4.3

RECENT DEVELOPMENT OF GLOBAL AND REGIONAL LOCAL ENSEMBLE
TRANSFORM KALMAN FILTERS (LETKF) AT JMA
1*

2

1

1

3

Takemasa Miyoshi , Shozo Yamane , Yoshiaki Sato , Kohei Aranami , and Takeshi Enomoto
1

Numerical Prediction Division, Japan Meteorological Agency

Chiba Institute of Science, and Frontier Research Center for Global Change, JAMSTEC
3

Earth Simulator Center, JAMSTEC

1. INTRODUCTION
At the Numerical Prediction Division, Japan
Meteorological Agency (NPD/JMA), a four-dimensional
local ensemble transform Kalman filter (4D-LETKF or
just LETKF hereafter, Hunt et al. 2004; Hunt 2005) is
being developed since August 2005. Thus far, we haveachieved working LETKF systems with threestate-of-the-art models: AFES (AGCM for the Earth
Simulator, Ohfuchi et al. 2004), GSM (JMA’s operational
Global Spectral Model), and NHM (a.k.a. MSM, JMA’s
operational nonhydrostatic Mesoscale Model). Here,
recent progress of the developments with AFES, GSM,
and NHM is outlined in section 2, 3, and 4, respectively.
2. AFES-LETKF
2.1 Project Overview
The AFES-LETKF project is a collaborative project
among the NPD/JMA, Chiba Institute of Science (CIS),
and Earth Simulator Center (ESC). The NPD/JMA, ESC,
and CIS develop the LETKF, AFES, and theexperimental system connecting the LETKF data
assimilation and AFES forecast, respectively. The model
resolution is chosen to be T159/L48, corresponding to
the grid of 480x240x48.
The LETKF FORTRAN90 codes are based on thelocal ensemble Kalman filter (LEKF, Ott et al. 2002;
2004) codes by Miyoshi (2005), with MPI/OpenMPparallelization and upgrading to LETKF. Miyoshi and
Yamane (2006, “MY06” hereafter) described details of
the first outcome of the AFES-LETKF, including the codedevelopment, perfect model experiments, andexperiments with real observations. Here, MY06 is* Corresponding author address: Takemasa Miyoshi,
Numerical Prediction Division, Japan Meteorological
Agency, 1-3-4 Otemachi, Chiyoda-ku, Tokyo 100-8122,
Japan. E-mail: miyoshi@naps.kishou.go.jp

briefly reviewed in section 2.2, followed by a brief
description of the recent progress of so-called ALERA(AFES-LETKF Experimental ReAnalysis) in section 2.3.
Moreover, recently Miyoshi et al. (2006) took advantagesof an intrinsic property of LETKF, i.e., not requiring local
patches, to propose an efficient implementation of
LETKF with the error covariance localized only byphysical distances, which solves the problem of analysis
discontinuities near the Poles. Miyoshi et al. (2006) isreviewed in section 2.4.
2.2 Brief Review of Miyoshi and Yamane (2006)
MY06 performed three kinds of data assimilation
experiments: 1) perfect model experiments with regularobserving network, 2) perfect model experiments withreal observing network, and 3) experiments with real
observations
exceptsatellite
radiances.
They
investigated sensitivities of the analysis accuracy to theensemble size and localization parameters. They also
investigated computational cost. In this section, theirmain findings are briefly reviewed.
AFES-LETKF (T159L48) ONE-STEP ANALYSIS ERRORS in TOTAL ENERGY
1.00E+22

ANALYSIS ERRORS in TOTAL ENERGY

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FIRST STEP
10 DAYS LATER(w/inflation)
10 DAYS LATER(w/o inflation)

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Figure 1. Analysis errors (total energy) at the first one-stepanalyses (solid line) and the analyses after 10-day cycles(broken lines) of LETKF with changing the ensemble size,
adapted from Fig. 3 of MY06. Dashed and dash-dottedlines show the cases with and without covariance inflation,
respectively. Due to the limited computational capability,
10-day cycle experiments have not been performed withmore than 320 and 160 ensemble members for the caseswith and without inflation, respectively.

