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160
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 322 (19 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
A Description of the Advanced Research WRF Version 2
 AVAILABLE FROM NCAR; P.O. BOX 3000; BOULDER, CO
, 2001
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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 280 (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
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
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 150 (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
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 127 (78 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 123 (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...
A Singular Evolutive Extended Kalman Filter For Data Assimilation In Oceanography
 Journal of Marine Systems
, 1996
"... In this work, we propose a modified form of the extended Kalman filter for assimilating oceanic data into numerical models. Its development consists essentially in approximating the error covariance matrix by a singular low rank matrix, which amounts in practice to making no correction in those dire ..."
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Cited by 104 (9 self)
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In this work, we propose a modified form of the extended Kalman filter for assimilating oceanic data into numerical models. Its development consists essentially in approximating the error covariance matrix by a singular low rank matrix, which amounts in practice to making no correction in those directions for which the error is attenuated by the system. This not only reduce the implementation cost to an acceptable level but may also improve the filter stability as well. The "directions of correction" of the filter evolve with time according to the model evolution, which is the most original feature of this filter, distinguishing it from other sequential assimilation methods based on the projection onto a fixed basis of functions. A method for initializing the filter based on the empirical orthogonal functions is also described. An example of assimilation based on the quasigeostrophic model for a square ocean domain with a certain wind stress forcing pattern, is given. Although this is ...
A description of
 the Advanced Research WRF version 2; NCAR Technical Note: NCAR/TN468+STR 2005; NCAR
, 2005
"... The Technical Note series provides an outlet for a variety of NCAR manuscripts that contribute in specialized ways to the body of scientific knowledge but which are not suitable for journal, monograph, or book publication. Reports in this series are issued by the NCAR Scientific Divisions; copies m ..."
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Cited by 97 (5 self)
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The Technical Note series provides an outlet for a variety of NCAR manuscripts that contribute in specialized ways to the body of scientific knowledge but which are not suitable for journal, monograph, or book publication. Reports in this series are issued by the NCAR Scientific Divisions; copies may be obtained on request from the Publications Office of NCAR. Designation symbols for the series include: EDD: Engineering, Design, or Development Reports Equipment descriptions, test results, instrumentation, and operating and maintenance manuals. IA: Instructional Aids Instruction manuals, bibliographies, film supplements, and other research or instructional aids. PPR: Program Progress Reports Field program reports, interim and working reports, survey reports, and plans for experiments. PROC: Proceedings Documentation of symposia, colloquia, conferences, workshops, and lectures. (Distribution may be limited to attendees.) STR: Scientific and Technical Reports Data compilations, theoretical and numerical investigations, and experimental results.
Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems
, 2001
"... This paper considers several filtering methods of stochastic nature, based on Monte Carlo drawing, for the sequential data assimilation in nonlinear models. They include some known methods such as the particle filter and the ensemble Kalman filter and some others introduced by the author: the seco ..."
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Cited by 97 (2 self)
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This paper considers several filtering methods of stochastic nature, based on Monte Carlo drawing, for the sequential data assimilation in nonlinear models. They include some known methods such as the particle filter and the ensemble Kalman filter and some others introduced by the author: the secondorder ensemble Kalman filter and the singular extended interpolated filter. The aim is to study their behavior in the simple nonlinear chaotic Lorenz system, in the hope of getting some insight into more complex models. It is seen that these filters perform satisfactory, but the new filters introduced have the advantage of being less costly. This is achieved through the concept of secondorderexact drawing and the selective error correction, parallel to the tangent space of the attractor of the system (which is of low dimension). Also introduced is the use of a forgetting factor, which could enhance significantly the filter stability in this nonlinear context.