January 18, 2013, DA Workshop, Tachikawa, Japan

Advances and Challenges in Ensemblebased Data Assimilation in Meteorology
Takemasa Miyoshi
RIKEN Advanced Institute for Computational Science
Takemasa.Miyoshi@riken.jp
With many thanks to

E. Kalnay, K. Ide, B. Hunt, S. Greybush, S. Penny, G.-Y. Lien, UMD
Weather-Chaos group, Y. Ota (NCEP/EMC, JMA)
J. Ruiz (Argentina), S.-C. Yang (Taiwan),
M. Kunii, K. Kondo, T. Enomoto, and N. Komori (Japan)

Data Assimilation (DA)
Observations

Numerical models
Data Assimilation©Vaisala

Data assimilation best combines
observations and a model, andbrings synergy.

DA has an impact.
SV w/ 4D-Var
JMA operational system

LETKF
under development

FCST

FCSTOBSOBS
Miyoshi and Sato (2007)
Using the same NWP model and observations.
DA matters!

WRF-LETKF studies at UMD
Goal: Improve TC forecasts byimproving the initial conditions
 WRF-LETKF system (Miyoshi and Kunii 2012)
 LETKF: Local Ensemble Transform Kalman Filter (Hunt et al. 2007)
 Adaptive inflation method (Miyoshi 2011)

 Several techniques to improve TC forecasts have been explored.
 Running-In-Place method (Yang, Miyoshi and Kalnay 2012)
 Including SST uncertainties (Kunii and Miyoshi 2012) Assimilating AIRS retrievals (Miyoshi and Kunii 2012)
 Estimating observation impact using the ensemble-based
method (Kunii, Miyoshi and Kalnay 2012) Based on the ensemble sensitivity method of Liu and Kalnay (2008)

 Two-way nested WRF-LETKF for higher-resolution
experiments

Studies on methods: towards optimal use of available observations

RUNNING-IN-PLACE (RIP)
Yang, Kalnay, and Hunt (2012, in press)
Yang, Miyoshi and Kalnay (2012, in press)
Yang, Lin, Miyoshi, and Kalnay (in progress)

Running-In-Place (RIP, Kalnay and Yang 2008)
4D-LETKF: Ensemble Kalman Smoother★

tntn-1x˜ a (t n −1 ) = x a (t n −1 ) + Xa (t n −1 )wa (t n )˜ (t ) = X (t )W (t )X
an −1

an −1an

Running-In-Place (RIP) method:wa = P˜ a YbT R−1 (y − H(x ));1˜
Wa = [(K −1)Pa ] 2

1. Update the state (★) at tn-1 using observations up to tn (smoother)
2. Assimilate the same observations again (dealing with nonlinearity)
3. Repeat as long as we can extract information from the same obs.

In OSSE, RIP is very promisingThis is a simulation study.
Time

Realistic observing
systems are assumed,including dropsondes
near the TC.
Vortex strength andstructure are clearlyimproved.

Yang, Miyoshi and Kalnay (2012)

Typhoon Sinlaku (2008)

TrackMSLPRIP impact on Sinlaku track forecast
This is the real case.
3-day forecast
Typhoon Sinaku (2008)

Flight data

SYNOP(+),SOUND(△),
DROPSONDE(○),
Typhoon center (X)

Obs
LETKF-RIP
LETKF

RIP better use the “limited observations”!

S.-C. Yang (2012)

WRF-LETKF: including additional sources of uncertainties

SST UNCERTAINTIESKunii and Miyoshi (2012, Weather and Forecasting)SST ensemble perturbations
SST is randomly perturbed around the SST analysis in the
WRF-LETKF cycle.
The SST perturbations are the differences between SST analyses on
randomly chosen dates. The perturbation fields are fixed in time.

Domain averageSingle member(K)Ens. Spread(K)Kunii and Miyoshi (2012)6-h forecast fields

The location and intensity are the best with the SST perturbation.
NOTE: There is no SST perturbation in the forecast, but only in the DA cycle.

Improvement in TC forecasts
1. TC intensity andtrack forecasts aregreatly improved.
(NO SST perturbationsin the forecast)

2. Improvement is not onlyin the single case.
(NO SST perturbationsin the forecast)WRF-LETKF: using satellite data

ASSIMILATION OF AIRS DATA
Miyoshi and Kunii (2012, Tellus)

Assimilation of AIRS retrievals
CTRL
Conventional (NCEP PREPBUFR)

AIRSConv. + AIRS retrievals (AIRX2RET - T, q)

Larger inflation is estimated due to the AIRS data.
 August-September 2008, focusing on Typhoon Sinlaku

AIRS impact on TC forecasts~28 samples

Too deep to resolve by 60-km WRF
 TC track forecasts for Typhoon Sinlaku (2008) weresignificantly better, particularly in longer leads.

