Toward a Real Time Mesoscale Ensemble Kalman Filter

1. Toward a Real Time Mesoscale Ensemble Kalman Filter http://www.atmos.washington.edu/~hakim “Analysis PDF of Record” Gregory J. Hakim Dept. of Atmospheric Sciences, University of Washington Collaborators: Ryan Torn (UW) Sebastien Dirren (UW) Chris Snyder (NCAR)

2. Two Distinct AOR Priorities • NDFD forecast verification. • Nationwide analyses; no critical delivery time? • An a posteriori approach could use max data. • Better centralized for uniformity? • No distribution costs; no hard deadlines. 2) Real-time mesoscale analyses & forecasts. • Regional analyses & short (<12 h) forecasts. • Delivery time critical; use available data. • A distributed/regional approach is helpful? • DA community resource (cf. MM5, WRF, etc.) • EnKF appears well suited.

3. Summary of Ensemble Kalman Filter (EnKF) Algorithm • Ensemble forecast provides background estimate & statistics (Pb) for new analyses. • Ensemble analysis with new observations. (3) Ensemble forecast to arbitrary future time.

4. Strengths & Weakness of EnKF • Probabilistic analyses & probabilistic forecasts. • prob. forecasts widely embraced. • prob. analyses don’t yet exist. • account for ensemble variance in NDFD verification? • Straightforward implementation; ~parallelization. • Do not need • background error covariance models. • adjoint models (cf. 4DVAR). • Weakness: Rank deficient covariance matrices. • ensemble may need to be very large. • Many ways to boost rank for small ensembles O(100).

5. Synoptic Scale Example • Weather Research and Forecasting Model (WRF). • 100 km grid spacing; 28 vertical levels. • Assimilate 250 surface pressure obs ONLY. • Perfect model assumption. • Observations = truth run + noise.

6. Surface Pressure Errors

7. ~500 mb Height Errors

8. Boundary Conditions (Ryan Torn)

9. Ensemble Surface Pressure & q

10. Ensemble 500 hPa Height & PV

11. Surface Cov(P, Plow) & Cov (V, Plow)

12. L Cov(Z500, Plow) & Cov (V500, Plow)

13. Covariance Convergence

14. 500 mb j Covariance, Ne = 20

15. 500 mb j Covariance, Ne = 40

16. 500 mb j Covariance, Ne = 60

17. 500 mb j Covariance, Ne = 80

18. 500 mb j Covariance, Ne = 100

19. Mesoscale Examples • 12 km grid spacing, 38 vertical levels. • 3-class microphysics. • TKE boundary layer scheme. • 60 ensemble members. • Assimilate surface pressure observations. • Hourly observations. • Drawn from truth run plus noise. • Realistic surface station distribution.

20. Observation Network

21. Surface Pressure Error Snapshot

22. Mesoscale Covariances 12 Z January 24, 2004 Camano Island Radar |V950|-qr covariance

23. Surface Pressure Covariance Land Ocean

24. Toward a Real-Time Mesoscale EnKF Prototype • Surface observations • (U,V,T,RH, green) • Radiosondes • (U,V,T,RH) • Scatterometer winds • (U,V over ocean, red) • ACARS • (U,V,T)

25. Summary Ensemble Kalman filter AOR opportunities: • Ensemble mesoscale analyses & short-term forecasts. • Lowers barriers-to-entry for DA. • Regional DA (prototype in progress at UW). • Community DA resource (cf. MM5, WRF). Background Error Covariances: • Automatic & flow dependent with EnKF. • Cloud field analyses no more difficult than, e.g., 500 hPa height. • Optimal ensemble size? • Vary strongly in space & time. • Difficult to assume mesoscale covariances, unlike synoptic scale.

26. THE END

27. EnKF Sampling Issues • Problem #1: “under-dispersive” ensembles. • overweight background relative to observations. • Solution: Inflate K by a scalar constant. • Problem #2: spurious far-field covariances. • affect analysis far from observation. • Solution: Localize K with a window function.

28. Computational & Plotting Domains

29. Analysis-update Equation analysis = prior + weighted observations

30. Traditional Kalman Filter Problem A forecast of Pb is needed for next analysis. • Problem: Pb is huge (N x N) and cannot be evolved directly. • Solution: estimate Pb from an ensemble forecast. • “Ensemble” KF (EnKF).

31. Current DA and Ensemble Forecasting 3D/4Dvar:Pbis~ flow independent. • Assumed spatial influence of observations. • Assumed field relationships (e.g. wind—pressure balance). • Pb assumptions for mesoscale are less clear. • Deterministic: a single analysis is produced. Ensemble forecasts • perturbed deterministic analyses (SVs, bred modes). EnKF: unifies DA & ensemble forecasting.

32. Kalman Gain

33. Application of Localization

34. Ensemble Tropopause q

35. L Cov(qtrop, Plow) & Cov (Vtrop, Plow)

36. Synoptic Observation Network

37. Application to an Extratropical Cyclone 23 March 2003.

38. Motivation • Probabilistic forecasts well accepted. • e.g. forecast ensembles. • Genuine probabilistic analyses are lacking. • singular vectors & bred modes are proxies. • Solving this problem creates opportunities. • probabilities: structural & dynamical information. • old: dynamics  data assimilation. • new: data assimilation  dynamics.

39. Ensemble Statistics • Ensemble-estimated covariance between x and y: • cov(x, y) = (x – x) (y – y)T. • Here, we normalize y by s(y). • cov(x, y) has units of x. • linear response in x given one-s change in y. • take y = surface pressure in the low center.

40. Mesoscale Challenges • Cloud fields & precipitation. • No time for “spin up.” • Complex topography. • Background covariances vary strongly in space & time. • can’t rely on geostrophic or hydrostatic balance. • Boundary conditions on limited-area domains.