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Ensemble members giving forecast values well beyond the M-climate extreme contribute no more to the Extreme Forecast Index (EFI) than members just matching the M-climate extreme.  The ‘Shift ‘Shift of Tails’ Tails’ (SOT) is an additional product that has been developed to address this "limitation".  The SOT index complements EFI by providing information about how extreme an event could potentially be.  Specifically, it compares the tails of the ensemble and M-climate distributions. 

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Fig8.1.9.3-5:  An example CDF for snowfall - snowfall is just considered as equivalent rainfall.   Moderately large positive EFI shows the equivalent rainfall distribution is higher than the M-climate distribution.  The positive upper tail SOT (quantile 90) indicates there are several ensemble members predicting extreme equivalent rainfall anomalies (above the 99th ER-M-climate percentile shown by the dashed green line).  This suggests uncertainty that a significant equivalent rainfall is forecast (only moderate EFI).  Note: 50%  50% of ensemble members forecast less than about 1mm precipitation (the lower part of the M-climate is only just above 0mm), but equally .  But 25% of ensemble members forecast more than about 2mm precipitation (significantly above M-climate where about 97% of precipitation less than 2mm).  If a significant snowfall occurs it could be an exceptional rainfall equivalent (fairly high SOT value of 0.8).  Confidence in extreme precipitation rises as SOT values increase - users should focus on SOT values >0.5.

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Fig8.1.9.3-6: The moderate positive EFI suggests the ensemble rainfall distribution is slightly above the ERM-climate distribution.  The negative upper tail SOT (quantile 90) indicates there are very few if any ensemble members predicting extreme equivalent rainfall anomalies anomalies (above the 99th M-climate percentile shown by the dashed green line).  This suggests uncertainty that larger than normal rainfall may be forecast (only moderate EFI - but note 70% ).  70% of ensemble members forecast less than about 1mm precipitation, equally .  But 15% of ensemble members forecast more than about 2mm precipitation), but although it is unlikely there will be an an exceptional rainfall rainfall event (only moderate SOT value of -0.6).

Fig8.1.9.3-7: An example of a rainfall CDF most frequently encountered where very few ensemble members forecast any rain at all.  The small negative EFI shows the ensemble rainfall distribution is lower than the M-climate distribution.  The negative upper tail SOT (quantile 90) indicates there are very few if any ensemble members (and in this case none of them) predict extreme equivalent rainfall (above the 99th ER-M-climate percentile shown by the dashed green line).  This suggests confidence that larger than normal rainfall will not occur (small EFI) and an exceptional rainfall event will not occur(SOT -1.2).

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