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413
Adaptive Sampling With the Ensemble Transform . . .
, 2001
"... A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filt ..."
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Cited by 328 (20 self)
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A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filters in that it uses ensemble transformation and a normalization to rapidly obtain the prediction error covariance matrix associated with a particular deployment of observational resources. This rapidity enables it to quickly assess the ability of a large number of future feasible sequences of observational networks to reduce forecast error variance. The ET KF was used by the National Centers for Environmental Prediction in the Winter Storm Reconnaissance missions of 1999 and 2000 to determine where aircraft should deploy dropwindsondes in order to improve 2472h forecasts over the continental United States. The ET KF may be applied to any wellconstructed set of ensemble perturbations. The ET KF
An Ensemble Adjustment Kalman Filter for Data Assimilation
, 2001
"... A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear ..."
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Cited by 294 (13 self)
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A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear
DistanceDependent Filtering of Background Error Covariance Estimates in an Ensemble Kalman Filter
, 2001
"... The usefulness of a distancedependent reduction of background error covariance estimates in an ensemble Kalman filter is demonstrated. Covariances are reduced by performing an elementwise multiplication of the background error covariance matrix with a correlation function with local support. This ..."
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Cited by 188 (31 self)
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The usefulness of a distancedependent reduction of background error covariance estimates in an ensemble Kalman filter is demonstrated. Covariances are reduced by performing an elementwise multiplication of the background error covariance matrix with a correlation function with local support. This reduces noisiness and results in an improved background error covariance estimate, which generates a reducederror ensemble of model initial conditions. The benefits
Analysis scheme in the ensemble Kalman filter, Monthly Weather Rev.
, 1998
"... ABSTRACT This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the ..."
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Cited by 153 (3 self)
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ABSTRACT This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.
Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter
 Physica D
, 2007
"... Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become availab ..."
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Cited by 152 (11 self)
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Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast ” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, I describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “Ensemble Kalman Filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. I discuss both the mathematical basis of this approach and its implementation; my primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. 1
Using Bayesian model averaging to calibrate forecast ensembles
 MONTHLY WEATHER REVIEW 133
, 2005
"... Ensembles used for probabilistic weather forecasting often exhibit a spreaderror correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distr ..."
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Cited by 144 (34 self)
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Ensembles used for probabilistic weather forecasting often exhibit a spreaderror correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distributions from different sources. The BMA predictive probability density function (PDF) of any quantity of interest is a weighted average of PDFs centered on the individual biascorrected forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts and reflect the models ’ relative contributions to predictive skill over the training period. The BMA weights can be used to assess the usefulness of ensemble members, and this can be used as a basis for selecting ensemble members; this can be useful given the cost of running large ensembles. The BMA PDF can be represented as an unweighted ensemble of any desired size, by simulating from the BMA predictive distribution. The BMA predictive variance can be decomposed into two components, one corresponding to the betweenforecast variability, and the second to the withinforecast variability. Predictive PDFs or intervals based solely on the ensemble spread incorporate the first component but not the second. Thus BMA provides a theoretical explanation of the tendency of ensembles to exhibit a spreaderror correlation but yet
Ensemble Kalman Filter Assimilation of Doppler Radar Data with a Compressible Nonhydrostatic Model: OSS Experiments
, 2004
"... A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general pur ..."
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Cited by 130 (79 self)
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A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general purpose nonhydrostatic compressible model is used with the inclusion of complex multiclass ice microphysics. New aspects compared to previous studies include the demonstration of the ability of EnKF method in retrieving multiple microphysical species associated with a multiclass ice microphysics scheme, and in accurately retrieving the wind and thermodynamic variables. Also new are the inclusion of reflectivity observations and the determination of the relative role of radial velocity and reflectivity data as well as their spatial coverage in recovering the full flow and cloud fields. In general, the system is able to reestablish the model storm extremely well after a number of assimilation cycles, and best results are obtained when both radial velocity and reflectivity data, including reflectivity information outside precipitation regions, are used. Significant positive impact of the reflectivity assimilation
A Hybrid Ensemble Kalman Filter / 3DVariational Analysis Scheme
"... A hybrid 3dimensional variational (3DVar) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfectmodel assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by ..."
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Cited by 124 (18 self)
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A hybrid 3dimensional variational (3DVar) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfectmodel assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by computing a set of parallel data assimilation cycles, with each member of the set receiving unique perturbed observations. The perturbed observations are generated by adding random noise consistent with observation error statistics to the control set of observations. Background error statistics for the data assimilation are estimated from a linear combination of timeinvariant 3DVar covariances and flowdependent covariances developed from the ensemble of shortrange forecasts. The hybrid scheme allows the user to weight the relative contributions of the 3DVar and ensemblebased background covariances. The analysis scheme was cycled for 90 days, with new observations assimilated every 12 h...
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