ENSEMBLE-BASED OBS IMPACT
Kunii, Miyoshi and Kalnay (2012, Mon. Wea. Rev.)
Ota, Kalnay, Miyoshi and Derber (under review)Forecast Sensitivity to Observations (FSO)
Estimated observation impact

TY Sinlaku

DegradingWith FSO approaches,
observation impacts canbe estimated without
performing expensive
data denial experiments(or OSEs).

Kunii, Miyoshi, Kalnay (2012)
ImprovingForecast sensitivity to observations
Observation impact can be calculated using an adjoint model(Langland and Baker 2004)
This difference comesfrom obs at 00hr
𝑓𝑓

𝐞𝐞𝑡𝑡|0 = 𝒙𝒙𝑡𝑡|0 − 𝒙𝒙𝑎𝑎𝑡𝑡
The error reduction (or increase) due to obs at 00 (i.e., obs impact):
𝐽𝐽 =𝐞𝐞𝑇𝑇𝑡𝑡|0 𝐶𝐶𝐞𝐞𝑡𝑡|0 − 𝐞𝐞𝑇𝑇𝑡𝑡|−6 𝐶𝐶𝐞𝐞𝑡𝑡|−6𝐽𝐽 ≈ 𝛿𝛿𝐲𝐲 𝑇𝑇 𝐊𝐊 𝑇𝑇 𝐌𝐌𝑇𝑇 𝐶𝐶 𝐞𝐞𝑡𝑡|0 + 𝐞𝐞𝑡𝑡|−6= 𝐞𝐞𝑡𝑡|0 − 𝐞𝐞𝑡𝑡|−6𝑓𝑓

𝑓𝑓

𝑇𝑇𝐶𝐶 𝐞𝐞𝑡𝑡|0 + 𝐞𝐞𝑡𝑡|−6𝑓𝑓𝒙𝒙𝑡𝑡|0 − 𝒙𝒙𝑡𝑡|−6 ≈ 𝐌𝐌(𝒙𝒙𝑎𝑎0 − 𝒙𝒙0|−6 )analysis increment!
𝑓𝑓

𝐊𝐊(𝒚𝒚0 − 𝐻𝐻𝒙𝒙0|−6 )Forecast sensitivity to observations
Observation impact can be calculated without an adjoint model(Liu and Kalnay 2008; Li et al. 2009; Kalnay et al. 2012)
𝐽𝐽 ≈ 𝛿𝛿𝐲𝐲 𝑇𝑇 𝐊𝐊 𝑇𝑇 𝐌𝐌𝑇𝑇 𝐶𝐶 𝐞𝐞𝑡𝑡|0 + 𝐞𝐞𝑡𝑡|−6(Langland and Baker 2004)

In the ensemble Kalman filter (EnKF),𝑇𝑇𝑇𝑇𝑎𝑎 𝑎𝑎−1𝐗𝐗 𝑎𝑎0 𝐗𝐗 𝑎𝑎0𝐗𝐗
𝐘𝐘𝐑𝐑0 0𝐊𝐊 =𝐇𝐇𝑇𝑇 𝐑𝐑−1 =𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 − 1
𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 − 1

𝐽𝐽 ≈ 𝛿𝛿𝐲𝐲 𝑇𝑇 𝐊𝐊 𝑇𝑇 𝐌𝐌𝑇𝑇 𝐶𝐶 𝐞𝐞𝑡𝑡|0 + 𝐞𝐞𝑡𝑡|−6𝐽𝐽 ≈1

𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 − 1

𝛿𝛿𝐲𝐲

𝑇𝑇𝑇𝑇

𝛿𝛿𝐲𝐲 𝑇𝑇 𝐑𝐑−1 𝐘𝐘0𝑎𝑎 𝐗𝐗 𝑎𝑎0 𝐌𝐌𝑇𝑇
=𝐶𝐶 𝐞𝐞𝑡𝑡|0 + 𝐞𝐞𝑡𝑡|−6
𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 − 1𝑇𝑇−1 𝑎𝑎 𝑓𝑓𝐑𝐑 𝐘𝐘0 𝐗𝐗 𝑡𝑡|0 𝐶𝐶 𝐞𝐞𝑡𝑡|0 + 𝐞𝐞𝑡𝑡|−6

We just need an ensemble of forecasts.

