EFI Charts

The Extreme Forecast Index and Shift of Tails are presented in chart form, either for each parameter separately, or on a composite chart that caters for temperature, precipitation and maximum gusts.

Impact of local time differences from UTC when using EFI and SOT charts

EFI and SOT charts and diagrams refer to 24hr periods (T+00 to T+24, T+24 to T+48, T+48 to T+60 etc, etc.) and the charts run from 00UTC to 24UTC  each day.   Thus, depending on the longitude, the period of the 24hr EFI and SOT will not match local time and charts of EFI probability may span over two days in local time.  So as examples:

  • in mid-western United States the period of the charts will be around late afternoon local time to late afternoon local time the next day.  
  • in Australia and the Far East the period of the charts will be around mid-morning local time to mid-morning local time the next day.
  • in the Near East and Eastern Africa the period of the charts will be around early morning local time to early morning local time the next day.

Severe storms may appear on two consecutive charts (e.g. afternoon local time severe storms in USA continuing through the evening local time before decaying will appear on two consecutive days but possibly with a lower probability in each period.  It is important to cater for the time differences when considering the probability of extreme weather.

EFI Web open access charts

To view Medium Range CDFs:

  1. In the main charts page, click Medium Range.
  2. Click Medium Range, Forecasts, Extreme Forecast Index.
  3. Display of Multi-parameter EFI.

3A. Select forecast time from drop-down menu.      3B. Select Area from drop-down menu.

4.  Display of EFI for individual parameters (precipitation etc).

4A. Select forecast day or period from drop-down menu.     4B. Select quantile.    4C. Select Area from drop-down menu.

Fig8.1.9.7-1:  To view Medium Range CDFs: 

Charts are available for:

Each parameter is available for all the following periods, or a subset of them: 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, 10-15, 1-10, 1-15 (each are valid for the periods 00-24UTC).  The period selected is under user control.

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 (precipitation, snowfall), or
  • a mean over a period (mean 2m temperature, wind speed, water vapour flux), or
  • a maximum or minimum over that period (minimum 2m temperature, maximum 2m temperature, maximum wind gust, maximum 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:  

  • maximum wind gusts, and maximum and minimum 2m temperatures are computed from the 6 hourly values.  These themselves represent extremes within the preceding 6 hours (found from values at every time step).
  • 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, 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).

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 (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.


Fig8.1.9.7-2: Example of EFI and SOT chart for mean temperature for the period T+48 to T+72 (VT 00UTC 30 Mar 2018 to VT 00UTC 31 Mar 2018), DT 00UTC 28 Mar 2018.

On Fig8.1.9.7-2 (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 or higher 10% ensemble results are.  For more information see the sections on Extreme Forecast Index (EFI) and Shift of Tails (SOT).

On Fig8.1.9.7-2 (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 Multi-parameter Interactive (clickable) EFI charts

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 (ensemble) distribution and the model climate (M-climate) distribution.  

Fig8.1.9.7-3: The global ““anomalous weather”” or ““interactive EFI”” chart DT 00UTC 19 Oct 2020 VT between T+00 and T+24 hours.  Corresponding charts may be selected for the 24 hr periods ending T+48, T+72, T+96, T+120, T+144, T+168.

The chart shows the geographical distribution of the EFI of the principal weather parameters: maximum 10m wind gust (purple), 24hr precipitation (green) and 2m temperature (solid colours), overlaid with the ensemble mean of the MSLP field.


This chart is "clickable"; positioning and clicking the mouse cursor over a point will produce a graphical output for the selected location.   The user has the option to select from the dropdown menu appearing at the top right:


Fig8.1.9.7-4: Examples of the diagrams produced from the above multi-parameter EFI chart (Fig8.1.9.7-4) when clicked on Lisbon (offshore Lisbon for the wavegram).  Corresponding diagrams at different forecast lead-times may be selected from the other 24 hr periods ending T+48, T+72, T+96, T+120, T+144, T+168.

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.


Fig8.1.9.7-5:  Examples of EFIs and CDFs from a series of ensemble runs for Valetta 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.


Cumulative Distribution Function Diagrams

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 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.


Fig8.1.9.7-6: 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 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.


Fig8.1.9.7-7: 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 ensemble forecast a little colder.   The steep CDF indicates high confidence in a forecast of about 2°C below normal temperature.


Fig8.1.9.7-8: 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 ensemble results.   Some 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.


Fig8.1.9.7-9: 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.

Extreme Forecast Index (EFI) and Shift of Tails (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 ensemble members forecast values exceed 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 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!).

The example given in Fig8.1.9.7-10 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.

 

Fig8.1.9.7-10: 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 ensemble member forecast values are markedly greater than those of the corresponding M-climate.  EFI>0.5 is coloured (see scales). SOT>0 if at least 10% of ensemble 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 ensemble forecast are.

Chart A (from a forecast 6 days ahead of the event) shows fragmented areas where SOT>0 (i.e. a few 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 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 ensemble 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 >2.0, 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)

 

Fig8.1.9.7-11: 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

The ensemble is designed to give an assessment of uncertainty.  However, occasionally the uncertainty becomes very large, with additionally a potential for very high or low forecast values to occur.  An example is shown in Fig8.1.9.7-12 where 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.  Certainly they should not take middle course.  Some customers may require an indication of very high or very low temperatures, even if at a low probability. 


 

Fig8.1.9.7-12: EFI and SOT chart  VT 22-23 July 2012 (T+156-180) from 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 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.


An example of high probability of an extreme event.  Rainfall in the desert.

Fig8.1.9.17-13:  Extreme Forecast Index for total precipitation during the 10 day period 00UTC 10 Apr 2023 to 00UTC 20 Apr 2023.   The forecast cumulative distribution function (CDF) suggests that during the period there is less than 10% probability of below 35mm precipitation, 90% probability of below 80mm precipitation, and 10% probability of greater than 80mm.  The forecast CDF (red) is well above the M-climate CDF (black) and shift of tails values are quite high.  For a desert region, quite moderate precipitation values can be devastating.


An example of high probability of an unusual event.  Very calm sea in the Mediterranean.

Fig8.1.9.17-14: An example of a forecast of exceptionally calm conditions in the Mediterranean.  The chart shows extreme forecast index (EFI) for wave height during the 24 hour period 00UTC 10 Apr 2023 to 00UTC 11 Apr 2023.  The colours on the cumulative frequency diagram show the results from the most recent ensemble runs; red is the latest.  The forecast cumulative distribution functions (CDF) of the last few runs suggest strongly that wave heights will be only just a few cm.  The forecast CDF (red) is well below the M-climate CDF (black) and EFI values are strongly negative. 

Differences in EFI over short distances.

At first sight the EFI values shown look unrealistic but can be explained by orography and structure of the atmosphere.  The positive (warm) EFI coincides with mountains, whilst the cold EFI in NW Spain is in a relatively high level plateau. It seems the inversion associated with the unusually intense anticyclone (>1040mb) is intersecting the mountains, with highly subsided air delivering higher temperatures where this mountains penetrate upwards. At the same time the lower level cold is fuelled by radiative cooling through the very dry air with light surface winds. 

Fig8.1.9.17-15: 24h mean 2m temperature EFI plot for NW Spain 00UTC 18 Dec to 19 Dec 2023, VT 12UTC 17 Dec 2023.   Large values for EFI of extreme cold and extreme warm close together . 

Additional Sources of Information

(Note: In older material there may be references to issues that have subsequently been addressed)