Applying a local ensemble transform Kalman filter to the JMA global model
Takemasa Miyoshi* † and Yoshiaki Sato**Numerical Prediction Division, Japan Meteorological Agency

02040-2002040-2002040

0100
200
300
400
500
600
700
800
900
1000
0100
200
300
400
500
600
700
800
900
1000

T-10

1

2-10

12-10A

12Figure 1. Analysis errors of height (m, left) and temperature(K, right) verified against radiosonde observations in eacharea for the cases with (red) and without (blue) satellite
radiances, temporally averaged over 31 days in August 2004
(adapted from Fig. 5 of MS07). Solid and dashed lines
indicate the bias and RMS errors, respectively.

†NH

0100
200300
400
500
600
700
800
900
1000

-200100200300
400
500
600
700
800
900
1000

0100200
300
400
500
600
700
800
900
1000

EQ

EQ

0100
200
300
400
500
600
700
800
900
1000

Z

0100
200
300
400
500
600
700
800
900
1000

SH

NH

0100
200
300
400
500
600
700
800
900
1000

SH

In the 2006 issue of the WGNE Blue Book, Miyoshi and Yamane (2006) reported their successful
implementation of the local ensemble transform Kalman filter (LETKF, Hunt 2005) with the AFES model(AGCM for the Earth Simulator). They made further comprehensive investigations; the results are now inpress in Monthly Weather Review (Miyoshi and Yamane 2007). In the meantime, based on theinvestigations on the Earth Simulator, LETKF has been developed with the JMA’s global model (GSM) ata TL159/L40 resolution, which is the same version as the one used in the operational ensemble prediction
system (EPS). In this short report, we briefly overview our preliminary results with the GSM-LETKF.
First, 20-member LETKF has been performed to ensure that the system works appropriately(Miyoshi and Sato 2007, hereafter “MS07”). MS07 investigated impacts by assimilating satellite
radiances. Fig. 1 shows the results by MS07, where we see clear advantages of the satellite radianceassimilation. Here, the parameter values are fixed with the 21x21x13 local patch (about 1000-km radius),5-grid (about 500-km) horizontal and 3-grid vertical Gaussian localization, and 10 % spread inflation.
Then, the ensemble size has been increased to be 50 with the same parameter values. Figs. 2 and 3
show the results, where we see significant improvements by the larger ensemble size. Still, LETKF shows

0100200300400500600700
800
9001000

Z0200200200100200300
400500
600
700
800
900
1000
40-10100200300
400500
600
700
800
900
1000
40-10100200300
400500
600
700
800
900
1000
40-1

T0

1

20

120A

12Figure 2. Similarly to Fig. 1, but for the cases of the LETKF
with 20 members (red), LETKF with 50 members (green),
and the operational 4D-Var (blue).

Corresponding author address: Numerical Prediction Division, Japan Meteorological Agency, 1-3-4Otemachi, Chiyoda-ku, Tokyo 100-8122, Japan. E-mail: miyoshi@naps.kishou.go.jp

generally larger errors than the operational 4D-Var (Kadowaki 2005).
After the above investigations, Miyoshi et al. (2007) developed a new version of the LETKF that
does not use local patches. Without local patches, there is no need to specify the local patch size, thus thenumber of the localization tuning parameters are reduced. Moreover, it solves the discontinuity problem
caused by the local patch near the Poles where the physical distances between successive grid points areshort. The new algorithm has been applied to the GSM-LETKF. Furthermore, we apply vertical
localization linear with the log-p coordinate, which is physically more meaningful. So far, the verticallocalization was applied linearly with the model coordinate; in the lower troposphere where the model hasa denser resolution, the vertical localization has been too narrow.
With the above upgrades, we obtained further improvements. Fig. 4 shows forecast verification
scores. The blue curve shows results by the LETKF without local patches, but with the same parameters(500-km horizontal and 3-grid vertical localization with 10 % spread inflation). Red curve shows thelatest results with tuned parameters (500-km horizontal and 0.5-hPa vertical localization with 30 % spreadinflation), which appears to be much closer to the operational 4D-Var. We are expecting furtherimprovements by refining the parameters and increasing the ensemble size up to 100.
Anomaly Cor.

100

80

[Global][Global]

100

60

40
072

144

216

[hour]
Figure 3. 9-day forecast anomaly correlations (%) of 500 hPa
height averaged over 31 days in August, 2004, for the cases ofthe LETKF with 20 members (red), LETKF with 50 members(green), and operational 4D-Var (blue).

8060

4004D-Var
LETKF-NLP
LETKF-NLP-I3D5V572144216[hour]
Figure 4. Similarly to Fig. 3, but for the LETKF without local
patches and a different sample period (August 1-15, 2004).
Blue and red lines indicate 50-member LETKF without local
patches with the original and tuned parameters, respectively.
Green line indicates the operational 4D-Var.

Acknowledgements
We thank Prof. Eugenia Kalnay, Drs. Shozo Yamane, Takeshi Enomoto, and Jeff Whitaker forfruitful discussions.
References
Hunt, B. R., 2005: Efficient Data Assimilation for Spatiotemporal Chaos: a Local Ensemble Transform
Kalman Filter. arXiv:physics/0511236v1, 25pp.
Kadowaki, T, 2005: A 4-Dimensional Variational Assimilation System for the JMA Global Spectrum
Model. CAS/JAC WGNE Research Activities in Atmospheric and Oceanic Modelling, 34, 1-17.
Miyoshi, T. and S. Yamane, 2006: Local ensemble transform Kalman filtering with an AGCM at aT159/L48 resolution. CAS/JAC WGNE Research Activities in Atmospheric and Oceanic Modelling,35, 1-19.
Miyoshi, T. and S. Yamane, 2007: Local ensemble transform Kalman filtering with an AGCM at aT159/L48 resolution. Mon. Wea. Rev., in press.
Miyoshi, T. and Y. Sato, 2007: Assimilating Satellite Radiances with a Local Ensemble Transform
Kalman Filter (LETKF) Applied to the JMA Global Model (GSM). SOLA, in press.
Miyoshi, T., S. Yamane, and T. Enomoto, 2007: Localizing the error covariance by physical distances
within a local ensemble transform Kalman filter. in preparation.