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 multi-class 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 multi-class 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

The 2-yr performance of a pseudo-operational (real time) limited-area ensemble Kalman filter (EnKF) based on the Weather Research and Forecasting Model is described. This system assimilates conventional observations from surface stations, rawinsondes, the Aircraft Communications Addressing and Reporting System (ACARS), and cloud motion vectors every 6 h on a domain that includes the eastern North Pacific Ocean and western North America. Ensemble forecasts from this system and deterministic output from operational numerical weather prediction models during this same period are verified against rawinsonde and surface observation data. Relative to operational forecasts, the forecast from the ensemble-mean analysis has slightly larger errors in wind and temperature but smaller errors in moisture, even though satellite radiances are not assimilated by the EnKF. Time-averaged correlations indicate that assimilating ACARS and cloud wind data with flow-dependent error statistics provides corrections to the moisture field in the absence of direct observations of that field. Comparison with a control experiment in which a deterministic forecast is cycled without observation assimilation indicates that the skill in the EnKF’s forecasts results from assimilating observations and not from lateral boundary conditions or the model formulation. Furthermore, the ensemble variance is generally in good agreement with the ensemble-mean error and the spread increases monotonically with forecast hour.

One aspect of implementing a limited-area 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 limited-area 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 ideal-ized low-dimensional model and limited-area 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 limited-area domain. For all methods tested, results show that errors for the

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Effect of lateral boundary perturbations on the breeding method and the local ensemble transform Kalman filter

This work examines the impact of coarsely resolved and temporally interpolated lateral boundary conditions (LBCs) on the dispersion of limited-area-model (LAM) ensemble forecasts. An expression is developed that links error variance spectra to ensemble spread while accounting for spatial and ensemble mean errors. The balances required by this expression are used to show that LBC constraints on small-scale error variance growth are sufficient to help cause underdispersive LAM ensemble simulations. The hypothesis is tested in a controlled and efficient manner using a modified barotropic channel model. Ten-member ensemble simulations are produced over many cases on a ‘‘global’ ’ periodic channel domain and each of four smaller nested LAM domains. Lateral boundary effects are specifically isolated since all simulations are perfect except for initial condition perturbations and the use of coarsely resolved and/or temporally interpolated ‘‘one-way’ ’ LBCs. This configuration excludes other analysis and external model system errors that are not caused directly by the implementation of LBCs. Statistical results accumulated over 100 independent cases demonstrate that LAM ensembles remain underdispersive even when using a complete set of LBCs from an external ensemble forecast. The small-scale constraints on error growth are present in any modeling system using coarsely resolved or temporally interpolated one-way LBC forcing. Although not tested here, similar limitations may apply to global variable-resolution models because of insufficient small-scale variance outside the perimeter of higher-resolution subdomains. The results of this work suggest the need to apply statistically consistent, small-scale LBC perturbations at every time step throughout the LAM simulations. 1.

This paper explores the use of large ensembles of model runs with randomly perturbed initial conditions for the calculation of error covariance fields, initial condition sensitivity fields, and perturbation impact fields. The calculation of error covariances from ensembles is familiar from ensemble Kalman filter (EnKF) techniques, but the calculation of sensitivity and impact fields from ensembles is new. This work is unlike previous EnKF work in that the ensemble members are randomly perturbed in each degree of freedom (DOF) of the model, rather than having perturbation fields based on expected errors in the analysis. In this work, all the DOFs of the model (or a subset) are independently and simultaneously perturbed and the response of the model to each perturbed DOF is sought by statistical technique. Sensitivity results are conceptually comparable to adjoint calculations. Error covariance, impact, and sensitivity fields constitute the three distinct kinds of fields that can be found from an ensemble. These fields can be found equivalently to first order as either covariances or partial derivatives from regression analysis. This paper makes use of ensembles of 2000 members of a mesoscale model, run for 6 hours over a domain in the

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