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93
Ensemble Data Assimilation without Perturbed Observations
 MON. WEA. REV
, 2002
"... The ensemble Kalman filter (EnKF) is a data assimilation scheme based on the traditional Kalman filter update equation. An ensemble of forecasts are used to estimate the backgrounderror covariances needed to compute the Kalman gain. It is known that if the same observations and the same gain are ..."
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Cited by 287 (21 self)
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The ensemble Kalman filter (EnKF) is a data assimilation scheme based on the traditional Kalman filter update equation. An ensemble of forecasts are used to estimate the backgrounderror covariances needed to compute the Kalman gain. It is known that if the same observations and the same gain are used to update each member of the ensemble, the ensemble will systematically underestimate analysiserror covariances. This will cause a degradation of subsequent analyses and may lead to filter divergence. For large ensembles, it is known that this problem can be alleviated by treating the observations as random variables, adding random perturbations to them with the correct statistics. Two important
Ensemble Square Root Filters
, 2003
"... Ensemble data assimilation methods assimilate observations using statespace estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics ..."
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Cited by 118 (8 self)
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Ensemble data assimilation methods assimilate observations using statespace estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics. This transformation may be performed stochastically by treating observations as random variables, or deterministically by requiring that the updated analysis perturbations satisfy the Kalman filter analysis error covariance equation. Deterministic analysis ensemble updates are implementations of Kalman square root filters. The nonuniqueness of the deterministic transformation used in square root Kalman filters provides a framework to compare three recently proposed ensemble data assimilation methods.
OBSTACLES TO HIGHDIMENSIONAL PARTICLE FILTERING
"... Particle filters are ensemblebased assimilation schemes that, unlike the ensemble Kalman filter, employ a fully nonlinear and nonGaussian analysis step to compute the probability distribution function (pdf) of a system’s state conditioned on a set of observations. Evidence is provided that the ens ..."
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Cited by 93 (5 self)
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Particle filters are ensemblebased assimilation schemes that, unlike the ensemble Kalman filter, employ a fully nonlinear and nonGaussian analysis step to compute the probability distribution function (pdf) of a system’s state conditioned on a set of observations. Evidence is provided that the ensemble size required for a successful particle filter scales exponentially with the problem size. For the simple example in which each component of the state vector is independent, Gaussian and of unit variance, and the observations are of each state component separately with independent, Gaussian errors, simulations indicate that the required ensemble size scales exponentially with the state dimension. In this example, the particle filter requires at least 1011 members when applied to a 200dimensional state. Asymptotic results, following the work of Bengtsson, Bickel and collaborators, are provided for two cases: one in which each prior state component is independent and identically distributed, and one in which both the prior pdf and the observation errors are Gaussian. The asymptotic theory reveals that, in both cases, the required ensemble size scales exponentially with the variance of the observation loglikelihood, rather than with the state dimension per se. 2
Sampling strategies and square root analysis schemes for the EnKF
"... this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a signific ..."
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Cited by 89 (2 self)
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this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a significant improvement in the EnKF results, using the same number of members in the ensemble
A Local Least Squares Framework for Ensemble Filtering
, 2003
"... Many methods using ensemble integrations of prediction models as integral parts of data assimilation have appeared in the atmospheric and oceanic literature. In general, these methods have been derived from the Kalman filter and have been known as ensemble Kalman filters. A more general class of m ..."
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Cited by 89 (9 self)
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Many methods using ensemble integrations of prediction models as integral parts of data assimilation have appeared in the atmospheric and oceanic literature. In general, these methods have been derived from the Kalman filter and have been known as ensemble Kalman filters. A more general class of methods including these ensemble Kalman filter methods is derived starting from the nonlinear filtering problem. When working in a joint state observation space, many features of ensemble filtering algorithms are easier to derive and compare. The ensemble filter methods derived here make a (local) least squares assumption about the relation between prior distributions of an observation variable and model state variables. In this context, the update procedure applied when a new observation becomes available can be described in two parts. First, an update increment is computed for each prior ensemble estimate of the observation variable by applying a scalar ensemble filter. Second, a linear regression of the prior ensemble sample of each state variable on the observation variable is performed to compute update increments for each state variable ensemble member from corresponding observation variable increments. The regression can be applied globally or locally using Gaussian kernel methods.
R.: Extended versus ensemble Kalman filtering for land data assimilation
 J. Hydrometeor
"... The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal e ..."
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Cited by 47 (0 self)
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The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal error correlations and treating catchments independently. Both filters provide satisfactory estimates of soil moisture. The average actual estimation error in volumetric moisture content of the soil profile is 2.2 % for the EKF and 2.2 % (or 2.1%; or 2.0%) for the EnKF with 4 (or 10; or 500) ensemble members. Expected error covariances of both filters generally differ from actual estimation errors. Nevertheless, nonlinearities in soil processes are treated adequately by both filters. In the application presented herein the EKF and the EnKF with four ensemble members are equally accurate at comparable computational cost. Because of its flexibility and its performance in this study, the EnKF is a promising approach for soil moisture initialization problems. 1.
Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter
 Water Resour. Res. 2005
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Cited by 47 (5 self)
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Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation
, 2010
"... 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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Cited by 47 (10 self)
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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
Particle filtering in geophysical systems
, 2009
"... The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic part ..."
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Cited by 46 (1 self)
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The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic particle filter (i.e., importance sampling using the prior as the importance density) does not work in highdimensional systems, but several variants are shown to have potential. Approximations to the full problem that try to keep some aspects
A VarianceMinimizing Filter for LargeScale Applications
, 2003
"... A truly varianceminimizing filter is introduced and its performance is demonstrated with the KortewegDeVries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled ..."
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Cited by 44 (1 self)
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A truly varianceminimizing filter is introduced and its performance is demonstrated with the KortewegDeVries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled