1. 2007/3/19 MRI, Tsukuba
Recent developments of the local ensemble transform Kalman filter (LETKF) at JMA
Takemasa Miyoshi (NPD/JMA)
Collaborators:
Shozo Yamane (CIS and FRCGC)
Yoshiaki Sato (NPD/JMA)
Kohei Aranami (NPD/JMA)
Takeshi Enomoto (ESC)

2. Outline
1. What is LETKF?
2. LETKF developments at JMA with three models:
AFES (AGCM for the Earth Simulator)
Collaborative work among the Forecast Department/JMA, JAMSTEC, and Chiba Institute of Science
NHM (JMA Nonhydrostatic Regional Model)
GSM (JMA Global Model)

3. EnKF = ensemble fcst. + ensemble update
A schematic of EnKF
Obs.
Analysis Ens. mean
FCST Ens. mean P
Generate ensemble members best representing the analysis errors
An initial condition with errors
T=t0
T=t1
T=t2
EnKF = ensemble fcst. + ensemble update

4. EnKF
EnKF considers flow-dependent error structures, or the “errors of the day”
“advanced” data assimilation method
4D-Var is also an “advanced” method. How different?
EnKF analyzes the analysis errors in addition to analysis itself
“ideal” ensemble perturbations

5. EnKF vs. 4D-Var EnKF 4D-Var “advanced” method? Y Simple to code?
N (e.g., Minimizer)
Adjoint model? N
Observation operator
Only forward
(e.g., TC center)
Adjoint required
Asynchronous obs?
Y (4D-EnKF)
Y (intrinsic)
Initialization after analysis?
Analysis errors?
Y (ensemble ptb)
Limitation
ensemble size
Assim. window
EnKF with infinite ensemble size and 4D-Var with infinite window are equivalent.

6. What is LETKF? Two categories of the EnKF (Ensemble Kalman Filter)
LETKF (Local Ensemble Transform Kalman Filter)
is a kind of ensemble square root filter (SRF)
is efficient with the parallel architecture
Perturbed observation (PO) method
Square root filter (SRF)
Classical
Relatively new
Already in operations (Canadian EPS)
Not in operations yet
Additional sampling errors by PO
No such additional sampling errors

7. AFES-LETKF (Miyoshi, Yamane, and Enomoto)
AFES: AGCM for the Earth Simulator
Resolution: T159/L48 – 480x240x48 grid points
40 ensemble members
Assimilate observations except satellite radiances
1.5-year cycle from May 2005 till Nov 2006: ALERA (AFES-LETKF Experimental Reanalysis)
This is the collaborative work among the Forecast Department/JMA, JAMSTEC, and Chiba Institute of Science. We used the Earth Simulator under support of JAMSTEC.

8. AFES-LETKF tested in Aug 2004
Sea-level pressure　August 16, UTC
LETKF
JMA
SPREAD
DIFFERENCE

9. Flow of analysis errors
500hPa Height
Analysis
(usually available by reanalysis)
Analysis ensemble spread
(analysis error field)
(available by EnKF)

10. Forecast verifications in Aug 2004
Adapted from Miyoshi and Yamane (2006)

11. Summary of the test
Test exp. have shown very good performance of the AFES-LETKF system
Miyoshi and Yamane, 2007: Mon. Wea. Rev., in press.

12. ALERA (AFES-LETKF Experimental ReAnalysis)
500Z RMS diff (1-day running mean)
ALERA - NCEP REANAL
Very stable!
Apply vertical localization of Ps

13. Summary ALERA (AFES-LETKF Experimental ReAnalysis)
Miyoshi, Yamane and Enomoto, 2007: SOLA, in press.
Stable performance over 1.5 years
The product of every 6-hour analysis of 40 ensemble members is useful for further studies
“Ensemble reforecasting”
Further verifications and analyses of the products are in progress

14. LETKF without local patches
SLP analysis ensemble spread after the first analysis step
The discontinuities caused by the local patches disappear.

15. NHM-LETKF (Miyoshi and Aranami)
NHM: JMA nonhydrostatic model (in operations)
Perfect model experiment in a small region
Miyoshi and Aranami, 2006: SOLA,
5-km grid spacing, 10 members
Experiment with real obs in July 2004
20-km grid spacing, 20 members

16. Perfect model experiment

17. Precipitation
NO DA
w/o rain obs
w/ rain obs
TRUTH
TIME

18. Exp. with real observations
Experimental settings
Experiment period
2004/6/25-7/15
Grid spacing
20 km
Region (# of grid points)
JMA operational (181x145x50)
Ensemble size 20
Gaussian localization length
Horizontal: 5-grid
Vertical: 3-grid
Local patch size
21x21x13
Covariance inflation
10% multiplicative spared inflation
Boundary condition
Fixed for all ensemble members

19. 6-hr fcst initiated at 00Z July 4, 2004
Operational hydrostatic MSM as of July 2004
LETKF ensemble mean

20. Ensemble spreads

21. Summary
Perfect model experiment indicates the LETKF works appropriately.
With real obs, LETKF reproduces similar analysis as the JMA operational MSM.
Growing modes appear inside the region; the effects of boundaries are limited near the boundaries
NOTE: Growing modes with longer wavelengths are artificially damped due to the fixed boundary.
NHM-LETKF is a useful tool for future studies in mesoscale NWP

22. GSM-LETKF (Miyoshi and Sato)
GSM: JMA global model (in operations)
Resolution: TL159/L48 – 320x160x48 grid points
20 and 50 ensemble members
Real obs including satellite radiances
Miyoshi and Sato, 2007: SOLA,

23. Assimilation of satellite radiances
AMSU-A
Vertical localization is required.
Normalized sensitivity function is used as the localization weights.
Canadian operational EnKF uses the Guassian function in the same manner as the conventional obs.
SSM/I

24. Spaghetti diagrams w/o satellite radiances w/ satellite radiances
w/o vertical localization
Too small spread
Caused by spurious covariance due to sampling errors
w/ satellite radiances
w/ vertical localization
Larger spread due to damping sampling errors

25. Residuals against JMA analysis
20 members
BIAS
SLP [hPa]
Red: w/ vertical local.
Blue: w/o vertical local.
Green: w/o satellite assim.
RMSE (solid)
SPREAD (dashed)
Too small SPREAD
Too large RMSE
SLP [hPa]

26. Effects by satellite radiances
RMSE and bias against radiosondes
Reduced RMSE of Z in mid-upper troposphere ( hPa), especially in the SH and Tropics
Blue: w/o satellite radiances
Red: w/ satellite radiances
Reduced negative bias of Z and T
20 members

27. Ensemble size 20  50 RMSE and bias against radiosondes
Blue: Operational 4D-Var
Red: 20-member LETKF
Green: 50-member LETKF
50 members > 20 members
Generally 4D-Var > LETKF
Exception: mid-upper tropospheric temperature in the SH
w/ satellite radiances

28. Z500 global forecast anomaly score
Anomaly Correlations (against own analyses)
Blue: Operational 4D-Var
Red: 20-member LETKF
Green: 50-member LETKF

29. Tuning parameters…in progress
Red: LETKF Blue: 4D-Var

30. Summary LETKF has been successfully applied to the three models:
AFES (AGCM for the Earth Simulator)
NHM (JMA nonhydrostatic regional model)
GSM (JMA global model)
GSM-LETKF with 50 members indicates identical performance to the operational 4D-Var system in the NH.
Ideas for further improvements
Further retuning
50 members  100 members
TL159  TL319
Adaptive bias correction for satellite radiances
Incremental method (high-resolution first guess)
The ALERA dataset will be available to researchers for free!

31. Thank you
for your attention!

32. ALERA system description
Ensemble size 40
Localization parameters
21x21x13 local patch
6-grid horizontal 3-grid vertical Gaussian localization
Covariance inflation parameter
10% multiplicative spread inflation (21% cov inflation)
Experimental period
May 1, 2005 towards present
(now computing… June, 2006)
Assimilated observations
Operationally used observations in JMA global cycle analysis
except satellite radiances

33. SLP analyses on May 2, 2006

34. KF and EnKF Kalman Filter Ensemble Kalman Filter Forecast equations
Ensemble forecasts
Approximated by
Kalman gain
[pxp] matrix inverse
Analysis equations
Solve for the ensemble mean
Ensemble perturbations

35. LETKF algorithm In the space spanned by Eigenvalue decomposition:
Analysis equations
LETKF analysis
Ensemble analysis increments