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Currently, every EFI field is based on a forecast interval of 24 hours or longer. Since each meteorological parameter is valid for a period, the content is either:
- an accumulated value (Precipitationprecipitation, Snowfallsnowfall), or
- a mean over a period (Mean mean 2m temperature, Wind wind speed, Water water vapour flux), or
- an extremum ( a maximum or minimum ) over that period (Minimum minimum 2m temperature, Maximum maximum 2m temperature, Maximum maximum wind gust, Maximummaximum significant wave height, CAPE, CAPE-shear).
Each 24-hour period variable is worked out as a post-processed value based on four 6-hourly forecast time step values (e.g. a mean over a 00-24UTC period is a mean of the 06-12-18 and the ending 00UTC fields). Additionally: Importantly, for Maximum
- maximum wind gusts, and
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- maximum and
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- minimum 2m temperatures are computed from the 6 hourly values
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- . These themselves represent extremes within the preceding 6 hours (
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- found from values at every time step).
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- CAPE and CAPE-shear is computed as the maximum of hourly values through the day (01, 02, 03, ... 24UTC).
- maximum significant wave height is computed as the maximum of just the 4 instantaneous 6-hourly values (06, 12, 18
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- ,
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- 24UTC).
On each chart:
- The EFI is shown by colours given by the scale above each chart (±0.3 is shown by the dashed coloured contours).
- The Shift of Tails (SOT) index is shown by black contours (for 0, 1, 2, 5, 8).
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- Quantile1: 1 in 100 occasions in the M-climate was lower than the value shown.
- Quantile10: 1 in 10 occasions in the M-climate was lower than the value shown.
- Quantile50: 1 in 2 occasions in the M-climate was lower than the value shown (i.e. the median)
- Quantile90: 1 in 10 occasions in the M-climate was greater than the value shown.
- Quantile99: 1 in 100 occasions in the M-climate was greater than the value shown.
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Fig8.1.4.7.2: Example of EFI and Shift of Tails SOT chart for mean temperature for the period T+48 to T+72 (VT 00UTC 30 Mar 2018 to VT 00UTC 31 Mar 2018), data time of forecast DT 00UTC 28 Mar 2018.
On the left chart:
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EFI values above/below ±0.8 usually signify a very unusual or extreme event. 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 lower or higher 10% ENS ensemble results are. For more information see the sections on Extreme Forecast Index (EFI) and Shift of Tails (SOT).
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Multi-parameter interactive charts are available showing the geographical distribution of the EFI of the principal weather parameters: maximum 10m wind gust, 24hr precipitation and 2m temperature, overlaid with the ensemble mean of the MSLP field. This chart highlights areas where there is a significant difference between the ensemble forecast (ENSensemble) distribution and the model climate (M-climate) distribution.
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Fig8.1.4.7.5: Examples of EFIs and CDFs from a series of ENS ensemble runs for Valetta valid for VT 30 Mar 2018. The location can be chosen by the user by the probe tool on ecCharts or by use of widgets on the dashboard.
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Attached to each grid point of the global EFI charts there is a CDF diagram for each of the EFI parameters, with information on M-climate at the grid point (always shown for the lead time 24-48h) and the available forecast distributions (all valid for the given day, but coming from different, consecutive ENS ensemble runs, so the lead times vary). On the right are shown the corresponding EFI values. These diagrams can be displayed interactively by clicking on the desired location on the EFI web charts, use of the probe tool on ecCharts, or selection of the widgets on the dashboard.
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Fig8.1.4.7.6A: CDF and associated EFI for NW Portugal area. There is a consistently high and increasing EFI for rainfall (reaching 80%) which is sufficient for forecasting a significant and maybe an extreme rainfall event. Some ENS ensemble members show rainfall totals much greater than M-climate maxima - the degree to which these totals exceed the M-climate maximum is not taken account of in the EFI calculation, but is used directly in calculating SOT. The EFI for maximum wind gust is greater than 50% in the last two forecasts but this is not really sufficient for forecasting a significant wind event. The steep and consistent temperature CDF indicates high confidence in a forecast of near normal temperatures around 14°C.
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Fig8.1.4.7.6B: CDF and associated EFI for Po Valley area. EFIs for mean temperature and wind gusts are consistently negative but not large. The CDF shows consistency between the temperature forecasts, with the last ENS ensemble forecast a little colder. The steep CDF indicates high confidence in a forecast of about 2°C below normal temperature.
