemble Kalman Filter
, 2007
"... Many ensemble Kalman filter data assimilation schemes benefit from spatial localization, often in both the horizontal and vertical coordinates. On the other hand, satellite observations are often sensitive to the dynamics over a broad layer of the atmosphere; that is, the observation operator that m ..."
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Many ensemble Kalman filter data assimilation schemes benefit from spatial localization, often in both the horizontal and vertical coordinates. On the other hand, satellite observations are often sensitive to the dynamics over a broad layer of the atmosphere; that is, the observation operator that maps the model state to the observed satellite radiances is a nonlocal function of the state. Similarly, errors in satellite retrieval observations can be correlated over significant distances. This nonlocality can present problems for assimilating satellite observations with local ensemble Kalman filter schemes. In this paper, we propose a technique in which the observation operator is applied to the global model state and then appropriate observations are selected to estimate the atmospheric state for each model grid point. The issue of how to choose appropriate observations is investigated with numerical experiments on a seven layer primitive equation model, the SPEEDY model. We assimilate both simulated point observations and either nonlocal radiancelike or
REVIEW Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation
, 2009
"... This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The nonGaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspe ..."
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This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The nonGaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these nonGaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in highdimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on secondorder moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and nonGaussian effects remain. They essentially originate in the nonlinear models and in the nonGaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are