In the first perfect model experiments with regularobserving network, MY06 investigated sensitivities andtiming. Fig. 1 indicates the sensitivity to the ensemble
size. The analysis errors are consistently decreased withincreasing the ensemble size, but the decreasing ratio issmaller with larger ensemble sizes. Fig. 2 shows thesensitivity to the local patch parameters. There is
non-negligible sensitivity, and too large localizations
destroy the filter stability. Thus, once the ensemble size
is fixed, tuning localization parameters is suggested. To
explain the sensitivity, MY06 also investigated how theerror covariance is localized with various localization
parameters. The cross-covariance structure includes
dynamical balance; they discussed that a severe
localization does not destroy the balance. The figures
showing the covariance (Figs. 6-9 in MY06) are notshown in this abstract. Timing is shown in Table 1. If we
use the same number of computational nodes as theensemble size, the computational time is less than 4minutes. The acceleration ratio (Fig. 10 of MY06, notshown) indicates almost 99.99% parallelization ratio withmore than 80 members. MY06 also investigated timingwith various local patch sizes, indicating quadratic
relationship (Fig. 11 of MY06, not shown).
Here, we skip the second perfect modelexperiments and summarize the results with real
observations. The AFES-LETKF analysis field looks
almost identical to the JMA operational analysis; mostareas show the difference less than 0.5 hPa in sea-levelpressure (Fig. 15 of MY06, not shown). MY06 performed
48-hour forecast experiments and verified the forecast
against own analyses. Fig. 3 shows the forecast
verification results, indicating similar performancesamong our LETKF and operational analyses (T213/L40
JMA operational analysis and T62/L28 NCEP/NCAR
reanalysis). Note that operational analyses assimilate
satellite radiances, which are known to have significant
positive impacts in the SH. Overall in the 48-hour
forecast verification, LETKF shows as good performanceas the operational analyses.

48-HR FCST RMSE (against own analyses)

Figure 2. Time series of analysis errors (total energy) of LETKF
with 40 ensemble members with various horizontal (a) andvertical (b) localization parameters, adapted from Fig. 5 of
MY06. Solid lines in (a) and (b) show the case of 21x21x7
local patch with 6.0-grid horizontal and 2.0-grid vertical
localization (denoted by 21x21x7, H6.0, V2.0). The line
legends show localization parameters for each line.
Table 1. Timing (sec.) of LETKF on the Earth Simulator,
adapted from Table 1 of MY06.
Ensemble
size

5
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10

382

195

115

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360

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107

66

40

1389

708

360

189

112

1583

824

413

220

1205

626

80
160

500Z RMSE [m]5040

LETKF-AFES2.2
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NNR-AFES2.2

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Figure 3. 48-hour forecast RMS errors of 500 hPa height (m),averaged over 16 days initialized on August 11 throughAugust 26 in 2004, adapted from Fig. 16 of MY06. The
errors are defined as the differences between 48-hour
forecasts and the own analyses. JMA-AFES2.2 indicatesthat JMA operational analyses are forecasted by AFES2.2,
and similarly for NNR (NCEP/NCAR reanalysis) andLETKF.

2.3 Experimental Ensemble Reanalysis: ALERA
Based on the successful implementation andpreliminary tests by MY06, we have been performing
longer-term data assimilation cycle experiments with real
observations except satellite radiances; the project iscalled “ALERA”, standing for AFES-LETKF Experimental
ReAnalysis. The ensemble size is fixed to be 40, and theexperimental period is from May 2005 towards today aslong as computational resources are available.
Since in general there is no guarantee that theensemble Kalman filter (EnKF) is stable for a long period,
the primary purpose of ALERA is to investigate thelong-term stability of the AFES-LETKF system. Fig. 4
shows time series over 1 year of the analysis ensemble
spreads and analysis differences between AFES-LETKF
and NCEP/NCAR reanalysis. The AFES-LETKF
performs stably for over 1 year. The discontinuity after
the initial one month is due to the system upgrade,
where we began to apply the vertical localization forsurface pressure observations. If the discontinuity isignored, AFES-LETKF has an about 1-week spin-up
period. After the spin-up, the analysis differences arequite stable. We see some seasonal variations: larger
analysis differences in winter hemisphere, especially in
the NH. However, spreads have smaller seasonal
amplitudes.
ALERA contains huge amount of information: 40
analysis members every 6 hours. At an analysis time,
Fig. 5 shows the spaghetti diagram of 500 hPa height
fields. ALERA contains this kind of map every 6 hours for
all variables at all vertical levels. Therefore, it isimportant to analyze the products more in detail, which is
now in progress.

Figure 4. Time series for 13 months from May 2005 of 500 hPa
height analysis ensemble spreads and analysis
differences between AFES-LETKF and NCEP/NCAR
reanalysis (CDAS) in each region.

