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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 consists of 50 members and the unperturbed control member (CTRL).

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Extended range ensemble perturbations

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

• The control member Analysis = the Analysis without any perturbations added.  
• The 50 sets of EDA perturbations and 100 sets of SVs are combined together to give 100 sets of global perturbations for model initialisation:
  • ENS member 1 Analysis = Analysis + (EDA member 1 - EDA mean) + SV Perturbation 1
    
  • ENS member 2 Analysis = Analysis + (EDA member 2 - EDA mean) + SV Perturbation 2
  •         and so on until
  • ENS member 49 Analysis = Analysis + (EDA member 49 - EDA mean) + SV Perturbation 49
  • ENS member 50 Analysis = Analysis + (EDA member 50 - EDA mean) + SV Perturbation 50
  • ENS member 51 Analysis = Analysis + (EDA member 1 - EDA mean) + SV Perturbation 51
  • ENS member 52 Analysis = Analysis + (EDA member 2 - EDA mean) + SV Perturbation 52
  •         and so on until
  • ENS member 99 Analysis = Analysis + (EDA member 49 - EDA mean) + SV Perturbation 99
  • ENS member 100 Analysis = Analysis + (EDA member 50 - EDA mean) + SV Perturbation 100

Quality of the individual perturbed analyses

An unavoidable consequence of modifying the initial conditions around the most likely estimate of the truth (i.e. the 4D-Var analyses) is that the perturbed analysis is on average slightly degraded.  The RMS distance from truth for a perturbed analysis is, in the ideal case, on average √2 times the RMS distance of the unperturbed analysis from the truth (see Fig5.1.3).

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Fig5.1.5: Schematic representation of the percentage of perturbed forecasts with lower root mean square error than the control forecast for regions of different sizes: Northern Hemisphere, Europe, a typical ““small”” Member State and a specific location.  With increasing forecast range, fewer and fewer perturbed members are worse than the control (from Palmer et al 2006).

Quality of the individual perturbed forecasts

Since the perturbed analyses have, ideally on average, 41% larger analysis errors than ensemble mean, this makes the individual ensemble forecasts on average less skilful than the unperturbed control forecast.   Predictive skill varies with season and geographical location, but on average:

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However, what the perturbed forecasts may lack in individual skill, they compensate for by their large number, their ability to form good median or ensemble mean values and reliable probability estimations.  The information from all the members in the ensemble should be used.  The low proportion of perturbed forecast members “better” than the control in the short range makes the task of trying to select the ensemble member with the best subsequent forecast very difficult and, perhaps, impossible.  There are no known methods to identify beforehand the “best” ensemble member beyond the first day or so (not least due to the effects of downstream spread of errors).

Additional sources of information

(Note: In older material there may be references to issues that have subsequently been addressed)

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