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Sub-seasonal range extreme forecast index (EFI), shift of tails (SOT) and cumulative distribution functions (CDF) is available for 2m temperature and precipitation.  These CDFs depict anomalies ( relative to the ER SUBS-M-Climate distribution).  This is unlike ECMWF the CDF used for 24h periods at for shorter ranges which that show absolute values.  The CDFs cover the following:

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Each CDF plot displays the latest forecast along with the sub-seasonal range model climate (ER-M-https://confluence.ecmwf.int/display/FUG/Section+5.3.2+SUBS-M-Climate%2C+the+sub-seasonal+model+climate) corresponding to it, and also all previous sub-seasonal range ensemble forecasts valid for the same 7-day period. The following percentiles are used to draw both ERSUBS-M-climate Climate and ensemble forecast CDFs: 0 (minimum), 1, 2, 5, 10, 25, 50 (median), 75, 90, 95, 98, 99 and 100 (maximum). For the forecasts, which have far fewer realisations than the ERSUBS-M-climateClimate, percentiles 0, 1 and 2 all take the same value, as do 98, 99 and 100.

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Fig8.2.4-2: The EFI and SOT for 2-metre weekly mean temperature anomalies, and CDF plots of temperature and precipitation anomalies for one site (see green pin). On the CDF widget the black curve represents the ERSUBS-M-climate Climate and coloured curves represent the different sub-seasonal range forecasts valid for the same 7-day period.

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For both precipitation and temperature, zero on the x-axis (and the thicker vertical gridline) simply corresponds to ERSUBS-M-climate Climate mean values (for the location, the time of year and the lead time displayed), because of course "anomaly" computations use these mean values as their reference points. This statement is true for all of the curves. However, for different lead times (i.e. the different coloured curves) the absolute value that is the mean will vary a little bit (due to model drift and under-sampling). In spite of such variations it is still reasonable, helpful and recommended to inter-compare the single black ERSUBS-M-climate Climate curve with all the coloured curves (even if this is only strictly valid for the same lead time that it represents - i.e. the red curve).

Note, incidentally, that the ERSUBS-M-climateClimate, as used here and on sub-seasonal range meteograms, is now based on re-forecasts initialised from ERA5 data; this is higher quality output, and has greater compatibility with actual forecasts, than was the case previously when the re-forecasts were initialised from ERA-Interim data (i.e. before model cycle 46r1 was introduced in June 2019).

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For precipitation, the plot design is such that the x-axis always starts from the ERSUBS-M-climate Climate minimum (black), for the given valid dates, for the lead time of the latest forecast (red). So the black curve should always begin from the graph's lower left corner (Fig8.2.4-3). Note that over the vast majority of the world this will equate to zero precipitation in the 7-day period; it is of course impossible to get less than zero. As the ERSUBS-M-climate Climate is a function of lead time the forecasts shown for different lead times (not red), which are referenced to (slightly) different ERSUBS-M-climates Climates to calculate anomalies, may not have the same "zero" starting point. On Fig8.2.4-3 for example the end of the dashed purple curve, corresponding to the T+504-672h forecast, probably also corresponds to zero rain, but lies left of the plot area shown (and so is not visible). Equally, such a curve could end just to the right of the lower left point of the graph, but could still correspond to zero rain in absolute terms. It all depends on how the ERSUBS-M-climate Climate for the given lead time compares with the ERindicated SUBS-M-climate shown Climate (black curve). In some very wet locations the ERSUBS-M-climate Climate CDF may have never been 0 (i.e. no completely dry weeks). In this case the x-axis would start from a value that in the ERSUBS-M-climate Climate (black) does not correspond to zero rain in absolute terms as shown on Fig8.2.4-3.

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Fig8.2.4-3: CDF plots for 7-day total precipitation anomalies. The plot design caters for two scenarios: (a) - which is very common - used when the ERSUBS-M-climate Climate minimum (black) = 0mm in absolute terms (bottom left corner = 0mm), and (b) - which is very rare - used when the ERSUBS-M-climate Climate minimum is >0mm. On (a) the purple curve, for example, does not start from "0" (the point where x- and y-axis intersect) because of lead time dependence of the M-climate. A similar situation in which a curve "disappears" off the left of the plot could occur in case (b), but has not done so on this example.

For temperature, the x-axis starts from the overall minimum encountered within all the displayed CDFs (ERSUBS-M-climate Climate and ensemble forecasts).

An example.

