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Generation of the Ensemble

Process of calculating ensemble perturbations

Ensemble forecasts require many alternative analyses and forecasts and each ensemble member requires its own global perturbation.  Importantly, the analysis and subsequent forecast of each ensemble member must be truly independent of all the others.  The process of deriving independent perturbed analyses for ENS members is to use:

• A 50 member Ensemble of Data Assimilations (EDA) is calculated over the globe.  The differences of each member from the EDA mean gives 50 different sets of global EDA perturbations.
• Sets of Singular Vectors (SVs) are separately calculated over the Northern and Southern Hemispheres, and over the tropics between 30°N and 30°S.  These are linearly combined (using coefficients randomly sampled from a Gaussian distribution) to give 100 different sets of global SV perturbations.

Medium range ensemble perturbations

The medium range 10 day ensemble uses 50 perturbed members and one unperturbed member (the medium range control member). consists of 50 members and the unperturbed control member (CONTROL-10).

The medium range 15 day ensemble consists of 50 members and the unperturbed control member (CONTROL-15).

• The control member Analysis = the Analysis without any perturbations added.  
• The 50 sets of EDA perturbations and 50 sets of SVs are

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• combined together to give 50 sets of global perturbations for model initialisation

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• :
  • ENS member 1 Analysis =

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• • Analysis + (EDA member 1 - EDA mean) + SV Perturbation 1
    
  • ENS member 2 Analysis =

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• • Analysis

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• • - (EDA member 2 - EDA mean) + SV Perturbation 2
  •         and so on

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• • until 
  • ENS member 49 Analysis =

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• • Analysis + (EDA member 49 - EDA mean) + SV Perturbation 49
  • ENS member 50 Analysis =

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• • Analysis

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• • - (EDA member 50 - EDA mean) + SV Perturbation 50

_{slide 16, https://confluence.ecmwf.int/download/attachments/72127032/lang_1_2017.pdf?version=1&modificationDate=1495727292709&api=v2Image Added}

Extended range ensemble perturbations

The extended range ensemble

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consists of 100 perturbed members and one unperturbed member (the extended range control member).

• The control member Analysis = the Analysis without any perturbations added.  
• The 50 sets of EDA perturbations and 100 sets of SVs are

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• combined together to give 100 sets of global perturbations for model initialisation

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• :
  • ENS member 1 Analysis =

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• • Analysis + (EDA member 1 - EDA mean) + SV Perturbation 1
    
  • ENS member 2 Analysis =

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• • Analysis + (EDA member 2 - EDA mean) + SV Perturbation 2
  •         and so on until
  • ENS member 49 Analysis =

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• • Analysis + (EDA member 49 - EDA mean) + SV Perturbation 49
  • ENS member 50 Analysis =

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• • Analysis + (EDA member 50 - EDA mean) + SV Perturbation 50
  • ENS member 51 Analysis =

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• • Analysis + (EDA member 1 - EDA mean) + SV Perturbation 51
  • ENS member 52 Analysis =

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• • Analysis + (EDA member 2 - EDA mean) + SV Perturbation 52
  •         and so on until
  • ENS member 99 Analysis =

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• • Analysis + (EDA member 49 - EDA mean) + SV Perturbation 99
  • ENS member 100 Analysis =

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• • Analysis + (EDA member 50 - EDA mean) + SV Perturbation 100

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Quality of the individual perturbed analyses

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