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Fig8.1.4.7.6C: CDF and associated EFI for Marseilles area. There is a consistently high and increasing EFI for wind (reaching 86%) which is sufficient for forecasting a significant and possibly extreme wind event. The CDF shows consistency between the stronger gust forecasts in last two ENS ensemble results. Some ENS ensemble members show wind gusts much greater than M-climate maxima - the degree to which these values exceed the M-climate maximum is not taken account of in the EFI calculation, but is used in calculating SOT. The steep and consistent mean temperature CDF indicates high confidence in a forecast of near normal temperatures around 16°C.
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The development and evolution of EFI and SOT over a sequence of charts can give an early insight into the likelihood of occurrence of out-of-the-ordinary weather and the confidence that may be assigned to developments. EFI values roughly indicate the extent to which ENS ensemble members forecast values exceeding exceed the corresponding M-climate. At At longer lead-times the number of such members may be quite low. However areas of SOT >1 on longer lead charts give an indication that at least some ENS ensemble members are showing extreme values. This shows there is a risk, albeit small, of out-of-the-ordinary weather within the marked area. As the forecast lead time shortens, EFI values will indicate any increase or decrease in the number of members exceeding the corresponding M-climate value. At the same time the isopleths of SOT will show the variation in the potential for extreme values and give an increasing definition of the risk area (if there is one!).
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Fig8.1.4.7.7: An example of the use of EFI and SOT during the period leading up to 05-06 September 2018. The evolution of this sequence illustrates the ability of EFI and SOT charts to allow early indication the risk of severe weather (SOT), with an indication of changes in confidence and definition of the area at risk (EFI). EFI EFI tends to be greater than 0.5 if the majority of ENS ensemble member forecast values are markedly greater than those of the corresponding M-climate. EFI>0.5 is coloured (see scales). SOT is greater than 0 SOT>0 if at least 10% of ENS ensemble members forecast an extreme event. Isopleths are for values of0of 0,1,2,5,8. The The actual SOT values show how extreme the top 10% of ENS ensemble forecast are.
Chart A (from a forecast 6 days ahead of the event) shows fragmented areas where SOT>0 (i.e. a few ENS ensemble members show an extreme event) so a very severe weather event is possible. However, generally low EFI values (<0.5) shows the majority of ENS ensemble members do not indicate an unusual event (even though a few do).
Chart B (from a forecast 4 days ahead of the event) shows an increasing area where SOT>0 so a very severe weather event is now rather more probable. EFI values are >0.5 (yellow) which shows that more ENS ensemble members indicate an unusual event (even though some do not).
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Chart D (from a forecast 0 days ahead of the event) shows the areas of SOT>0 and EFI>0.5 are tightly defined, giving confidence to the user in pinpointing the areas at risk. There is an elongated internal area where SOT>1.0, even SOT >2.0, so a very severe event is possible. EFI values are more widely >0.8 (dark orange) so confidence of at least a severe event is growing (for those areas)
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Very high uncertainty illustrated by EFI and SOT
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The ensemble is designed to give an assessment of uncertainty. However,
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occasionally the uncertainty becomes very large, with additionally a potential for very high or low forecast values to occur. An example is shown in Fig8.1.4.7.9 where
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ensemble members showed widely differing yet potentially extreme hot or cold temperatures. These cases are relatively rare, usually associated with a sharp upper trough and associated front separating widely dissimilar airmasses. Users should accept the uncertainty and tailor their forecasts to reflect the impact on users
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. Certainly they should not take middle course. Some customers may require an indication of very high
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or very low temperatures, even if at a low probability.
Fig8.1.4.7.9: EFI and SOT chart valid VT 22-23 July 2012 (T+156-180) from ENS data time ensemble DT 00UTC 15 July 2012, with associated Cumulative Distribution Function (CDF) and meteogram with M-climate for the marked position. The uncertainty is clear on the meteograms. The CDF shows some ENS ensemble members indicating temperature values above M-climate maximum and some below M-climate minimum and thus the SOT will show values for both the warm and cold tails. This is shown on the chart where the SOT lines (black) overlap. The airmasses are clearly very different as there is a large positive EFI indicative of high temperatures over eastern Europe and a large negative EFI indicative of low temperatures over western Europe.
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- Read more about EFI in seasonal forecasts (EFI in seasonal forecasts is not available operationally).
- Watch a comprehensive lecture on forecasting extreme events using EFI and SOT.
Updated/Amended 30/12/19 - Minor changes.
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