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User Guide to ECMWF Forecast Products > Derived products from the EPS > The Extreme Forecast Index (EFI) > 
The cumulative distribution function The interpretation of the EFI  
   

Calculating the EFI

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The cumulative distribution function
Calculating the EFI
The interpretation of the EFI
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The Extreme Forecast Index is calculated according to the formula

Eq1.png

where Ff(p) denotes the proportion of EPS members lying below the p quantile of the climate record. The EFI is computed five days ahead for

·         10 m wind (daily mean)

·         10 m wind gusts (daily maximum)

·         2 m temperature (daily mean)

·         Precipitation (daily values up to day 5 and for the intervals 1-5, 2-6 and 1-10 days).

EFI_6.gif

Figure 52: The EFI can have both negative and positive values: positive for positive anomalies (upper figures) and negative for negative anomalies (lower figures).

If the EPS probability distribution agrees with the M-climate distribution then EFI = 0. If the probability distribution (mean, spread and asymmetry) does not agree with the climate probability distribution, the EFI takes non-zero values. In the special case where all the EPS members forecast values above the absolute maximum in the M-climate, the EFI = +1; if they all forecast values below the absolute minimum in the M-climatethe EFI = -1 (see Figure 52).

Negative EFI values are only really of interest for temperature anomalies, since tem­perature is the only variable which is of particular interest when it has negative anom­alies, such as cold spells. Absence of precipitation might be important for certain agricultural activities, similarly weak winds are of significance for sailing; however, although such weather may be regarded as “unusual” in some locations, it is not catered for in the EFI.

Experience suggests that EFI values of 0.5 - 0.8 (irrespective of sign) can be generally regarded as signifying that “unusual” weather is likely and values above 0.8 as usually signifying that “very unusual” or extreme weather is likely.

A convenient way to depict the current EPS forecast together with previous runs verifying at the same time (“lagged EPS”) is to depict the CDF from previous runs (see Figure 53).

EFI_10.gif

Figure 53: A schematic illustration of the CDF (left) and pdf (right) for forecasts of 12-hour accumulated precipitation. The last EPS forecast +48 hour ahead (blue curves) is presented together with the climate (black curves) and the EPS forecasts two and four days back (dark green and light green curves respectively).




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