Mesoscale Ensemble Data Assimilation and Prediction System


Figure 1: A description of Obs-nudging and 4D-REKF FDDA formulations.

A Four-Dimensional Relaxation Ensemble Kalman Filter (4D-REKF) mesoscale analysis and forecasting system has been developed by RAL’s numerical weather prediction (NWP) modeling group. 4D-REKF is built upon the multi-model (MM5 and WRF), multi-approach (perturbations), and multi-scale (nested-grid) E-RTFDDA (Ensemble Real-Time Four-Dimensional Data Assimilation and forecasting system). E-RTFDDA was developed at RAL and has been deployed for real-time operational weather forecasting at the Army Dugway Proving Ground and in wind energy forecast applications. E-RTFDDA model members employ Newtonian-relaxation 4D data assimilation algorithms to achieve rapid cycling of continuous 4D analysis and forecasting. To take advantage of E-RTFDDA ensemble prediction, 4D-REKF uses Kalman gains that can be computed using the multi-model E-RTFDDA forecasts. The Kalman gains are ingested into E-RTFDDA models to replace the simple distance-dependent observation weighting functions in the original nudging model. A Local Ensemble Kalman Filter (LEKF) approach is employed to take account of multi-observations. 

4D-REKF retains and leverages the advantages of both traditional Newtonian-relaxation and Ensemble Kalman Filter data assimilation schemes. It eliminates the shortcoming of empirical specification of spatial weight functions in the current station-nudging FDDA formulation. It also extends the traditional (intermittent) EnKF data assimilation method to a 4D continuous data assimilation paradigm that greatly mitigates the dynamic shocks associated with the intermittent EnKF processes. Furthermore, 4D-REKF also greatly reduces the critical dependency on the background error covariance inflation with the traditional EnKF and permits effective assimilation of all observations that may be available at irregular locations and times.  Figure 1 describes the general formulation of the 4D-REKF FDDA scheme. 4D-REKF enhances both the accuracy of model initial conditions and also the initial condition perturbation approach, and thus improves the overall capabilities of E-RTFDDA ensemble prediction.


4D-REKF was enhanced for assimilation of Doppler radar radial velocity measurements. This work involves a major change of the data structures that can handle the radar observation data and Kalman gains effectively. Unlike the radial velocity assimilation, radar reflectivity measurements are assimilated with hydrometeor and latent heat nudging (HLHN) scheme.  A convective weather case, during PECAN-2015 field campaign, that contains a supercell severe convection storm and three mesoscale convective systems, was selected to performing the radar data assimilation experiments. Numerical experiments were designed to test the validity of the scheme and its implementation. Preliminary results show welcoming potentials for using the scheme to improve short-range forecasting of convection systems.   

To validate the 4D-REKF data assimilation system, OSSE experiments based on the "perfect-model-perfect-observations" approach have been conducted. For comparison, WRF 3DVAR, 4DVAR, GSI, and NCAR DART-EnKF have also been tested with the same OSSE framework and the data.  The verification results of this OSSE study indicate that 4D-REKF outperforms other existing WRF data assimilation technologies. Figure 1 presents an example showing the bias and RMSE of various meteorological variables in 4D-REKF at the end of 6-hour data assimilation in comparison to those of WRF 3DVAR, 4DVAR, NCAR DART-EnKF, and GSI. The bias and RMSE in the standard Station-Nudging FDDA are also shown in the figure.

The 4D-REKF FDDA scheme has been deployed as a component of the operational E-RTFDDA system running at the US Army Dugway Proving Ground, Utah. Assessment of the impact of 4D-REKF is ongoing, but the preliminary results suggest that the “raw” Kalman gains computed from the ensemble forecasts are not sufficiently accurate. Further refinements to the Kalman gains estimation and new hybrid Kalman gain schemes that combine real-time ensemble-based background error covariance and historical regime-based background error covariance were formulated.


4D-REKF is still at an early stage of initial operating capability. Further evaluation and enhancement are necessary to fully exploit the power of the technology.  The limited representativeness of Kalman gains computed from mesoscale ensemble forecasts of excessively small number of ensemble members is still the main challenge for effectively taking the advantage of 4D-REKF.  Empirical algorithms will be explored to address the fact that ensemble mesoscale forecasts often lead to formation of sporadic, unrepresentative local structures in the Kalman gains that introduce noise and lessen the effectiveness of data assimilation. Refinement to 4D-REKF with cross-variable (covariance) “observation-nudging” capabilities for assimilating Doppler radar radial velocities should be studied. Finally, performance of 4D-REKF for real-time semi-operational runs at the US Army Dugway Proving Ground will be assessed and refined. The scheme will also be deployed for other applications.