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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
Ensemblebased atmospheric data assimilation
, 2004
"... Ensemblebased data assimilation techniques are being explored as possible alternatives to current operational analysis techniques such as 3 or 4dimensional variational assimilation. Ensemblebased assimilation techniques utilize an ensemble of parallel data assimilation and forecast cycles. The ..."
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Cited by 43 (2 self)
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Ensemblebased data assimilation techniques are being explored as possible alternatives to current operational analysis techniques such as 3 or 4dimensional variational assimilation. Ensemblebased assimilation techniques utilize an ensemble of parallel data assimilation and forecast cycles. The backgrounderror covariances are estimated using the forecast ensemble and are used to produce an ensemble of analyses. The backgrounderror covariances are flow dependent and often have very complicated structure, providing a very different adjustment to the observations than are seen from methods such as 3 dimensional variational assimilation. Though computationally expensive, ensemblebased techniques are relatively easy to code, since no adjoint nor tangentlinear models are required, and previous tests in simple models suggest that dramatic improvements over existing operational methods may be possible. A review of the ensemblebased assimilation is provided here, starting from the basic concepts of Bayesian assimilation. Without some simplification, full Bayesian assimilation is computationally impossible for model states of large dimension. Assuming normality of error statistics and linearity of error growth, the state and its error covariance may be predicted optimally using Kalman filter (KF) techniques. The ensemble Kalman filter (EnKF) is then described. The EnKF is an approximation to the KF in that backgrounderror covariances are estimated from a finite ensemble of forecasts. However, no assumptions about linearity of error growth are made. Recent algorithmic variants on the standard EnKF are also described, as well as methods for simplifying the computations and increasing the accuracy. Examples of ensemblebased assimilations are provided in simple and more realistic dynamical systems.
4DVar or Ensemble Kalman Filter?
 TELLUS
, 2007
"... We consider the relative advantages of two advanced data assimilation systems, 4DVar and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation wi ..."
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Cited by 42 (5 self)
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We consider the relative advantages of two advanced data assimilation systems, 4DVar and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4DVar, variance inflation in EnKF, and the effect of model errors and reduced observation coverage. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4DVar. For infrequent observations, when ensemble perturbations grow nonlinearly and become nonGaussian, 4DVar attains lower errors than EnKF. If the model is imperfect, the 4DVar with long windows requires weak constraint. Similar results are obtained with a quasigeostrophic channel model. EnKF experiments made with the primitive equations SPEEDY model provide comparisons with 3DVar and guidance on model error and ‘observation localization’. Results obtained using operational models and both simulated and real observations indicate that currently EnKF is becoming competitive with 4DVar, and that the experience acquired with each of these methods can be used to improve the other. A table summarizes the pros and cons of the two methods.
A local ensemble transform Kalman filter data assimilation system for the NCEP global model. Tellus, 59A, to appear. Preprint available at http://www.weatherchaos.umd.edu/publications.php
, 2007
"... This paper describes the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme and its implementation on the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model at the University of Maryland. Numerical results are shown for both simulated observ ..."
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Cited by 32 (6 self)
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This paper describes the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme and its implementation on the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model at the University of Maryland. Numerical results are shown for both simulated observations and observations of the real atmosphere. The role of flowdependent information in data assimilation is discussed based on the results of the numerical experiments. Preliminary assimilation results with AMSUA radiance observations are also presented. 1
A comparative study of 4DVAR and a 4D ensemble Kalman filter: perfect model simulations with Lorenz96, Tellus A 59 (2007
"... We formulate a four dimensional Ensemble Kalman Filter (4DLETKF) that minimizes a cost function similar to that in a 4DVAR method. Using perfect model experiments with the Lorenz96 model, we compare assimilation of simulated asynchronous observations with 4DVAR and 4DLETKF. We find that both s ..."
