1. Probabilistic Mesoscale Analyses & Forecasts Progress & Ideas Greg Hakim University of Washington www.atmos.washington.edu/~hakim Brian Ancell, Bonnie Brown, Karin Bumbaco, Sebastien Dirren, Helga Huntley, Rahul Mahajan, Cliff Mass, Guillaume Mauger, Phil Mote, Angie Pendergrass, Chris Snyder, Ryan Torn, & Reid Wolcott. Collaborators:

2. Plan 1.State estimation & forecasting on the mesoscale. 2.The UW “pseudo-operational” system. 3.Ensemble methods for mining & adapting the “data cube.” Analysis & prediction is fundamentally probabilistic!

3. State Estimation Limitations of observations. –Errors. –Sparse in space & time. –Limited info about unobserved fields & locations. –Not usually on a regular grid. Limitations of models. –Errors. –Often not cast in terms of observations (e.g. radiances) –Space & time resolution trade off. Combine strengths of obs & models…

4. Fusing Models and Observations State estimation (“data assimilation”). –combine obs & model estimate of obs. Benefits of ‘fusion’ –Better state estimates. –Observations influence other (unobserved) fields. –Can use observations to improve models. –Observing network design. –Adaptive control.

5. One-dimensional Examples

6. Scalar One-dimensional Example less error than obs and model!

7. Observation (green) & Background (blue) PDFs

8. Analysis (red) PDF---higher density!

9. More-Accurate Observation

10. Less-Accurate Observation

11. More than one dimension: Covariance Relationships between variables (spread obs info) Weight to observations and background Kalman Filter: propagate the covariance Ensemble KF: propagate the square root (sample)

12. State-dependent Cov Matrices EnKF“3DVAR” Cov(Z 500,Z 500) Cov(Z 500,U 500 ) “3DVAR” EnKF

13. Ensemble Covariances 3D-VAR covarianceensemble covariance temperature-temperature covariance

14. Mesoscale Example: cov(|V|, q rain )

15. Sampling Error

16. Summary of Ensemble Kalman Filter (EnKF) Algorithm (1)Ensemble forecast provides background estimate & statistics (P b ) for new analyses. (2)Ensemble analysis with new observations. (3) Ensemble forecast to arbitrary future time.

17. Real Time Data Assimilation at the University of Washington Operational since 22 December 2004 90-member WRF EnKF assimilate obs every 6 hours 36 km grid over NE Pacific and western NOAM Experimental 12 km grid over Pacific Northwest Transition from research to operations was a direct result of CSTAR support.

18. www.atmos.washington.edu/~enkf

19. UW EnKF System Weather Research and Forecasting model, (WRF) 45 km resolution, 33 vertical levels 90 ensemble members 6 hour analysis cycle ensemble forecasts to t+24 hrs at 00 and 12 UTC assimilate rawinsonde, ACARS, cloud drift winds, ASOS, buoy and ship data

20. System Performance WindsMoisture UW EnKF GFS CMC UKMO NOGAPS

21. No Assimilation Member WindsMoisture WRF EnKFNo Assimilation Member

22. GFS Initialized Member WindsMoisture WRF EnKFGFS Initialized Member

23. Applications of Ensemble Data Example: Forecast sensitivity and observation impact Can rapidly evaluate many metrics & observations –Allows forecasters to do “what if” experiments. cf. adjoint sensitivity: –new adjoint run for each metric –Also need adjoint of DA system for obs impact.

24. Sensitivity to SLP

25. Analysis difference (no-buoy – buoy), Shift frontal wave to the southeast

26. 6-hour forecast difference

27. 12-hour forecast difference

28. 18-hour forecast difference

29. 24-hour forecast difference Predicted Response: 0.63 hPa Actual Response: 0.60 hPa

30. Observation Impact Example Typhoon Tokage (2004)

31. Observation Impact Squares – rawinsondes Circles – surface obs. Diamonds – ACARS Triangles – cloud winds Compare forecast where only this 250 hPa zonal wind observation is assimilated to forecast with no observation assimilation

32. F00 Forecast Differences Sea-level Pressure500 hPa Height

33. F24 Forecast Differences Sea-level Pressure500 hPa Height

34. F48 Forecast Differences Sea-level Pressure500 hPa Height

35. Ensemble Opportunities Short-term mesoscale probabilistic forecasts ensemble population matters (cf. medium range) “Hybrid” data assimilation flow-dependent covariance in 4dvar cost function. Kalman smoother with strong model constraint. Observation targeting, thinning, and QC. “Adaptive” forecast grids & metrics update forecasts on-the-fly with new observations. Jim Hansen (NRL)

36. Summary Analysis & prediction is fundamentally probabilistic! –Future plans should embrace this fact Ensembles are not just for prediction & assimilation –Observations: impact; QC; targeting; thinning –Models: calibration and adaptation; forget “plug-n-play” –Data mining: user-defined metrics; “instant updates”