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116
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
Ensemble data assimilation with the ncep global forecast system
, 2007
"... Realdata experiments with an ensemble data assimilation system using the NCEP Global Forecast System model were performed and compared with the NCEP Global Data Assimilation System (GDAS). All observations in the operational data stream were assimilated for the period 1 January–10 February 2004, ex ..."
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Cited by 51 (7 self)
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Realdata experiments with an ensemble data assimilation system using the NCEP Global Forecast System model were performed and compared with the NCEP Global Data Assimilation System (GDAS). All observations in the operational data stream were assimilated for the period 1 January–10 February 2004, except satellite radiances. Because of computational resource limitations, the comparison was done at lower resolution (triangular truncation at wavenumber 62 with 28 levels) than the GDAS realtime NCEP operational runs (triangular truncation at wavenumber 254 with 64 levels). The ensemble data assimilation system outperformed the reducedresolution version of the NCEP threedimensional variational data assimilation system (3DVAR), with the biggest improvement in datasparse regions. Ensemble data assimilation analyses yielded a 24h improvement in forecast skill in the Southern Hemisphere extratropics relative to the NCEP 3DVAR system (the 48h forecast from the ensemble data assimilation system was as accurate as the 24h forecast from the 3DVAR system). Improvements in the datarich Northern Hemisphere, while still statistically significant, were more modest. It remains to be seen whether the improvements seen in the Southern Hemisphere will be retained when satellite radiances are assimilated. Three different parameterizations of background errors unaccounted for in the data assimilation system (including
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.
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
Model Error Estimation Employing an Ensemble Data Assimilation Approach
, 2006
"... A methodology for model error estimation is proposed and examined in this study. It provides estimates of the dynamical model state, the bias, and the empirical parameters by combining three approaches: 1) ensemble data assimilation, 2) state augmentation, and 3) parameter and model bias estimation. ..."
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Cited by 40 (16 self)
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A methodology for model error estimation is proposed and examined in this study. It provides estimates of the dynamical model state, the bias, and the empirical parameters by combining three approaches: 1) ensemble data assimilation, 2) state augmentation, and 3) parameter and model bias estimation. Uncertainties of these estimates are also determined, in terms of the analysis and forecast error covariances, employing the same methodology. The model error estimation approach is evaluated in application to Korteweg–de Vries–Burgers (KdVB) numerical model within the framework of maximum likelihood ensemble filter (MLEF). Experimental results indicate improved filter performance due to model error estimation. The innovation statistics also indicate that the estimated uncertainties are reliable. On the other hand, neglecting model errors—either in the form of an incorrect model parameter, or a model bias—has detrimental effects on data assimilation, in some cases resulting in filter divergence. Although the method is examined in a simplified model framework, the results are encouraging. It
A TwoStage Ensemble Kalman Filter for Smooth Data Assimilation
, 2005
"... The ensemble Kalman Filter (EnKF) and variants derived therefrom have become important techniques in data assimilation problems. One breakdown of the EnKF method is that in the case of sparsely observed, accurate data, least squares properties of the EnKF create posterior ensemble members that are n ..."
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Cited by 27 (12 self)
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The ensemble Kalman Filter (EnKF) and variants derived therefrom have become important techniques in data assimilation problems. One breakdown of the EnKF method is that in the case of sparsely observed, accurate data, least squares properties of the EnKF create posterior ensemble members that are not compatible with the dynamic model. We propose a modification of Kalman and EnKF filters by imposing a constraint either by projection or by a penalty. A twostep ensemble Kalman Filter is proposed that imposes smoothness as a penalized constraint. The smoothing step consists of another application of the same EnKF code with the smoothness constraint as an independent observation. The utility of the method is demonstrated on a nonlinear dynamic model of wildfire.
A comparison of hybrid ensemble transform Kalman filterOptimum Interpolation and ensemble squareroot filter analysis schemes
, 2007
"... A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A twolayer primitive equation model was used under perfectmodel assumptions. A simplified observation network was used ..."
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Cited by 21 (6 self)
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A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A twolayer primitive equation model was used under perfectmodel assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static backgrounderror covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF backgrounderror covariance was estimated fully from the ensemble. For 50member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity
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 18 (5 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.
A deterministic formulation of the ensemble Kalman filter: An alternative to ensemble square root filters
 Tellus
"... The use of perturbed observations in the traditional ensemble Kalman filter (EnKF) results in a suboptimal filter behaviour, particularly for small ensembles. In this work, we propose a simple modification to the traditional EnKF that results in matching the analysed error covariance given by Kalman ..."
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Cited by 18 (4 self)
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The use of perturbed observations in the traditional ensemble Kalman filter (EnKF) results in a suboptimal filter behaviour, particularly for small ensembles. In this work, we propose a simple modification to the traditional EnKF that results in matching the analysed error covariance given by Kalman filter in cases when the correction is small; without perturbed observations. The proposed filter is based on the recognition that in the case of small corrections to the forecast the traditional EnKF without perturbed observations reduces the forecast error covariance by an amount that is nearly twice as large as that is needed to match Kalman filter. The analysis scheme works as follows: update the ensemble mean and the ensemble anomalies separately; update the mean using the standard analysis equation; update the anomalies with the same equation but half the Kalman gain. The proposed filter is shown to be a linear approximation to the ensemble square root filter (ESRF). Because of its deterministic character and its similarity to the traditional EnKF we call it the ‘deterministic EnKF’, or the DEnKF. A number of numerical experiments to compare the performance of the DEnKF with both the EnKF and an ESRF using three small models are conducted. We show that the DEnKF performs almost as well as the ESRF and is a significant improvement over the EnKF. Therefore, the DEnKF combines the numerical effectiveness, simplicity and versatility of the EnKF with the performance of the ESRFs. Importantly, the DEnKF readily permits the use of the traditional Schur productbased localization schemes. 1.
Assimilation of Surface Pressure Observations using an Ensemble Filter in an Idealized Global Atmospheric Prediction System
, 2005
"... An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held–Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model’s state at all levels when only observations of surface pressure (PS) are avail ..."
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Cited by 17 (2 self)
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An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held–Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model’s state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation’s prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude highfrequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined. The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model’s spatial domain. This suggests