Figure 5. Spaghetti diagram of 500 hPa height (m) for the
ALERA analysis ensemble on 12Z July 1, 2005.

2.4 LETKF Implementation with Error Covariance
Localization only by Physical Distances
Although the LEKF requires local patches, notrequiring local patches is an intrinsic property of the
LETKF. Miyoshi et al. (2006, “MYE06” hereafter) took
advantages of the property to propose an efficient
LETKF implementation with the error covariancelocalized only by physical distances to solve the problemof analysis discontinuities in the Polar Regions. As
shown in the top panel of Fig. 6, the analysis ensemble
spread by MY06 shows rectangular shapes
corresponding to local patches. We see discontinuities atthe edges of the local patch, especially near the Poles,
which is not preferable. If we drop the local patches andlocalize the error covariance only by physical distances,such discontinuities disappear completely, as shown inthe bottom panel of Fig. 6. The latter looks much morenatural. In fact, the analysis accuracy is improved in the
Polar Regions (Fig. 7).
Now that the error covariance is localized only byphysical distances, the number of localization tuning
parameters is reduced to be just horizontal and verticalphysical length scales. This is a major advantage
considering the tuning process. However, due to theadditional computations of accurate physical distances, it
is essential to optimize the algorithm. An efficient sorting
algorithm has been implemented to optimize thesearching process of observations and to minimize thedistance computations. Overall, the computation isaccelerated by about three times. The details of theefficient implementation are described in MYE06. The
new implementation without local patches would be our
future choice.

3. GSM-LETKF
3.1 Project Overview

Figure 6. Ensemble spread of sea-level pressure (hPa) on 00Z
August 1, 2004 (first analysis) with the original LETKF by
MY06 (top) and the modified LETKF without local patches(bottom), both assimilating the same observations(adapted from Fig. 2 of MYE06).

Figure 7. Zonal mean of the root mean square differences
against JMA operational analysis of sea-level pressure(hPa) for the original (solid, with local patches) and new(dashed, without local patches) versions of LETKF,
temporally averaged for 21 days from 11 to 31 August
2004 (adapted from Fig. 5 of MYE06).

Based on results by MY06 on the Earth Simulator,
LETKF has been developed with JMA operational global
model (GSM) and adapted into JMA’s operational
experimental system known as NAPEX (Numerical
Analysis and Prediction EXperiment system, originallydeveloped by K. Onogi and maintained by NPD). The
NAPEX includes major operational global NWP
components at JMA; for example, the observational
quality control procedure is embedded. The model
resolution is chosen to be TL159/L40, the same as theoperational EPS. At this moment, three kinds ofpreliminary experiments have been completed: 1)
20-member LETKF without satellite radiances, 2)
20-member LETKF with satellite radiances, 3)50-member LETKF with satellite radiances. These
results clarify the effects by assimilating satellite
radiances and increasing the ensemble size from 20 to
50. Using the first two experiments with 20 members,
Miyoshi and Sato (2006, “MS06” hereafter) investigatedthe effects by satellite radiances. MS06 is reviewed in
section 3.2. The results of the 50-member experimentare described in section 3.3.
3.2 Brief Review of Miyoshi and Sato (2006)
It is not straightforward how to assimilate satellite
radiances within EnKF. MS06 found that assimilating
satellite radiances without localizing the vertical error
covariance resulted in large analysis errors. Increasing
the covariance inflation reduces the analysis errors,
which suggests that we extract too much informationfrom satellite radiances due to spurious covariancecomponents among vertically distant points. In fact, thesurface pressure analysis ensemble spread is greatly
reduced by satellite radiances, although we do notassimilate satellite channels sensitive to surfacepressure.
Therefore, MS06 proposed a way to localize thevertical error covariance to reduce sampling errors.
Precisely, MS06 normalized the observational sensitivity
function to be used as a localization weighting function.
Namely, the levels at which a specific satellite channel issensitive have smaller localization weights in
assimilating the channel, and vice versa. Thissignificantly contributes to assimilate satellite radiances
effectively and to keep the analysis ensemble spread to

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Figure 8. 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 MS06). Solid and dashedlines indicate the bias and RMS errors, respectively.

