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315
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 283 (12 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 189 (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
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
OnLine Estimation of Error Covariance Parameters for Atmospheric Data Assimilation
, 1994
"... We present a simple scheme for online estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximumlikelihoodapproach in which estimates are produced on the basis of a single batch of simultaneous observations. Singlesample covariance estimation is ..."
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Cited by 122 (10 self)
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We present a simple scheme for online estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximumlikelihoodapproach in which estimates are produced on the basis of a single batch of simultaneous observations. Singlesample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the singlesample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: timedependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be th...
Data assimilation via error subspace statistical estimation. Part I: Theory and schemes
, 1999
"... A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean–atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the const ..."
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Cited by 96 (15 self)
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A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean–atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the constraints and issues particular to ocean–atmosphere data assimilation are emphasized. An approximation to the optimal criterion satisfying the goals and addressing the issues is obtained using heuristic characteristics of geophysical measurements and models. This leads to the notion of an evolving error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. The concept of error subspace statistical estimation (ESSE) is defined. In the present minimum error variance approach, the suboptimal criterion is based on a continued and energetically optimal reduction of the dimension of error covariance matrices. The evolving error subspace is characterized by error singular vectors and values, or in other words, the error principal components and coefficients. Schemes for filtering and smoothing via ESSE are derived. The data–forecast melding minimizes variance in the error subspace. Nonlinear Monte Carlo forecasts integrate the error subspace in time. The smoothing is based on a statistical approximation approach. Comparisons with existing filtering and smoothing procedures
The Maximum Likelihood Ensemble Filter as a . . .
, 2008
"... The Maximum Likelihood Ensemble Filter (MLEF) equations are derived without the differentiability requirement for the prediction model and for the observation operators. Derivation reveals that a new nondifferentiable minimization method can be defined as a generalization of the gradientbased un ..."
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Cited by 65 (20 self)
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The Maximum Likelihood Ensemble Filter (MLEF) equations are derived without the differentiability requirement for the prediction model and for the observation operators. Derivation reveals that a new nondifferentiable minimization method can be defined as a generalization of the gradientbased unconstrained methods, such as the preconditioned conjugategradient and quasiNewton methods. In the new minimization algorithm the vector of first order increments of the cost function is defined as a generalized gradient, while the symmetric matrix of second order increments of the cost function is defined as a generalized Hessian matrix. In the case of differentiable observation operators, the minimization algorithm reduces to the standard gradientbased form. The nondifferentiable aspect of the MLEF algorithm is illustrated in an example with onedimensional Burgers model and simulated observations. The MLEF algorithm has a robust performance, producing satisfactory results for tested nondifferentiable observation operators.
A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation
 IN REVIEW
, 2005
"... A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assump ..."
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Cited by 48 (4 self)
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A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assumption of a perfect forecast model. Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radialvelocity and reflectivity observations where rain was present. 4DVAR produces generally better analyses than the EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, the EnKF typically produces better analyses than 4DVAR after several assimilation cycles, especially for model variables not functionally related to the observations. The advantages of the EnKF in later cycles arise at least in part from the fact that the 4DVAR scheme implemented here does not use a forecast from a previous cycle as background or evolve its error covariance. Possible reasons for the initial advantage of 4DVAR are deficiencies in the initial ensemble used by the EnKF, the temporal smoothness constraint used in 4DVAR, and nonlinearities in the evolution of forecast errors over the assimilation window.
Assimilation of Simulated Polarimetric Radar Data for a Convective Storm Using the Ensemble Kalman Filter. Part I: Observation Operators for Reflectivity and Polarimetric Variables
 MONTHLY WEATHER REVIEW VOLUME 136
, 2006
"... A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators ..."
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Cited by 43 (31 self)
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A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators of polarimetric radar variables that are needed when directly assimilating these variables into stormscale numerical weather prediction (NWP) models, using either variational or ensemblebased assimilation methods. The simulator takes as input the results of highresolution NWP model simulations with ice microphysics and produces simulated polarimetric radar data that may also contain simulated errors. It is developed based on calculations of electromagnetic wave propagation and scattering at the S band of wavelength 10.7 cm in a hydrometeorcontaining atmosphere. The Tmatrix method is used for the scattering calculation of raindrops and the Rayleigh scattering approximation is applied to snow and hail particles. The polarimetric variables are expressed as functions of the hydrometeor mixing ratios as well as their corresponding drop size distribution parameters and densities. The presence of wet snow and wet hail in the melting layer is accounted for by using a new, relatively simple melting model that defines the water fraction in the melting snow or hail. The effect of varying density due to the melting snow or hail is also included. Vertical cross sections and profiles of the polarimetric variables for a simulated mature multicellular squallline system and a supercell storm show that polarimetric signatures of the bright band in the stratiform region and those associated with deep convection are well captured by the simulator.
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 42 (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.
Accounting for the Error due to Unresolved Scales in Ensemble Data Assimilation: A Comparison of Different Approaches
 3132 MONTHLY WEATHER REVIEW VOLUME
, 2005
"... Insufficient model resolution is one source of model error in numerical weather predictions. Methods for parameterizing this error in ensemble data assimilations are explored here. Experiments were conducted with a twolayer primitive equation model, where the assumed true state was a T127 forecast ..."
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Cited by 42 (4 self)
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Insufficient model resolution is one source of model error in numerical weather predictions. Methods for parameterizing this error in ensemble data assimilations are explored here. Experiments were conducted with a twolayer primitive equation model, where the assumed true state was a T127 forecast simulation. Ensemble data assimilations were performed with the same model at T31 resolution, assimilating imperfect observations drawn from the T127 forecast. By design, the magnitude of errors due to model truncation was much larger than the error growth due to initial condition uncertainty, making this a stringent test of the ability of an ensemblebased data assimilation to deal with model error. Two general methods, “covariance inflation ” and “additive error, ” were considered for parameterizing the model error at the resolved scales (T31 and larger) due to interaction with the unresolved scales (T32 to T127). Covariance inflation expanded the background forecast members ’ deviations about the ensemble mean, while additive error added specially structured noise to each ensemble member forecast before the update step. The method of parameterizing this model error had a substantial effect on the accuracy of the ensemble data assimilation. Covariance inflation produced ensembles with analysis errors that were no lower than the analysis errors from threedimensional variational (3DVar) assimilation, and for the method to avoid filter