Space and Time Mesoscale Analysis System — Theory and Application 2007 Yuanfu Xie

1. Space and Time Mesoscale Analysis System — Theory and Application 2007 Yuanfu Xie Forecast Application Branch Global Systems Division Earth System Research Laboratory Oceanic and Atmospheric Research National Oceanic and Atmospheric Administration Department of Commerce President Bush of United States

2. Difference between a conventional 3DVAR and STMAS; STMAS application in front detection; STMAS radar initial experiment; Future possible OSSE for new observation data; Summary. Outline

3. In most cases, DA usually has two information sources: background and observation (QCed). Information sources of data assimilation Observation Background True atmosphere

4. Assumption I:xb-xtand xo-xtare random variables following a Gaussian distribution; Assumption II: The covariances, B and O of the Gaussian distributions are known; With these assumptions, the largest probability of a best analysis is to maximize Exp[-(x-xb)TB-1(x-xb) -(y-yo)TO-1(y-yo)]; Thus a 3DVAR is to minimize: (x-xb)TB-1(x-xb) +(y-yo)TO-1(y-yo). Assumptions in a 3DVAR

5. Are these variables random? Which are the state variables whose background error follows a Gaussian distribution? Which are the state variables whose observation error follows a Gaussian distribution? How much do we know these covariance, B and O? Questionsfor a 3DVAR

6. Knowledge about these covariance is little. The B matrix is a covariance correlating millions of variables. It is difficult to estimate this covariance statistically. For O, more research and investigation are needed. Both are flow dependent! B and O

7. Treat the background and observation as random variables; Assume these random errors Gaussian; Use a recursive filter and some simple statistical error accumulation to approximate B; Use a diagonal matrix to approximate O. 3DVAR: Current Status

8. Any function can be approximated by a sequence of Fourier base functions, sine and cosine. DA is underdetermined problem. Thus, longer wave is needed to retrieve from observations first as observations are sparse. Fourier series application in data assimilation

9. Minimize distance of observations and truncated Fourier series: Minimize || uT - uo ||. The uTcan be any smooth function representing long waves. A sequence of variational retrievals

10. It is a sequential 3DVAR analysis; Error covariance can be added as weighted normal: Minimize || uT - uo ||O = (uT - uo)TO-1 (uT - uo). Background can be added as well: Min (uT - ub)TB-1 (uT - ub)+ (uT - uo)TO-1 (uT - uo). Balances may be treated as penalty: Min (uT - ub)TB-1 (uT - ub)+ (uT - uo)TO-1 (uT - uo)+P Space-Time Mesoscale Analysis System (STMAS)

11. Assuming a cold front is missing from the background. The true atmosphere differs from the background by the function (above) over the domain (bottom with dots indicating mesonet observation network. Example

12. Conventional 3DVAR solutions using recursive filters 0.9 0.5 0.7 These analyses are intended to approximate the truth:

13. Different Implementation of STMAS Recursive filter Wavelet Multigrid

14. STMAS can retrieve resolvable information from a given obs network; It is variational and has all of the advantages of dealing with radar, satellite, balances and covariance. Mutigrid STMAS is very efficient. Discussion

15. STMAS application—Joint effort with MIT LL for FAA

16. Dashed Orange: 70 km Range of MIGFA KLOT August 23, 2006 O’Hare First MIGFA Detection of Outflow 22:45 UTC

17. Dashed Orange: 70 km Range of MIGFA KLOT August 23, 2006 O’Hare Outflow Reaches O’Hare 23:46 UTC

18. Dashed Orange: 70 km Range of MIGFA KLOT August 24, 2006 O’Hare Outflow Continues Through O’Hare 00:01 UTC

19. Dashed Orange: 70 km Range of MIGFA KLOT August 24, 2006 O’Hare Fullest Detection 00:44 UTC

20. STMAS for frontal boundary detection

21. STMAS verificationcomparing to HPC

22. STMAS verificationcomparing to radar reflectivity

23. Thermodynamic StabilityModifying NWP model forecast by STMAS surface analysis VIL and Satellite Mosaic 04/02/2006 21:00 UTC RUC CAPE RUC & STMAS CAPE *The RUC 3-Hour Forecast Used in Comparison

24. Tested an analytic function; Experiment is performed at an area where there is no conventional obs (CWB); Use a symmetry assumption to derive a first or second order approximation of the wind; Add real radar radial wind. STMAS initial radar experiment on a typhoon case

25. STMAS: Analytic test Analytic wind field Analytic radial wind

26. STMAS: Analytic test (Cont.) Convention obs only Radial wind only

27. STMAS: Analytic test (Cont.) Conventional+radial Conventional+radial+One Introduce OSSE issue

28. OSSE New instrument? “ ” True Atmosphere Old Observation instrument Nature Run Analysis and Forecast system

29. Benefit - Cost evaluation (design and decision); Operational experience (simulation and learning); Optimal design: where, when and what to observe for gaining best results (design and demonstration). OSSEDesign, Simulation and Demonstration More importantly, OSSE can be done even before an observation network is physically built.

30. U V RADIAL TRUE ANA_CNVTN_24PTS ANA_RADAR ANA_RADAR_CNVTN_24PTS

31. U RADIAL VECTOR WIND V TOP: TRUE BOTTOM: ANA_RADAR

32. VECTOR RADIAL U V TOP : ANA_CNVTN_25PTS BOTTOM: ANA_RADAR_CNVTN_25PTS

33. RADIAL VECTOR U V TOP : ANA_CNVTN_441PTS BOTTOM: ANA_RADAR_CNVTN_441PTS

34. A real typhoon case in 2006; No conventional observation data available; Use a derived wind field by CWB in STMAS to examine weather STMAS can provide additional information. STMAS: A typhoon test

35. STMAS: A typhoon test (Cont.) u v Analysis: radial+derived wind Analysis: Derived wind only Derived wind

36. STMAS: A typhoon test (Cont.) u v Analysis of radial+derived wind Substract (-) Derived wind (where it is available) Analysis of Derived wind Substract (-) Derived wind (where it is available)

37. Instead of treating obs and background as random, STMAS gains information from the resolvable observations; A multigrid implementation of STMAS is extremely efficient, e.g., a whole CONUS grid analysis with 5 km resolution takes less than 2 minutes for analyzing 6 variables; STMAS radar radial wind analysis is quite interesting, particularly for strong cyclones. Its numerical forecast impact is to be study. Summary