be an appropriate size. Fig. 8 shows the analysis errors
verified against radiosonde observations, where we see
significantly smaller errors by satellite radiances. MS06
performed 9-day forecast experiments, which also
indicate advantages of assimilating satellite radiances (cf.
Fig. 6 of MS06).
3.3 Results of 50-member Experiment
After MS06 found an appropriate way to assimilate
satellite radiances, the ensemble size was increased to
50 to compare with the operational 4D-Var analysis(TL319/L40 outer and T106/L40 (equivalent toTL159/L40) inner resolutions). Fig. 9 shows the analysis
errors verified against radiosondes, indicating that50-member LETKF outperforms 20-member LETKF. Still,
generally 4D-Var outperforms LETKF even with 50
members. The difference between LETKF and 4D-Var issmaller in the SH than in the NH; LETKF isadvantageous in data-poor regions. One of the parts
where LETKF outperforms 4D-Var is around the mid-

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Figure 9. Similarly to Fig.8 but for the cases of the LETKF with
20 members (red), LETKF with 50 members (green), andthe operational 4D-Var (blue).
100[Global]

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[hour]
Figure 10. 9-day forecast anomaly correlations (%) of 500 hPa
height for the cases of the LETKF with 20 members (red),
LETKF with 50 members (green), and operational 4D-Var(blue).

troposphere (500 – 300 hPa) in the SH. It is noted that
we see larger improvements by increasing the ensemble
size in middle to upper troposphere, whereas the
improvements are small at lower levels. This is not thecase with what Anderson et al. reported (Khare, pers.
comm.); EnKF is advantageous at lower levels with their
80-member EAKF (ensemble adjustment Kalman filter,
Anderson 2000) applied to T85 CAM (NCAR climate

community model) compared with the T254 NCEPGDAS (operational 3D-Var global data assimilation). The
weakness of our LETKF at lower levels would be partly
due to the vertical localization; we force zero error
covariance beyond 3 vertical levels, so that near thesurface, where the model resolution is dense, we might
not extract enough information from observations.
9-day forecast experiments are performed. Fig. 10shows 500 hPa height forecast anomaly correlations,where we see large improvements by increasing theensemble size from 20 to 50. However, still 4D-Var
clearly outperforms LETKF.
4. NHM-LETKF
4.1 Project Overview
JMA is operating a nonhydrostatic mesoscalemodel (NHM or a.k.a. MSM) with 5-km grid spacing. To
initialize the NHM, hydrostatic regional 4D-Var with
10-km outer and 20-km inner grid spacing is inoperations. Since EnKF is generally applicable to any
dynamical models with minimal modifications, LETKF isapplied to NHM. Miyoshi and Aranami (2006, “MA06”
hereafter) developed the LETKF system and tested witha perfect model scenario. Following the successful
investigations by MA06, real observations are
assimilated. Here, MA06 is overviewed in section 4.2,
followed by the preliminary results assimilating real
observations in section 4.3.

Figure 11. Time series of temperature RMSE (K, solid lines) andensemble spread (K, broken lines), averaged horizontally
except boundary points and vertically from the 2nd to 40thlevels. Black, and red lines show analysis and first guessin the case assimilating all observing elements except
precipitation rate (w/o rain), adapted from Fig. 2 of MA06.
Green lines show the case assimilating only windobservations (only u, v). For comparison, RMSE andensemble spread in the case without data assimilation are
shown in blue lines. Solid and broken lines indicate RMSE
and spread, respectively.

4.2 Brief Review of Miyoshi and Aranami (2006)
MA06 developed the LETKF system considering
the differences in boundary conditions and prognostic
variables (3-dimensional pressure and water-related
quantities). They performed 10-member LETKF with
NHM at a 5-km grid spacing under the perfect model
assumption. The model domain is almost a square ofabout 300 km by 300 km with 65x63x50 grid points. The
model parameters are chosen to be the same as theones used in operations. Horizontal winds (1.0 m/s),
temperature (1.0 K), and relative humidity (10 %) are
observed every 2x2x2 grid points (parenthesis indicatesobservational error standard deviations). Surfacepressure (1.0 hPa) and precipitation rate (1.0 mm/hr) arealso observed at surface every 2x2 grid points. The
temporal frequency of observations is every 10 minutes.
The data assimilation cycle interval is 1 hour, thus the
4-dimensional assimilation is performed with 6 time

Figure 12. Precipitation pattern and wind vectors at 11Z, after 4
analysis steps, adapted from Fig. 4 of MA06. Each panel
indicates the cases with no data assimilation (top left),
LETKF without precipitation assimilation (bottom left),
LETKF with precipitation assimilation (top right), and thetrue state (bottom left).

