1. Assimilation of radar observations in mesoscale models using approximate background error covariance matrices (2006 Madison Flood Case) 1

2. The forecasting of severe thunderstorms is important. –Flood is potentially life-threatening Why I used radar –Continuously observe dynamically evolving severe thunderstorms with high resolution Why I used EnKF –Flow dependent, less computation Why they have a problem. –Conflict between "non-linearity of observation operator and the "Gaussian assumption" of EnKF 2

3. Outline Problem –WRF problem : no-deep convection in WRF –EnKF problem : non-Gaussian problem Applications –WRF/EnKF reviews Solution –Perturbation method –Background error approximation –Weighting technique –Validation Discussion and Summary 3

4. Flash Flood/Flood Facts Flash floods/floods are the #1 cause of deaths associated with thunderstorms Nearly 100 people die nationwide each year Most fatalities occur at night Nearly half of fatalities are vehicle related Responsible for billions of dollars of damage each year 4 Skywarntmreview by Phil Hysell The U.S. Natural Hazard Statistics

5. NOAA’s annual compilations of flood loss statistics 5

6. July 27, 2006 Madison 6

7. 1500z Surface Analysis 7

8. 1800z Surface Analysis 8

9. 1630 UTC KMKX on 27 July 2006 9

10. 1944 UTC KMKX on 27 July 2006 10

11. Radar Observation WRF without Radar Assimilation 11

12. Severe convection was not forecasted and WRF does not simulate it CAPE values near 2000 Jkg-1 But, the radar captured the convection initiation and it developed very quickly into the severe deep convections surface temperature 79 F dew point temperature 72 F Synoptic overviewObservation overview Potential instability 12

13. Forecasting by inverse methods 13 1.What is the EnKF? 3. How EnKF works? 2. Two information

14. Kalman gain in EnKF 14 Kalman Filter Ensemble Kalman Filter

15. Experiment setup (S: Spin-up time after two initializations, R: Radar data assimilation in WRF, F: Forecast after Radar data assimilation) Center point43.071N 89.37W Latitude Longitude Domain size700 x1582 km 2 142 x285 km 2 Mother dom. Nest dom. Spatial resolution7.12 km 1.42 km dx, dy in the mother dom. in the nest dom. WRF Radar assimilation 15

16. Perturbation Method 16

17. ControlEXP 1EXP 2 State vectors Ensemble runs Without Assimilation Observation operator in Kalman Gain Without Assimilation Observation operator in Observation increment Without Assimilation Model variables for EnKF implementation Observation simulation (Z-Qr relationship) Reflectivity Z Reflectivity Z Reflectivity Z Observations No Assimilation Reflectivity Z Reflectivity Z 17

18. EXP 1 : Non-Gaussian problems 18

19. EXP 2 : New method (New method in general form) 19 (PDFs modulation between different physical properties) Normalization

20. 20 Kalman Filter EnKF Conventional H matrix-free approximation New approximation with weighting factor and rescaling factor NEW method in EnKF

21. 21 NEW method in EnKF

22. Result Summary ControlEXP 1EXP 2 Observation operator in Kalman Gain - Problem No deep convection Non- Gaussian good Correlation Results No flood forecast unrealistic unstable update Stable realistic update 22

23. 1630 UTC1730 UTC1900 UTC2100 UTC 23

24. Results of Cont, EXP 1 & EXP 2 24

25. 25 Assimilation and Forecast of EXP1 and EXP2

26. 26 Weighting experiment to find realistic scale of forecasting

27. 27 Vertical cross section Potential temperature evolution

28. 28 RADA R 123 45 6 7 8 9 1011 121314 15

29. Assimilation of highly non-linear observations into a numerical weather prediction model -Proper perturbation method to generate physically meaningful ensemble members -Maintenance of Gaussian distribution in Kalman gain (Normalizing and Rescaling process ) -Resolve the systemically underestimated background errors during the successive assimilation cycles and find practical forecasting scale.(Weighting technique) Good initial results for Madison flood case 29

30. Acknowledge Ralf Bennartz Thanks for WRF workshop in NCAR, multiprocessor machine, motivation and understanding what is science! Mark Kulie John Rausch Longtao Wu 30

31. Thank you! Question ? 31