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ENS members giving forecast values well beyond the M-climate extreme contribute no more to the 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 point.  The Shift of Tails (SOT) index complements the EFI by providing information about how extreme an event could potentially be.  Specifically, it compares the tails of the ENS and M-climate distributions. 


SOT compares the tails of both distributions of M-climate and ENS based on the 90th and 99th (upper tail) percentiles - and for temperature only, also 1st and 10th (lower tail) percentiles.  Positive SOT values indicate that at least 10% of the ensemble is forecasting an extreme event.  A high value of SOT shows how extreme the top 10% ENS results are.


 Fig8.1.4.9: An example CDF for M-climate (black) and ENS (red). The 99th percentile of the M-climate (Qc(99), shown in green) is taken as the M-climate extreme.  The SOT is defined as the ratio of the departure from the M-climate extreme at the 90th percentile level of the ENS (Qf(90)) against the M-climate (Qc(90)). 


 Fig8.1.4.10:  An example CDF for snowfall.  In this case EFI=0.36 but SOT=0.8.  EFI is positive hence forecast suggests snow, but the relatively low EFI implies uncertainty.  However, SOT>0 indicates there are some ENS members predicting extreme snowfall (above the 99th M-climate percentile shown by the green line).

EFI and SOT are computed for many weather parameters, and for different forecast ranges and accumulation periods.  Charts may be accessed via the ECMWF web pages.



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