Kalnay et al. (2012)

Denying negative impact data improves forecast!
Estimated observation impact

Typhoon track forecast isactually improved!!
Improved
forecast

36-h forecasts
Observed
track

TY Sinlaku

Original
forecast

Kunii, Miyoshi, Kalnay (2012)

Impact of WC-130J dropsondes

Kunii, Miyoshi, Kalnay (2012)

An issue on localization
𝐽𝐽 ≈1

𝑇𝑇𝑎𝑎 𝑓𝑓𝑇𝑇−1𝛿𝛿𝐲𝐲 𝐑𝐑 𝐘𝐘0 𝐗𝐗 𝑡𝑡|0 𝐶𝐶 𝐞𝐞𝑡𝑡|0 + 𝐞𝐞𝑡𝑡|−6

𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 − 1
The ensemble-based covariance needs localization.

We need to consider a “mobile” localization function.
cf. Bishop and Hodyss (2009)Ideas for “mobile” localizaitona) Nonlinear incremental evolutionb) Constant advection

Kalnay et al. (2012)

Impact of mobile localization
Results from idealized experiments with the Lorenz-96 model.

mobile localization

immobile localization

Kalnay et al. (2012)

Impact estimates with NCEP GFS
Ota et al. (2012)

Degrading

Improving

Improving

RAOB (In-situ)

Degrading

AMSU-A (Satellite)

Impact estimates with NCEP GFS

Ota et al. (2012)
ImprovingImpact of AIRS channels
improving dry component

improving moisture degrading

Ota et al. (2012)

RAOB impacts
Ota et al. (2012)

Improving

DegradingFuture research ideas
 Regional ocean coupling Considering flow-dependent SST perturbations.

 Higher-resolution runs, multi-scale considerations
 We need more localization with higher resolution, but tight localization only
allows using data for high-frequency components.

 Model parameter estimation, multi-model EnKF
 Expanding to WRF-Chem Aerosols, air-quality, lidar data assimilation

A CHALLENGE:
MULTI-SCALE TREATMENT
Miyoshi and Kondo (in preparation)

Motivation
Localization plays an essential rolein an EnKF to cope with limited
ensemble size.

Raw covariance field estimatedfrom 20 ensemble members

Higher resolution requires morelocalization, limiting the use ofobservations.
Localized covariance field

We look for better use ofobservations by separating thescales.

An idea of scale separation
 Extracting larger-scale covariance by spatial smoothing
Raw covariance at T30

With 1000-km localization

More noise

Using smoothed perturbations

With 1000-km localization

Less noiseScale-separated analysis increments
We will construct analysis increments at high (h) and low (l)resolutions separately.

𝛿𝛿𝑥𝑥 = 𝛿𝛿𝑥𝑥ℎ + 𝛿𝛿𝑥𝑥𝑙𝑙

𝛿𝛿𝑥𝑥𝑙𝑙 is obtained by smoothed (low-resolution) forecast ensemble
perturbations.
 Using larger localization

𝛿𝛿𝑥𝑥ℎ is obtained by the regular EnKF (smaller localization) minus 𝛿𝛿𝑥𝑥𝑙𝑙 ′(different from 𝛿𝛿𝑥𝑥𝑙𝑙 ).
 𝛿𝛿𝑥𝑥𝑙𝑙 ′ is similar to 𝛿𝛿𝑥𝑥𝑙𝑙 , but with smaller localization.

In this study, we use the T30L7 SPEEDY model (Molteni 2003),
with 500-km (smaller) and 1000-km (larger) localization settings.

Results are promising.
Successfully reducing the errors at almost all scales.
1-month average global analysis error power spectrum
500-km localization standard LETKF
1000-km localization standard LETKF
500-1000-km dual-localization LETKF

Wave numberImprovements are almost everywhere for all variables.
1-month average RMS errors
500-km regular
Z=1

Z=41000-km regular

500-1000-km dualSummary• EnKF was proposed by Evensen in 1994, and theEnvironment Canada first started using EnKF for
operational NWP in 2005. We have achieved
quite a lot to improve EnKF performances so far.
• We still have a lot more to improve. Challenges
include…
– Multi-scale treatment– Model errors• multi-model, model parameter optimization– Nonlinear, non-Gaussian filters/smoothersWe are hiring researchers.
Please feel free to contact me for details.

Thank you very muchfor your kind attention!!