Initial Ensemble Perturbations using the Ensemble Transform Technique Mozheng Wei*, Zoltan Toth, Yuejing Zhu, Dick Wobus* and Craig Bishop** NOAA/NCEP/EMC, USA *SAIC at NOAA/NCEP/EMC ** Naval Research Lab, CA, USA IAMAS 2005, Beijing,

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Initial Ensemble Perturbations using the Ensemble
Transform TechniqueMozheng Wei, Zoltan
Toth,Yuejing Zhu, Dick Wobus and Craig
Bishop NOAA/NCEP/EMC, USA SAIC at
NOAA/NCEP/EMC Naval Research Lab, CA, USA
IAMAS 2005, Beijing, August 9, 2005
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MOTIVATION FOR EXPERIMENTS

• EPS and DA systems must be consistent for best
  
• performance of both.
• DA provides best estimates of initial
  uncertainties, i.e. analysis
• error covariance, for EPS.
• EPS produces accurate flow dependent forecast
  (background)
• covariance for DA.

Best analysis error variances
EPS
DA
Accurate forecast error covariance
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DESCRIPTION OF 4 METHODS TESTED

• 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 2005) 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
• Issue of pert inflation is challenging for large
  variation of obs
• Computationally expensive
• Built on ETKF DA assumptions gt NOT consistent
  with 3/4DVAR
• Ensemble Transform (ET) (Bishop Toth 1999, Wei
  et. al 2005b)
• Dynamical recycling with orthogonalization
  (inverse analysis error variance norm)
• Variance constrained statistically by fixed
  analysis error estimate mask
• Constraint does not work well with only 10
  ensemble members
• ET plus rescaling (Wei et al. 2005b)

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NCEP GLOBAL ENSEMBLE PLAN 2005
(Wei et. al 2005b)
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 for short
6-hour fcsts.
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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EXPERIMENTS

• Time period
• Jan 15 Feb 15 2003
• Data Assimilation
• NCEP SSI (3D-VAR)
• Model
• NCEP GFS model, T126L28
• Ensemble
• 2x5 or 10 members, no model perturbations
• Evaluation
• 7 measures, need to add probabilistic forecast
  performance

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Initial energy spread, Rescaling factor
distribution
?ET
?ETKF
?Breeding
?ETrescaling
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?AC
?RMS error
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S - 20/80 ET X -10 ET/rescaling E -10 ETKF O -
10 breeding
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S - 20/80 ET X -10 ET/rescaling E -10 ETKF O -
10 breeding
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S - 20/80 ET X -10 ET/rescaling E -10 ETKF O -
10 breeding
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S - 20/80 ET X -10 ET/rescaling E -10 ETKF O -
10 breeding
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S - 20/80 ET X -10 ET/rescaling E -10 ETKF O -
10 breeding
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S - 20/80 ET X -10 ET/rescaling E -10 ETKF O -
10 breeding
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SUMMARY and DISCUSSION

• All tests in context of 5-10 perturbations
• 80-member ET with rescaling improves the
  forecast
• Plan to experimentally exchange members
  with NRL
• (Will have total of 160 members)
• 4-dim time-dependent estimate of analysis error
  variance
• Need to develop procedure to derive from
  SSI (GSI) 3DVAR
• ETRescaling looks promising
• Orthogonalization appears to help breeding
• Cheaper than ETKF, can also be used in targeting
• If ensemble-based DA can not beat 3/4DVAR
• Initial ens cloud need to be repositioned to
  center on 3/4DVAR analysis
• No need for sophisticated ens-based DA algorithm
  for generating initial
• perts?
• Good EPS
  Good DA