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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).

• 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

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Consequently, the proportion of the perturbed analyses that are better than the control (i.e. unperturbed) analysis (CTRLcontrol) for a specific location and for a specific parameter (e.g. 2m temperature or MSLP at Paris) is only 35% (see Fig5.1.4).  Considering more than one grid point lowers the proportion even further.

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If an ensemble member is closer to the truth than to the CTRL control in one place (e.g. Paris) it might not be so in another (e.g. Berlin).  Indeed, the larger the area, the less likely that any of the perturbed members are better than the non-perturbed CTRL unperturbed control analysis. For a region the size of a small ECMWF Member State, only about 7% of the perturbed analyses are, on average, better than the CTRL control analysis. For the larger Member States this decreases to only 2%.

With respect to the forecasts, in the short range only a small number of the perturbed forecasts are, on average, more skilful than the CTRL control forecast.  However, with increasing forecast range the average proportion of perturbed forecasts that are better than the CTRL control forecast increases, eventually approaching 50% asymptotically.

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

The resolution of the ENS is half that of the HRES.  Despite this, the ensemble CTRL forecast performs very similarly to HRES to Day10 (the limit of HRES forecasts) regarding synoptic pattern.  Differences are most noticeable for small-scale extreme weather events, where HRES is able to generate, for example, stronger winds and higher precipitation values.

Quality of the individual perturbed forecasts

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Fig5.1.6: Schematic image of the RMS root mean square error of the ensemble members, EM ensemble mean and CTRL control forecast as a function of lead-time.  The asymptotic predictability limit is defined as the average difference between two randomly chosen atmospheric states.  In a perfect ensemble system the RMS root mean square error of an average ensemble member is √2 times the error of the EMensemble mean.

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 CTRL control in the short range makes the task of trying to select the ENS 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).

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