ENSEMBLE PERTURBATIONS FOR SUBSEASONAL FORECASTING

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ENSEMBLE PERTURBATIONS FOR SUBSEASONAL FORECASTING

• CTB PROPOSAL July 2007
• Ensemble group at EMC/NCEP. Collaborators from
  GSFC/NASA

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NCEP Global Ensemble Systems
GEFS
CFS
Proposed GEFS

• Uncoupled prediction system
• No lower boundary conditions uncertainty
• Runs out to 16 days
• Lacks large hindcast dataset
• Adaptive bias correction scheme in place
• ET ensemble method
• State-of-the-art method
• Upgrades frequently
• DA/model systems

• Fully coupled OLA model
• Captures variability and uncertainty of coupled
  system
• out to 9 months
• Large hindcast dataset
• Operational forecast system frozen to ensure high
  quality bias correction
• Lacks periodic upgrades
• Lagged ensemble method
• Is not centered on the latest and best analysis.
  Initial variance arbitrary.

• Fully coupled OLA model
• Captures variability and uncertainty of coupled
  system
• out to 30 days
• Large hindcast dataset
• Real-time
• Upgrades frequently
• ET coupled
• Represents analysis uncertainty of the coupled
  ocean-atmosphere system

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Perturbation Schemes Atmosphere
CURRENT Ensemble Transform (ET)
16 days
6 hrs
0Z
6Z
12Z
18Z

• GFS (atmosphere only) 28 Levels, T126
• All variables are perturbed in each level
• 80 ET perturbations every 6 hrs. 60 are
  short-range (6 hrs)
• 20 perturbations every 6 hrs integrated forward
  16 days.

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ET formulation
From Mozheng Wei
ET transform based on analysis error variances
The transformed perturbations ( )
are orthogonal with respect to an inverse error
variance norm. However, they are not centered,
i.e. the sum of perturbations is not zero.
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Centering perturbations
From Mozheng Wei
ET ensures perturbations are orthogonal and
uniformly centered around the best initial
conditions.
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Extending set of variables to include ocean
PROPOSED Ensemble Transform (ET)
30 days
16 days
6 hrs
0Z
6Z
12Z
18Z

• GFS coupled with MOM4
• All variables are perturbed in each level
• 80 ET perturbations each 6 hrs
• Once a day 20 perturbations will be integrated
  forward for 30 days and 60 for 16 days

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ET for the coupled system

• Goal represent well the analysis uncertainty of
  the coupled system.
• Choice of rescaling factor
• atmosphere KE for one layer (2D) later, TE 3D
• ocean heat content of top layers or depth of
  ocean mixed layer (2D) 3D in future
• Ocean data assimilation every 6 hrs, thus ocean
  variables to rescale every 6 hrs as the
  atmosphere
• Case dependent estimate of analysis uncertainty
  is needed
• Research to asses whether exciting slow modes
  affect analysis uncertainty
• Ocean analysis is in 24 hrs delayed mode

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Objective of CTB proposal

• Construct and test an ensemble system for
  sub-seasonal (out to 30-45 days) forecasting
• Characteristics
• Coupled OLA model (from GCWMB/EMC)
• Latest version of DA/modeling systems ( )
• Real-time hindcast (piggy backing on GEFS
  project)
• State-of-the-art ensemble generation scheme
  (GEFS)
• Large portion of the project leveraged
• Next generation GEFS

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Existing approaches at NCEP GEFS

• Uncoupled prediction system
• Runs out to 16 days
• Lower boundary conditions and its uncertainty not
  realistically represented
• Lacks large hindcast dataset
• No high quality-bias estimation for long leads
• Adaptive bias correction scheme in place
• State-of-the-art ensemble scheme
• Upgrades frequently to incorporate best
  available
• Data assimilation system, Numerical model,
  Ensemble technique

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Frequent upgrades Benefits
1-day gain in skill in 4 yrs
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Existing approaches GEFS (contin.)

• Ensemble size 20 members every 6hrs
• 80 ET members daily
• Model resolution T126 L28
• Lower resolution than current operational GFS
• Non-negligible skill at day 16
• Evaluation scheme for deterministic and
  probabilistic forecasts available

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Probabilistic forecast skill
WINTER
GFS
Skill of Climatology
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Existing approaches CFS

• Fully coupled OLA model
• Captures variability and uncertainty of coupled
  system out to 9 months
• Large hindcast dataset
• Operational forecast system frozen to ensure high
  quality bias correction
• Lacks periodic upgrades of DA/modeling system
• Lagged ensemble generation scheme
• Is not centered on the latest and best analysis.
• Initial error introduced in ensemble hurts
  performance of sub-seasonal forecasts
• Initial variance arbitrary does not reflect
  analysis uncertainty (too large)

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30-member ensemble generated from previous 15 days
f00
Best analysis at initial time
Most recent forecast
Ensemble mean at initial time
Lagged perturbations
Initial perturbations on Feb 3rd 2007
Ensemble Transform perturbations
Example of 16-day ensemble forecast
f00

• Lagged ensemble at initial time
• Not centered on best analysis
• Increased forecast error
• Has unrealistically large spread
• Unreliable prob. forecasts
• Decreased forecast skill

Instantaneous
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Potential skill gain if initial errors due to
lagged were removed

• RMSE of CFS monthly forecasts of Nino 3.4.
  Annual average
• Paremeterization of internal and model error

RMSE Individual and lagged ensemble means
Current vs repositioned
Individual members repositioned
lagged
No model error
Running all members simulateneously
Lead (in days)
Lead (in days)

• Ensemble mean outperforms the individual members
• Repositioning does not require additional
  computer resource or model improvement

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Existing approaches CFS (Contin.)

