The use of Ensemble Transform technique for generating initial ensemble perturbations Mozheng Wei*, Zoltan Toth, Yuejian Zhu, Dick Wobus*, Craig Bishop** NCEP/EMC, MD *SAIC at NCEP/EMC ** Naval Research Lab NOAA Thorpex PI Workshop, Jan. 17,

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The use of Ensemble Transform technique for
generating initial ensemble perturbationsMozheng
Wei, Zoltan Toth, Yuejian Zhu, Dick Wobus,
Craig Bishop NCEP/EMC, MDSAIC at NCEP/EMC
Naval Research Lab NOAA Thorpex PI
Workshop, Jan. 17, 2006
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OUTLINE

• Motivation for Experiments
• A Summary of Tested Schemes
• Experimental Results
• A Summary and Discussion
• Ongoing Work and Plan

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Links between EFS and DA

• Is there a best way to generate ensemble
  perturbations?
• Capture dynamically relevant initial growing
  perturbations
• Purely dynamically based (e.g. breeding)
• No added stochastic noise to initial perts
• Initial perts are restrained by using analysis
  error information
• What is the best way to combine fcst and
  observation data? (4D-VAR, or various
  ensemble based Kalman filters)
• Use dynamical information (fcst error covariance)
  from ensemble
• fcst system
• Describe observational errors through statistical
  methods (independent of ensemble fcsts)
• Produce accurate analysis error variance
• To some extent, EFS and DA can be developed
  separately, but for ideal performance of both,
  they need to be coupled.

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MOTIVATION FOR EXPERIMENTS

• EFS and DA systems must be consistent for best
  
• performance of both.
• SSI/GSI currently provides best estimate of
  analysis, GSI will be
• used to derive analysis uncertainties
  (error variance) for EFS.
• EFS produces flow dependent forecast
  (background) error
• covariance to be tested in GSI later.
  

A Hybrid DA-EFS system
Best analysis error variances
EFS
GSI
Accurate forecast error covariance
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DESCRIPTION OF 4 METHODS TESTED

• ET plus rescaling
• As ET, additional constraint (regional
  rescaling as in breeding).
• Ensemble Transform (ET) (Bishop Toth 1999,
  initially for adaptive observation)
• Dynamical recycling with orthogonalization
  (inverse analysis error variance norm)
• Variance constrained statistically by
  flow-dependent analysis error estimate.
• Constraint does not work well with only 10
  ensemble members
• BREEDING with regional rescaling (Toth Kalnay,
  1993 1997)
• Simple scheme to dynamically recycle
  perturbations
• Variance constrained statistically by fixed
  analysis error estimate mask
• Limitations No orthogonalization fixed
  analysis variance estimate used.
• ETKF (Bishop et al. 2001 Wang Bishop 2003 Wei
  et. al 2006) used as perturbation generator
  (not DA)
• Dynamical recycling with orthogonalization in obs
  space
• Variance constrained by distribution error
  variance of observations
• Constraint does not work well with only 10
  ensemble members
• Computationally expensive for current time
  allocation for ensemble forecasts
• Built on ETKF DA assumptions gt NOT consistent
  with 3/4DVAR

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ET Formulation
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ET Formulation
Simplex transformation is to center analysis
perts around the analysis, and preserve the
analysis error covariance.
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Experiment Configuration
At every cycle, both ET and Simplex
Transformation (ST) are carried out for all 80
perts. Only 20 members are used for long fcsts.
ST is imposed on the 20 perts to ensure they
are centered around the analysis. 60 fcsts are
short 6-hour.
41-60, ST 16-day fcsts
01-20, ST 16-day fcsts
21-40, ST 16-day fcsts
61-80, ST 16-day fcsts
time
00z
00z
06z
12z
18z
80-perts, ET,ST
80-perts, ET,ST
80-perts, ET,ST
80-perts,ET,ST
80-perts, ET,ST
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Initial energy spread distribution
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Ave correlation between fcst and ana perts
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Initial energy spread Rescaling factor
distribution
?ET(10)
?ETKF(10)
?Breeding(10)
?ET/rescaling(10)
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Spread for Temp at 500mb ET80/80
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Pert versus Error Correlation Analysis (PECA)
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Fcst variance explained by ensemble (from
scatter-plots)
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S - 20/80 ET X -10 ET/rescaling O - my10
breeding E -10 ETKF
Dotted resolution Solid reliability
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S - 20/80 ET X -10 ET/rescaling O - my10
breeding E -10 ETKF
ROC the Relative Operating Characteristic
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S - 20/80 ET X -10 ET/rescaling O - my10
breeding E -10 ETKF
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S - 20/80 ET X -10 ET/rescaling O - my10
breeding E -10 ETKF
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S - 20/80 ET X -10 ET/rescaling O - my 10
breeding E -10 ETKF
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SUMMARY OF RESULTS

• The main difference between Breeding and
  ET/rescaling is
• Paired strategy vs. Simplex
  structure
• Variance distribution (geographically)
• Breeding and ET/rescaling are similar.
• RMSE, PAC of ensemble mean forecast
• Paired breeding and ET/rescaling are best, ET
  second, ETKF last.
• All probability scores are improved, especially
  in the tropics.
• Explained variance (scatterplots) ET best,
  ET/rescaling,ETKF, breeding.
• Perts vs. Fcst error correlation (PECA)
  Important for DA
• ET/rescaling best, breeding second.
• 80-90 of variances can be explained by 80 ET
  perts, great for DA
• Growth rate (not shown) ET/rescaling is
  slightly higher.
• Effective number of degrees of freedom (Important
  for DA)
• ET is higher due to simplex structure
  (not shown).
• Time consistency of perturbations (PAC between
  fcst vs. analysis perts excellent for all, ET
  highest (0.999, breeding lowest, 0.988)

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Ongoing Work and Plan
29-42, ST 16-day fcsts
01-14, ST 16-day fcsts
15-28, ST 16-day fcsts
43-56, ST 16-day fcsts
time
00z
00z
06z
12z
18z
56-perts, ET,ST
56-perts, ET,ST
56-perts, ET,ST
56-perts, ET,ST
56-perts,ET,ST
At every cycle, both ET and Simplex
Transformation (ST) are carried out for all 56
perts. Only 14 members are used for long fcsts.
ST is imposed on the 14 perts to ensure they
are centered around the analysis. 42 fcsts are
short 6-hour. Number of members will be increased
to 20/80 configuration later when resources are
available.
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Next Step

• Derive flow dependent 3-D analysis error
  variance from GSI to restrain the initial
  perturbations.
• Test the use of ensemble based forecast error
  covariance to improve GSI performance.

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Ensemble Perturbations vs. NMC Method
Wei and Toth (2003, MWR)
Ensemble perts can better explain their
respective 1-day fcst errors than the NMC method
50 EC ensembles at 1-day lead time can explain
about 80 of fcst error variance over contiental
scale (middle panel) 80 ET based perts cana
explain 90 forecast error variance at 6-hour
lead time (right panel).