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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
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 278 (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
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
Evaluation of a shortrange multimodel ensemble system
, 2001
"... Forecasts from the National Centers for Environmental Prediction’s experimental shortrange ensemble system are examined and compared with a single run from a higherresolution model using similar computational resources. The ensemble consists of five members from the Regional Spectral Model and 10 ..."
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Cited by 43 (4 self)
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Forecasts from the National Centers for Environmental Prediction’s experimental shortrange ensemble system are examined and compared with a single run from a higherresolution model using similar computational resources. The ensemble consists of five members from the Regional Spectral Model and 10 members from the 80km Eta Model, with both inhouse analyses and bred perturbations used as initial conditions. This configuration allows for a comparison of the two models and the two perturbation strategies, as well as a preliminary investigation of the relative merits of mixedmodel, mixedperturbation ensemble systems. The ensemble is also used to estimate the shortrange predictability limits of forecasts of precipitation and fields relevant to the forecast of precipitation. Whereas error growth curves for the ensemble and its subgroups are in relative agreement with previous work for largescale fields such as 500mb heights, little or no error growth is found for fields of mesoscale interest, such as convective indices and precipitation. The difference in growth rates among the ensemble subgroups illustrates the role of both initial perturbation strategy and model formulation in creating ensemble dispersion. However, increase spread per se is not necessarily beneficial, as is indicated by the fact that the ensemble subgroup with the greatest spread is less skillful than the subgroup with the least spread. Further examination into the skill of the ensemble system for forecasts of precipitation shows the advantage gained from a mixedmodel strategy, such that even the inclusion of the less skillful Regional Spectral Model members improves ensemble performance. For some aspects of forecast performance, even ensemble configurations with as few as five members are shown to significantly outperform the 29km MesoEta Model. 1.
Simulation of interannual variability of tropical storm frequency in an ensemble of GCM integrations
 J. Climate
, 1997
"... The present study examines the simulation of the number of tropical storms produced in GCM integrations with a prescribed SST. A 9member ensemble of 10yr integrations (1979–88) of a T42 atmospheric model forced by observed SSTs has been produced; each ensemble member differs only in the initial at ..."
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Cited by 31 (5 self)
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The present study examines the simulation of the number of tropical storms produced in GCM integrations with a prescribed SST. A 9member ensemble of 10yr integrations (1979–88) of a T42 atmospheric model forced by observed SSTs has been produced; each ensemble member differs only in the initial atmospheric conditions. An objective procedure for trackingmodelgenerated tropical storms is applied to this ensemble during the last 9 yr of the integrations (1980–88). The seasonal and monthly variations of tropical storm numbers are compared with observations for each ocean basin. Statistical tools such as the Chisquare test, the F test, and the t test are applied to the ensemble number of tropical storms, leading to the conclusion that the potential predictability is particularly strong over the western North Pacific and the eastern North Pacific, and to a lesser extent over the western North Atlantic. A set of tools including the joint probability distribution and the ranked probability score are used to evaluate the simulation skill of this ensemble simulation. The simulation skill over the western North Atlantic basin appears to be exceptionally high, particularly during years of strong potential predictability. 1.
A conceptual framework for predictability studies
 J. Climate
, 1999
"... A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate tra ..."
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Cited by 28 (0 self)
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A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate transformations and applies to multivariate predictions irrespective of assumptions about the probability distribution of prediction errors. For univariate Gaussian predictions, the PP reduces to conventional predictability measures that are based upon the ratio of the rms error of a model prediction over the rms error of the climatological mean prediction. Since climatic variability on intraseasonal to interdecadal timescales follows an approximately Gaussian distribution, the emphasis of this paper is on multivariate Gaussian random variables. Predictable and unpredictable components of multivariate Gaussian systems can be distinguished by predictable component analysis, a procedure derived from discriminant analysis: seeking components with large PP leads to an eigenvalue problem, whose solution yields uncorrelated components that are ordered by PP from largest to smallest. In a discussion of the application of the PP and the predictable component analysis in different types of predictability studies, studies are considered that use either ensemble integrations of numerical models or autoregressive models fitted to observed or simulated data. An investigation of simulated multidecadal variability of the North Atlantic illustrates the proposed methodology. Reanalyzing an ensemble of integrations of the Geophysical Fluid Dynamics Laboratory coupled general circulation model confirms and refines earlier findings. With an autoregressive model fitted to a single integration of the same model, it is demonstrated that similar conclusions can be reached without resorting to computationally costly ensemble integrations. 1.
Presentday capabilities of numerical and statistical models for atmospheric extratropical seasonal simulation and prediction
 Bulletin of the American Meteorological Society
, 1999
"... A statistical model and extended ensemble integrations of two atmospheric general circulation models (GCMs) are used to simulate the extratropical atmospheric response to forcing by observed SSTs for the years 1980 through 1988. The simulations are compared to observations using the anomaly correlat ..."