slots. 10% multiplicative spread inflation (21%covariance inflation) is applied.
Fig. 11 shows time series of the temperature
analysis root mean square errors (RMSE), where they
are decreasing even without data assimilation since theperfect boundary conditions are given. Still, LETKF
indicates clear advantages. Spreads are larger in thefirst guess than in the analysis, which indicates the
LETKF ensemble perturbations are actually growing inan hour. Even assimilating only winds, we see significant
error reduction. Assimilating precipitation causes slightnegative impacts (not shown).
Fig. 12 shows precipitation patterns and windvectors at 11Z, after four data assimilation steps. The
true state indicates strong precipitation in theblue-circled area, where we see no sign of precipitationin the case without data assimilation. Assimilation all
observed data (including precipitation) recovers this
precipitation, although without precipitation assimilation,
it is not reproduced well. On the contrary, the convective
cell in the blown circle is better captured in the casewithout precipitation assimilation. In fact, the convective
system is already damped in the case with precipitation
assimilation, where we see diverging flow near surface.
The timing was a little earlier for the convective systemin the case with precipitation assimilation.
In summary, the NHM-LETKF system works
appropriately with NHM containing explicit cloud
microphysics. Assimilating precipitation has negative
impacts in general, but positive impacts are observed forsome specific precipitation systems.

are artificially small near the boundaries, especiallyabout 20 grids (400 km) which corresponds to thedamping area. Still, we see large spreads beyond 7 m/s
in the region; the errors are actually growing and not
damped by the fixed boundaries. The ensemble spreads
vary dynamically to show flow-dependent behaviors. The
stable LETKF performance would explain that the error
growth inside the region is not significantly affected by
the fixed boundary conditions.
5. SUMMARY AND DISCUSSIONLETKF has been applied to three state-of-the-art
models: AFES, GSM and NHM. It has been shown that
LETKF works appropriately with the three models withreal observations. Since LETKF analyzes the analysis
errors, it would provide additional information that has
not been available before. The new information has a lotof potential usages such as supporting targeted
observations. Although there are remaining problems
including precipitation assimilation, it is worth continuing

4.3 Assimilation of Real Observations
After the successful preliminary investigation by
MA06, real observations used in JMA’s operational
mesoscale analysis are assimilated with NHM-LETKF.
The model domain is extended to be the same as the
JMA operational mesoscale system (about 3600km x
2900km). The resolution is reduced to be 20-km grid
spacing with 181x145x50 grid points. The ensemble size
is chosen to be 20. The data assimilation cycle begins on
June 25, 2004.
Fig. 13 shows 6-hour forecast fields (i.e., first
guess) of the NHM-LETKF and JMA operational
mesoscale NWP systems. Although NHM-LETKF
indicates a little higher pressure, the position of the lowpressure system and precipitation pattern shows good
agreements.
Fig. 14 shows analysis ensemble spreads after the
first analysis step and a few week cycle processes.
Since a large number of observations are available overJapan, the area with small spreads indicates the shapeof Japan after the first analysis step. Due to the fixedboundary conditions for all ensemble members, spreads

Figure 13. 3-hour accumulated precipitation (mm/hr, shades)
and sea-level pressure (contour) of NHM-LETKF 6-hour
forecast ensemble mean (top) and JMA operational
mesoscale 6-hour forecast (bottom) valid on 06Z July 4,2004.

independent, so that we could use the same LETKF for
both global and mesoscale data assimilation andensemble prediction systems.
Based on the pioneering works described above,
our future directions to improve the LETKF to acomparable level with the operational 4D-Var is toincrease the ensemble size up to about 100, to tune theerror covariance localization and inflation, and possibly
to increase the model resolution. The new
implementation of LETKF without local patches
described in section 2.4 would play an important role intuning localization. We also plan to investigate theperformance of the LETKF as an ensemble prediction
system (EPS), so that it could be applied to theoperational EPS at first. To apply in operations, it isimportant to find that the LETKF system outperforms thecurrent operational systems, which is very challenging
as shown in the present study.
ACKNOWLEDGEMENTS

Figure 14. Horizontal pattern of the analysis ensemble spreads
stof wind speed (m/s) at the 21 vertical level, after first
analysis step (00Z June 25, 2004, top) and a few weekcycle processes (06Z July 4, 2004, bottom).