• Ensemble size Twice daily
• 60 members are formed per month for seasonal
  predictions
• Not optimal for sub-seasonal predictions
• Weak predictive signal requires large ensemble
• Yet, skill is deteriorated if lagged members
  included
• Atmospheric model resolution T62 L64
• Skill of CFS lower than GFS for short-range
• System not optimized for this short period

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Anomaly Correlation NH. Single Forecast
Difference must be larger for ensembles
GFS CDAS CFS
GFS
CFS
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Science Readiness

• To design a system that optimally captures
  initial and forecast states of both fast and slow
  sub-components
• Follows from recommendations from a recent
  workshop on bridging the gap between weather and
  climate numerical predictions (Toth et al 2007)
• Initial ensemble perturbations for coupled
  systems
• Research results available with the breeding
  technique (Cai et al 2003, Yang et al 2006)
• Ensemble Transform method
• Tested for the atmosphere (Mozheng et al 2006)

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Computational Readiness

• Proposed ensemble system will replace current
  GEFS
• The Central Computing System for 2007 can
  accommodate the extra CPU needed if model
  resolution is kept
• The extra CPU needed due to
• Increase in forecast lead Factor of 1.25
• Ocean/Ice model integrations 2.0 ?
• Real-time hindcast 1.3
• Physics upgrade 1.5

Total 4.8 times
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Technical Readiness

• Initial conditions
• The project will use a truncated version of the
  operational GFS analysis (at T126 resolution),
  and the operational ocean analysis
• Models
• will use operational GFS and MOM4 with ice model
  and a coupler expected available soon for
  testing.
• Hindcast generation
• Ongoing EMC development effort to test the
  real-time GEFS hindcast.

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REAL-TIME GENERATION OF HIND-CAST DATASET?
Todays Julian Date TJD
TJD 30
TJD - 30
Actual ensemble generated today
2006
Time
2005
2004
2003
1968
1967
Hind-casts for TJD30 generated today
Hind-casts (or its statistics) for TJD/- 30
saved on disc
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Synergies/Leverages

• GEFS developments Full use of ensemble
  generation, hind-cast generation,
  evaluation/verification infrastructure
• CFS Latest versions of ocean DA, model, new
  reanalysis will be operationally implemented into
  sub-seasonal ensemble as/when they become
  available
• GEOS-5 Latest versions of ocean DA for MOM4,
  NASA-funded RD for subseasonal and seasonal
  forecasts with GEOS-5
• NAEFS Sub-seasonal forecasting benefiting from
  major past and ongoing developments in bias
  correction, downscaling, product generation.
• Week-2 2m temperature (precipitation) products.
  CPC, EMC, and the Canadian Meteorological Center
  (CMC). New system could provide weeks 3 4
  forecasts.
• THORPEX Pacific-Asian Regional Campaign (T-PARC)
  and International Polar Year (IPY) New
  probabilistic sea ice forecast products developed
  jointly with T-PARC / IPY collaborators
• River flow / drought forecasting Sub-seasonal
  ensemble forecasts will be coupled with river
  flow model used experimentally with GEFS system
  and drought monitoring tools to be applied with
  GEFS
• Inter-comparisons Various forecast products from
  the proposed system, including MJO predictions,
  will be compared with those from alternative
  forecast systems such as the NASA GEOS-5 coupled
  system and the linear inverse model from
  NOAA-ESRL.

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Broader impact

• Short-range prediction improvement. Due to the
  use of a coupled OLA model, the sub-seasonal GEFS
  may improve upon the performance of current GEFS
  in areas where coupling plays an important role,
  such as tropical cyclone prediction, even on the
  shorter, 1-2 weeks time scale.
• Seamless suite of forecasts. The proposed system
  offers an opportunity to produce forecasts from
  weather to sub-seasonal lead times with the same
  forecast system, a stated goal of the THORPEX and
  climate research communities (Toth et al 2007)
• Future designs of climate prediction systems.
  Ensemble perturbation and hind-cast generation
  methods proposed may influence the design of
  future prediction systems, possibly leading
  toward a more unified weather and climate
  forecast systems.
• Multi-model approach. The two independent
  prediction systems (GEOS-5 and subseasonal GEFS)
  assessed in this project will contribute to the
  national multi-model prediction approach.
  Multi-model forecasts have demonstrated benefit
  for seasonal predictions. This project will help
  assess whether combining the two systems improves
  the quality of subseasonal predictions as well.