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Cited by 24 (1 self)
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A statistical model and extended ensemble integrations of two atmospheric general circulation models (GCMs) are used to simulate the extratropical atmospheric response to forcing by observed SSTs for the years 1980 through 1988. The simulations are compared to observations using the anomaly correlation and rootmeansquare error of the 700hPa height field over a region encompassing the extratropical North Pacific Ocean and most of North America. On average, the statistical model is found to produce considerably better simulations than either numerical model, even when simple statistical corrections are used to remove systematic errors from the numerical model simulations. In the mean, the simulation skill is low, but there are some individual seasons for which all three models produce simulations with good skill. An approximate upper bound to the simulation skill that could be expected from a GCM ensemble, if the model’s response to SST forcing is assumed to be perfect, is computed. This perfect model predictability allows one to make some rough extrapolations about the skill that could be expected if one could greatly improve the mean response of the GCMs without significantly impacting the variance of the ensemble. These perfect model predictability skills are better than the statistical model simulations during the summer, but for the winter, presentday statistical forecasts already have skill that is as high as the upper bound for the GCMs. Simultaneous improvements to the GCM mean response and reduction in the GCM ensemble variance would be required for these GCMs to do significantly better than the statistical
Multiresolution ensemble forecasts of and observed tornadic thunderstorm system. Part II: Storm scale experiments
, 2007
"... Using a nonhydrostatic numerical model with horizontal grid spacing of 24 km and nested grids of 6 and 3km spacing, the authors employ the scaled lagged average forecasting (SLAF) technique, developed originally for global and synopticscale prediction, to generate ensemble forecasts of a tornadic ..."
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Cited by 20 (9 self)
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Using a nonhydrostatic numerical model with horizontal grid spacing of 24 km and nested grids of 6 and 3km spacing, the authors employ the scaled lagged average forecasting (SLAF) technique, developed originally for global and synopticscale prediction, to generate ensemble forecasts of a tornadic thunderstorm complex that occurred in northcentral Texas on 28–29 March 2000. This is the first attempt, to their knowledge, in applying ensemble techniques to a cloudresolving model using radar and other observations assimilated within nonhorizontally uniform initial conditions and full model physics. The principal goal of this study is to investigate the viability of ensemble forecasting in the context of explicitly resolved deep convective storms, with particular emphasis on the potential value added by fine grid spacing and probabilistic versus deterministic forecasts. Further, the authors focus on the structure and growth of errors as well as the application of suitable quantitative metrics to assess forecast skill for highly intermittent phenomena at fine scales. Because numerous strategies exist for linking multiple nested grids in an ensemble framework with none obviously superior, several are examined, particularly in light of how they impact the structure and growth of perturbations. Not surprisingly, forecast results are sensitive to the strategy chosen, and owing to the
Boundary conditions for limitedarea ensemble Kalman filters
, 2006
"... One aspect of implementing a limitedarea ensemble Kalman filter (EnKF) involves the specification of a suitable ensemble of lateral boundary conditions. We propose two classes of methods to populate a boundary condition ensemble. In the first class, the ensemble of boundary conditions is provided b ..."
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Cited by 14 (5 self)
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One aspect of implementing a limitedarea ensemble Kalman filter (EnKF) involves the specification of a suitable ensemble of lateral boundary conditions. We propose two classes of methods to populate a boundary condition ensemble. In the first class, the ensemble of boundary conditions is provided by an EnKF on a larger domain and is approximately a random draw from the probability distribution function for the forecast (or analysis) on the limitedarea domain boundary given the available observations. The second class perturbs around a deterministic estimate of the state using assumed spatial and temporal covariance relationships. Methods in the second class are relatively flexible and easy to implement. Experiments that test the utility of these methods are performed for both an idealized lowdimensional model and limitedarea simulations using the Weather Research and Forecasting (WRF) model; all experiments employ simulated observations under the perfect model assumption. The performance of the ensemble boundary condition methods is assessed by comparing the results of each experiment against a control “global ” EnKF that extends beyond the limitedarea domain. For all methods tested, results show that errors for the
2007: A data assimilation case study using a limitedarea ensemble Kalman filter
"... Ensemble Kalman filter (EnKF) data assimilation experiments are conducted on a limitedarea domain over the Pacific Northwest region of the United States, using the Weather Research and Forecasting model. Idealized surface pressure, radiosoundings, and aircraft observations are assimilated every 6 h ..."
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Cited by 9 (2 self)
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Ensemble Kalman filter (EnKF) data assimilation experiments are conducted on a limitedarea domain over the Pacific Northwest region of the United States, using the Weather Research and Forecasting model. Idealized surface pressure, radiosoundings, and aircraft observations are assimilated every 6 h for a 7day period in January 2004. The objectives here are to study the performance of the filter in constraining analysis errors with a relatively inhomogeneous, sparseobservation network and to explore the potential for such a network to serve as the basis for a realtime EnKF system dedicated to the Pacific Northwest region of the United States. When only a single observation type is assimilated, results show that the ensemblemean analysis error and ensemble spread (standard deviation) are significantly reduced compared to a control ensemble without assimilation for both observed and unobserved variables. Analysis errors are smaller than background errors over nearly the entire domain when averaged over the 7day period. Moreover, comparisons of background errors and observation increments at each assimilation step suggest that the flowdependent filter corrections are accurate in both scale and amplitude. An illustrative example concerns a misspecified mesoscale 500hPa shortwave trough moving along the British Columbia coast, which is corrected by surface pressure observations alone. The relative impact of each observation type upon different variables and vertical levels is also discussed. 1.