We thank members of the chaos/weather group of
the University of Maryland, especially Prof. Eugenia
Kalnay for fruitful discussions. We also thank Dr. Wataru
Ohfuchi of ESC and Dr. Tadashi Tsuyuki, Yoshiaki
Takeuchi, Yuzo Yotsuya, and Ko Koizumi of NPD/JMA
for kind support for the LETKF projects. The
AFES-LETKF experiments have been performed on the
Earth Simulator under support of JAMSTEC.
REFERENCES

the development towards operations.
After the successful preliminary investigations, weare now at the stage to improve the performance to becompared to the operational system. The operational
EnKF system with perturbed observations by
Houtekamer et al. (2005) has been proven to becomparable to the operational 4D-Var at CMC (Canadian
Meteorological Centre). Whitaker et al. (2006) reported
EnKF with 100 members is comparable to operational
T254 NCEP GDAS (operational 3D-Var). Anderson et al.
(Khare, pers. comm.) also reported that their EAKF with
T85 CAM was comparable to T254 NCEP GDAS. These
pioneering works greatly encourage us that we could
improve our LETKF to be comparable to the operational
4D-Var at JMA. If LETKF is proven to be at least
comparable to 4D-Var, it would be the choice for the
future operational system. LETKF is much more efficient
to maintain, since it does not require the linearized
model and its adjoint. Moreover, it is essentially model

Anderson, J. L., 2001: An ensemble adjustment Kalmanfilter for data assimilation. Mon. Wea. Rev., 129,2884-2903.
Houtekamer, P. L., H. L. Mitchell, G. Pellerin, M. Buehner,
M. Charron, L. Spacek, and B. Hansen, 2005:
Atmospheric Data Assimilation with an Ensemble
Kalman Filter: Results with Real Observations. Mon.
Wea. Rev., 133, 604-620.
Hunt, B. R., E. Kalnay, E. J. Kostelich, E. Ott, D. J. Patil,
T. Sauer, I. Szunyogh, J. A. Yorke, and A. V. Zimin,
2004: Four-dimensional ensemble Kalman filtering.
Tellus, 56A, 273-277.
Hunt, B. R., 2005: Efficient Data Assimilation for
Spatiotemporal Chaos: a Local Ensemble Transform
Kalman Filter. arXiv:physics/0511236v1, 25pp.
Miyoshi, T., 2005: Ensemble Kalman filter experimentswith a primitive-equation global model. Ph.D.
dissertation, University of Maryland, 197pp.

Miyoshi, T. and K. Aranami, 2006: Applying a Fourdimensional Local Ensemble Transform Kalman
Filter (4D-LETKF) to the JMA Nonhydrostatic Model(NHM), SOLA, 2, 128-131.
Miyoshi, T. and Y. Sato, 2006: A vertical covariancelocalization technique to assimilate satellite
radiances with an ensemble Kalman filter. Mon.
Wea. Rev., submitted.
Miyoshi, T. and S. Yamane, 2006: Local ensemble
transform Kalman filtering with an AGCM at a
T159/L48 resolution. Mon. Wea. Rev., submitted.
Miyoshi, T., S. Yamane, and T. Enomoto, 2006:
Localizing the error covariance by physicaldistances within a local ensemble transform Kalmanfilter. Tellus, submitted.
Ohfuchi, W., H. Nakamura, M. K. Yoshioka, T. Enomoto,K. Takaya, X. Peng, S. Yamane, T. Nishimura, Y.
Kurihara, and K. Ninomiya, 2004: 10-km meshmeso-scale resolving simulations of the global
atmosphere on the Earth Simulator: Preliminary
outcomes of AFES (AGCM for the Earth Simulator).
J. Earth Simulator, 1, 8-34.
Ott, E., B. R. Hunt, I. Szunyogh, M. Corazza, E. Kalnay,
D. J. Patil, J. A. Yorke, A. V. Zimin, and E. J.
Kostelich,
2002:
Exploiting
Local
Low
Dimensionality of the Atmospheric Dynamics for
Efficient
Ensemble
KalmanFiltering.
arXiv:physics/0203058v3.
Ott, E., B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J.
Kostelich, M. Corazza, E. Kalnay, D. J. Patil, and J.
A. Yorke, 2004: A local ensemble Kalman filter foratmospheric data assimilation. Tellus, 56A,
415-428.
Whitaker, J. S., T. M. Hamill, X. Wei, Y. Song and Z. Toth,
2006: Ensemble Data Assimilation with the NCEP
Global Forecast System. Mon. Wea. Rev.,submitted.