An Efficient Ensemble Data Assimilation Approach and Tests with Doppler Radar Data

1. An Efficient Ensemble Data Assimilation Approach and Tests with Doppler Radar Data Jidong Gao Ming Xue Center for Analysis and Prediction of Storms, University of Oklahoma, Norman

2. Research Goals • To develop an efficient ensemble Kalman filter (EnKF) method for high-resolution NWP, by using a dual resolution approach. • To evaluate the efficiency and accuracy of the method through OSSEs, with simulated radar radial velocity data for a supercell storm.

3. Introduction • EnKF was first introduced by Evensen (1994) and has become very popular in recent years • Recently, the EnKF method has been successfully applied to the radar data assimilation problem (e.g., Snyder and Zhang 2003; Zhang et al. 2004; Dowell et al. 2004; Tong and Xue 2005). • Effective assimilation of radar data is essential for initializing convective-scale NWP models

4. Radar Data Assimilation • The EnKF data assimilation method is especially suitable for radar data assimilation because • Radar only observes Vr and Z, and data coverage is usually incomplete • All other variables have to be ‘retrieved’ • EnKF ‘retrieves’ the unobserved variables via background error covariance obtained through a forecast ensemble • But, EnKF is expensive, because of the need for running a usually rather large ensemble of forecasts and analyses

5. The Methodology • In this work, we propose a dual-resolution (DR) hybrid ensemble DA strategy, with the goal of improving the EnKF efficiency • With the method, an ensemble of forecasts and analyses is run at a lower resolution (LR), while a single system of analysis and forecast is performed at a higher resolution (HR) • The LR forecast ensemble provides estimated background error covariance for the HR analysis • The HR forecast is used to replace or partially adjust the mean of the LR analysis ensemble

6. Lower-resolution analysis and forecast ensemble LR EnKF Analysis LR EnKF Analysis LR EnKF Analysis replace mean replace mean replace mean covariance covariance covariance HR EnKF HR EnKF HR EnKF Single higher-resolution analysis and forecast

7. OSSEs with a Simulated Supercell Storm • A truth simulation is created using ARPS with the Del City supercell sounding, at Dx = 2 km • The model domain: 92 x 92 x 16 km3. • LR has Dx=4 km, HR has Dx=2 km • Dz = 500 m. • Vr data collected at grid point locations are assimilated, at 5 min intervals • 20 ensemble members are used

8. List of EnKF OSSEs

9. RMS Errors of the Analyses for the Three Experiments HR EnKF (EXP1) LR EnKF (EXP2) DR EnKF (EXP3)

10. q’(contours), Z(color shades) and Vh (vectors) at Surface EXP1 HR-EnKF Truth EXP3 DR-EnKF EXP2 LR-EnKF

11. q’, Z and Vh at Surface after 80 min assimilation Truth EXP1 HR-EnKF EXP3 DR-EnKF EXP2 LR-EnKF

12. W at 6 km AGL after 80 min assimilation Truth EXP1 HR-EnKF EXP2 LR-EnKF EXP3 DR-EnKF

13. 2-h Forecasts of q’, Z and Vh at surface Truth EXP1 HR EXP3 DR EXP2 LR

14. 2-h Forecasts of w at 6 km AGL Truth EXP1 HR EXP3 DR EXP2 LR

15. Summary and Discussion • A new efficient dual-resolution (DR) approach for EnKF is proposed and tested with simulated radar data for a supercell storm. • It is shown that the EnKF analysis using DR is almost as good as the HR analysis, but is much better than the LR analysis. • For this case, we save CPU 3-4 times. However, depending on the resolution one choose, the method have the potential to save CPU 10-50 times more than Original EnKF methods.

16. Summary and Discussion • My new experiments: using Dx =Dy= 4km with model EnKF run, to provide error structure for Dx =Dy= 1km, single model run. The result is also very positive.