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Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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.

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Adjacent to each EFI chart is a duplicate chart showing a user-selectable quantile of the the M-Climate for the same quantity.  Quantiles available are:

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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.

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.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.  

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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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

ecCharts and Dashboard Widgets

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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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

Cumulative Distribution Function Diagrams

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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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

Extreme Forecast Index (EFI) and Shift of Tails (SOT) versus Lead Time

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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).

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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.

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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.

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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

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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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

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.  

Note: HRES and Ensemble Control Forecast (ex-HRES) are scientifically, structurally and computationally identical.  With effect from Cy49r1, Ensemble Control Forecast (ex-HRES) output is equivalent to HRES output shown in the diagrams.   At the time of the diagrams, HRES had resolution of 9km and ensemble members had a resolution of 18km.

Additional Sources of Information

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