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Cited by 25 (3 self)
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We formulate a four dimensional Ensemble Kalman Filter (4DLETKF) that minimizes a cost function similar to that in a 4DVAR method. Using perfect model experiments with the Lorenz96 model, we compare assimilation of simulated asynchronous observations with 4DVAR and 4DLETKF. We find that both schemes have comparable error when 4DLETKF is performed sufficiently frequently and when 4DVAR is performed over a sufficiently long analysis time window. We explore how the error depends on the time between analyses for 4DLETKF and the analysis time window for 4DVAR. 1
2008b: An Ensemblebased Fourdimensional Variational Data Assimilation Scheme
 Part II: Observing System Simulation Experiments with the Advanced Research WRF
"... The incremental approach of fourdimensional variational (4DVar) data assimilation (Courtier et al. 1994) and Ensemble Kalman filters (EnKF, Evensen 1994) are well known as two advanced data ..."
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Cited by 22 (2 self)
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The incremental approach of fourdimensional variational (4DVar) data assimilation (Courtier et al. 1994) and Ensemble Kalman filters (EnKF, Evensen 1994) are well known as two advanced data
2008: Accelerating the spinup of Ensemble Kalman Filtering
"... Ensemble Kalman Filter (EnKF) has that disadvantage that the spinup time needed to reach its asymptotic level of accuracy is longer than the corresponding spinup time in variational methods (3DVar or 4DVar). This is because the ensemble has to fulfill two independent requirements, namely that th ..."
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Cited by 17 (3 self)
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Ensemble Kalman Filter (EnKF) has that disadvantage that the spinup time needed to reach its asymptotic level of accuracy is longer than the corresponding spinup time in variational methods (3DVar or 4DVar). This is because the ensemble has to fulfill two independent requirements, namely that the mean be close to the true state, and that the ensemble perturbations represent the “errors of the day”. As a result, there are cases such as radar observations of a severe storm, where EnKF may spinup too slowly to be useful. A scheme is proposed to accelerate the spinup of EnKF applying a nocost Ensemble Kalman Smoother, and using the observations more than once in each assimilation window in order to maximize the initial extraction of information. The performance of this scheme is tested with the Local Ensemble Transform Kalman Filter (LETKF) implemented in a Quasigeostrophic model, which requires a very long spinup time when initialized from a cold start. Results show that with the new “running in place” scheme the LETKF spinsup and converges to the optimal level of error at least as fast as 3DVar or 4DVar. Additional computations (24 iterations for each window) are only required during the initial spinup, since the scheme naturally returns to the original LETKF after spinup is achieved. 1.
Fourdimensional local ensemble transform Kalman filter: numerical experiments with a global circulation model. Tellus 59A
, 2007
"... We present an efficient variation of the Local Ensemble Kalman Filter (Ott et al. 2002, 2004) and the results of perfect model tests with the Lorenz96 model. This scheme is locally analogous to performing the Ensemble Transform Kalman Filter (Bishop et al. 2001). We also include a fourdimensional ..."
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Cited by 14 (4 self)
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We present an efficient variation of the Local Ensemble Kalman Filter (Ott et al. 2002, 2004) and the results of perfect model tests with the Lorenz96 model. This scheme is locally analogous to performing the Ensemble Transform Kalman Filter (Bishop et al. 2001). We also include a fourdimensional extension of the scheme to allow for asynchronous observations. 1.
Ensemble Kalman Filter: Current Status and Potential
 P. SAKOV AND P. OKE, “IMPLICATIONS OF THE FORM OF THE ENSEMBLE TRANSFORMATION IN THE ENSEMBLE SQUARE ROOT FILTERS” MON.WEA.REV.,136
, 2008
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2007: Local ensemble transform Kalman filter with realistic observations
"... (LETKF) (Hunt et al. 2006) is an efficient data assimilation scheme of the square root ensemble ..."
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Cited by 7 (3 self)
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(LETKF) (Hunt et al. 2006) is an efficient data assimilation scheme of the square root ensemble