The EFI (and SOT) are presented in chart form, either for each parameter separately, or on a composite chart that caters for temperature, precipitation and maximum gusts.
EFI Web charts
Charts are available for:
- mean 2m temperature EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7, 1-3, 2-4, 3-5, 4-6, 5-7, 6-8, 7-9, 1-5, 2-6, 3-7, 4-8, 5-9, 1-10, 10-15, 1-15.
- minimum 2m temperature EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7.
- maximum 2m temperature EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7.
- maximum wind gust EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7.
- wind speed EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7, 1-3, 2-4, 3-5, 4-6, 5-7, 6-8, 7-9, 1-5, 2-6, 3-7, 4-8, 5-9, 1-10, 10-15, 1-15.
- maximum significant wave height EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7.
- snowfall EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7.
- CAPE EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7.
- CAPE-shear EFI for the periods: Days 1, 2, 3, 4, 5, 6, 7.
Each are valid for the periods 0000-24UTC in the days shown. The period selected is under user control.
Currently, every EFI field is based on a forecast range of 24 hours or longer. Since each meteorological parameter is valid for a period, the content is either an accumulated value (e.g. precipitation), a mean over a period (e.g. mean 2m temperature or mean wind) or an extremum (maximum or minimum) over that period (e.g. wind gust). 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). Importantly, for maximum wind gusts and maximum and minimum 2m temperature, the 6 hourly values used themselves represent extrema within the preceding 6 hours (diagnosed by interrogating the ENS at every time step). On the other hand the maximum significant wave height is computed as the maximum of just the 4 instantaneous 6-hourly values.
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).
Extreme values of EFI (close to +1 or -1) and positive values of SOT signify that a very unusual event is expected.
Adjacent to each EFI chart is a duplicate chart showing a user-selectable quantile of the M-Climate for the same quantity. Quantiles available are:
- 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
- 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
Fig220.127.116.11: Example of EFI and Shift of Tails chart for mean temperature for the period T+48 to T+72 (00UTC 30 Mar 2018 to 00UTC 31 Mar 2018), data time of forecast 00UTC 28 Mar 2018.
On the left chart:
- Blue colours over Portugal indicate EFI between 0.8 and 0.9 for a colder than normal event. Positive SOT is indicated within the black zero SOT contour.
- Orange and red colours over parts of Italy and Sicily indicate EFI between 0.8 and 1.0 for a warmer than normal event. A small positive SOT is indicated within the black zero SOT contour.
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 10% ENS results are. For more information see the sections on Extreme Forecast Index (EFI) and Shift of Tails (SOT).
On the right chart:
Colours indicate the quintile90 temperature ranges of the M-climate where only one in 10 occasions have reached greater values than shown (i.e. on only 1 in 10 occasions during the construction of M-climate for each location and on this date have the temperatures indicated by the colours been exceeded). The chart shows on only 1 in 10 occasions are mean temperatures likely to be above 15°C-20°C in parts of southern Italy and Sicily. The high EFI and locally positive SOT in these areas suggests unusually high mean temperatures may be expected. Selection of quintile10 would allow a similar assessment of how unusually cold the mean temperature in Portugal is likely to be.
Composite or Interactive EFI charts
Clickable charts are available showing the geographical distribution of the EFI of the principal weather parameters: maximum 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 (ENS) distribution and the model climate (M-climate) distribution. Clicking on the chart will produce the option to select, for that location. These are:
Fig18.104.22.168:The global “anomalous weather” or “interactive EFI” chart from 00UTC 09 May 2017 between T+48 and T+72 hours. It shows the geographical distribution of the EFI of the principal weather parameters: maximum wind gust (purple), 24hr precipitation (green) and 2m temperature (solid colours), overlaid with the ensemble mean of the MSLP field.
ecCharts and Dashboard Widgets
For a location chosen by the probe tool on ecCharts or by selection of a widget on the dashboard:
- A range of CDFs are available:
- 24hour mean 2m temperature.
- 24hour minimum 2m temperature.
- 24 hour maximum 2m temperature.
- 24 hour maximum wind gust.
- 24 hour precipitation.
- A range of EFIs are available:
- 2m temperature.
- 24 hour maximum wind gust.
- 24 hour total precipitation.
Fig22.214.171.124: Examples of EFIs and CDFs from a series of ENS runs for Valetta valid for 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.
CDF Diagrams - "Cumulative Distribution Functions"
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 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.
Fig126.96.36.199A: 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 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.
Fig188.8.131.52B: 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 forecast a little colder. The steep CDF indicates high confidence in a forecast of about 2°C below normal temperature.
Fig184.108.40.206C: 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 results. Some ENS 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.
Fig220.127.116.11D:CDF and associated EFI for NE Poland area. There is a strong and consistent negative EFI for temperature. The CDF traces are steep and very similar over last four forecast runs and imply high confidence in out of the ordinary cold mean temperatures about 8°C below normal.
EFI and SOT versus Lead Time
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 members forecast values exceeding the corresponding M-climate. 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 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!).
The example given in Fig18.104.22.168 was associated with a frontal wave system that, although not appearing very dramatic on the synoptic charts, produced significant rainfall as it moved briskly northeastward across parts of northern USA and eastern Canada.
Fig22.214.171.124: 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 tends to be greater than 0.5 if the majority of ENS member forecast values markedly greater than those of the corresponding M-climate. EFI>0.5 is coloured (see scales). SOT is greater than 0 if at least 10% of ENS members forecast an extreme event. Isopleths are for values of 0,1,2,5,8. The actual SOT values show how extreme the top 10% of ENS forecast are.
Chart A (from a forecast 6 days ahead of the event) shows fragmented areas where SOT>0 (i.e. a few ENS 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 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 members indicate an unusual event (even though some do not).
Chart C (from a forecast 2 days ahead of the event) shows the areas of SOT>0 and EFI>0.5 are better defined indicating the area most at risk to severe weather. EFI values >0.8 suggest that a severe event is probable,whilst having some internal areas where SOT>1.0 indicates some potential for a very severe weather event.
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, 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)
Fig126.96.36.199: Observed rainfall totals include some above 50mm/24hr and one above 100mm/24hr over eastern Canada during the period 05/12UTC to 06/12UTC September 2018.
Very high uncertainty illustrated by EFI and SOT
ENS is designed to give an assessment of uncertainty, but occasionally the uncertainty becomes very large with additionally potential for very high or low forecast values to occur. An example is shown in Fig188.8.131.52 where ENS 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 and certainly should not take middle course. Some customers may require an indication of very high temperatures even if at a low probability. Forecasts from HRES may help in making a decision. However, HRES weighting compared to ENS members decreases with lead-time and HRES should be considered as having no more weight than any other ENS member beyond about Day7.
Fig184.108.40.206: EFI and SOT chart valid 22-23 July 2012 (T+156-180) from ENS data time 15 July 2012, with associated CDF and meteogram with M-climate for the marked position. The uncertainty is clear on the meteograms. The CDF shows some ENS 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.
Additional Sources of Information
(Note: In older material there may be references to issues that have subsequently been addressed)
- 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.