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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 of 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. 

SOT compares the tails of both distributions of M-climate and ensemble based on the 90th and 99th (upper tail) percentiles.  In addition, only for 2 m temperature, a lower tail (cold temperature) SOT value is computed, based on the 1st and 10th percentiles.  In each case positive SOT values indicate that at least 10% of the ensemble is forecasting an "extreme event".  A high value of SOT shows just how extreme the 10% ensemble outlier results are.

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Fig8.1.9.3-1: This example corresponds to a large positive EFI (red ensemble forecast curve well to the right of the black M-Climate curve). The positive upper tail SOT (quantile 90) indicates several ensemble members are predicting extreme warm temperatures (above the 99th M-climate percentile shown by the dashed green line).  This suggests unusually warm temperatures may be confidently forecast (large positive EFI), but very extreme temperatures are only a minimal risk (because SOT is only +0.4).  Larger high tail SOT implies the warm end of the ensemble range is more extreme.

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Fig8.1.9.3-2: This example corresponds to a fairly large positive EFI (red ensemble forecast curve well to the right of the black M-Climate curve).  The negative upper tail SOT (quantile 90) indicates that the warmest ensemble members are not predicting an extreme warm outcome (above the 99th M-climate percentile shown by the dashed green line).  However one ensemble member (extreme top end of red curve) is relatively extreme (albeit still short of the extreme of the M-climate temperature distribution).  This suggests warm temperatures may be confidently forecast (fairly large positive EFI) but will be unexceptional (SOT –0.7) compared with the M-climate, unless the single warm outlier solution discussed actually occurs.

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Fig8.1.9.3-4: This example corresponds toa large negative EFI (red ensemble forecast curve well to the left of the M-Climate black curve).  The positive lower tail SOT (quantile 10) indicates there are several ensemble members predicting extreme cold temperatures (below the 1st M-climate percentile shown by the dashed green line).  This suggests unusually cold temperatures may be confidently forecast (large negative EFI), but very extreme cold temperatures are only a minimal risk (because SOT is only +0.4).  Larger low tail SOT implies the cold end of the ensemble range is more extreme.

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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).  50% of ensemble members forecast less than about 1mm precipitation (the lower part of the M-climate is only just above 0mm).  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 M-climate distribution.  The negative upper tail SOT (quantile 90) indicates there are very few if any ensemble members predicting extreme equivalent rainfall 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).  70% of ensemble members forecast less than about 1mm precipitation.  But 15% of ensemble members forecast more than about 2mm precipitation, although it is unlikely there will be an exceptional rainfall event (only moderate SOT value of -0.6).

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