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

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

4. Assumptions in a 3DVAR
Assumption I: xb-xt and xo-xt are 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).

5. Questions for a 3DVAR 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?

6. B and O 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!

7. 3DVAR: Current Status
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.

8. Fourier series application in data assimilation
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.

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

10. Space-Time Mesoscale Analysis System (STMAS)
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

11. Example
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.

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. Discussion
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.

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

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

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

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

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

20. STMAS for frontal boundary detection

21. STMAS verification comparing to HPC

22. STMAS verification comparing to radar reflectivity

23. Thermodynamic Stability Modifying NWP model forecast by STMAS surface analysis
VIL and Satellite
Mosaic
04/02/ :00 UTC
RUC CAPE
RUC & STMAS CAPE
Convective Available Potential Energy (CAPE) defines the vertically integrated positive buoyancy of a rising parcel.
VIL: Vertical integrated liquid.
*The RUC 3-Hour Forecast Used in Comparison

24. STMAS initial radar experiment on a typhoon case
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.

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
“ ”
True Atmosphere
Old
Observation
instrument
Nature Run
Analysis and
Forecast
system

29. OSSE Design, Simulation and Demonstration
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).
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 V
RADIAL
VECTOR WIND
TOP: TRUE BOTTOM: ANA_RADAR

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

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

34. STMAS: A typhoon test 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.

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. Summary
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.