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Fig8.2.4-5: ecChart of sub-seasonal Range EFI and SOT (quantile 10) for weekly T2m anomaly, from DT:00UTC 25 Jul 2019, VT: week ending 5 Aug 2019.  The chart highlights an area where 2m temperatures are expected to be very much on the cold side of the ERSUBS-M-climate Climatedistribution (as taken from re-forecasts).  The CDF diagram at Fig8.2.4-3(a) would be similar to that for Nizhniy Novgorod.  The purple area on map shows where EFI is below -0.9.  SOT values (quantile 10) are shown in green boxes, the feint line is where SOT=1. Actual EFI and SOT values at the green pin site are shown in the lowest white box. The sub-seasonal range meteogram with ERSUBS-M-climate Climate (red), and the time-series (blue) of both EFI and SOT (quantile 10) values for Nizhniy Novgorod illustrate the expected evolution.

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Fig8.2.4-6:  ecChart of sub-seasonal Range EFI and SOT (quantile 10) for weekly T2m anomaly, from DT:00UTC 25 Jul 2019, VT:week ending 29 Aug 2019.  The chart shows that the distribution of possible mean 2m temperatures is overall close to the ERSUBS-M-climate Climate distribution, implying that the actual model forecast on this occasion is unable to add much to a (model-free) forecast that purely reflects reflects climatological probabilities.  The CDF diagram at Fig8.2.4-3(b) would be similar to that for Nizhniy Novgorod.

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The EFI temperature chart shows the weekly mean EFI for 2 m temperatures.  This is derived from the distribution of ensemble forecast 2 m temperatures compared with the temperature distribution in the ERSUBS-M-climateClimate.

The EFI precipitation chart shows the weekly mean EFI for precipitation.  This is derived from the distribution of ensemble forecast precipitation compared with the precipitation distribution in the ERSUBS-M-climateClimate.

Click on the central small icon in the bottom right of the web frame to show the colour scale of values appropriate to each display.

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Cumulative Distribution Function (CDF)s for ensemble temperature and rainfall forecasts may be constructed from ensemble sub-seasonal range forecasts.   It is important to note that here it is anomalies from the "norm" that are considered rather than absolute temperature or rainfall values.  The anomalies for the sub-seasonal range climate (ERSUBS-M-climateClimate) (black line) are the frequencies of departures from the mean (here defined as the "norm") of the ERSUBS-M-climate Climate for the date in question (i.e. the light green lines on the diagram indicate the value at 50% probability and marked as 0°C anomaly).   Some anomalies are positive, some in the tails of the plot are extremely positive; some are negative, some some in the tails of the plot extremely negative.   The CDF for the ensemble values is constructed from the anomaly of the temperature forecast by each ensemble member (red line) as a departure from the mean or "norm" of the ERSUBS-M-climateClimate.

Extreme Forecast Index (EFI) and Shift of Tails (SOT) are derived in the same way as for the medium range products.

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Fig8.2.4-7: The large positive EFI shows the ensemble temperature anomaly distribution is for warmer anomalies much above the ERSUBS-M-climate Climate anomaly distribution.  The positive upper tail SOT (quantile 90)  indicates indicates there are several ensemble members predicting extreme warm temperature anomalies anomalies (above the 99th ERSUBS-M-climate Climate percentile shown by the dashed green line).  This suggests a warm a warm temperature anomaly may be confidently forecast (large positive EFI), probably exceptional but not necessarily extreme (SOT+0.4).  Confidence in extreme temperatures rises as SOT values increase - users should focus on SOT values >0.5.

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Fig8.2.4-8: The large positive EFI shows the ensemble temperature anomaly distribution is for warmer anomalies much above the ERSUBS-M-climate Climate anomaly distribution.  The negative upper tail SOT (quantile 90)  indicates indicates generally ensemble members are not predicting an extreme temperature anomaly (above the 99th ERSUBS-M-climate Climate percentile shown by the dashed green line) - however, note one ensemble member (extreme top end of red curvered curve)  is predicting is predicting an extreme temperature anomaly (above the 99th ERSUBS-M-climate Climate percentile) though less extreme than the extreme of ERSUBS-M-climate Climate anomaly.   This suggests a warm a warm temperature anomaly is confidently forecast (fairly large positive EFI), but will be unexceptional (SOT –0.7) compared with ERSUBS-M-climate Climate - but nevertheless one member does suggest a near exceptional warm anomaly is possible.

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Fig8.2.4-9: The small positive EFI suggests the frequencies of ensemble temperature anomaly distribution is near or a little above the ERSUBS-M-climate Climate anomaly distribution.  The negative lower tail SOT (quantile 10)  indicates generally ensemble members are not predicting an extreme temperature anomaly (below the 1st ERSUBS-M-climate Climate percentile shown by the dashed green line) - however note one ensemble member (extreme bottom end of red curve) is predicting an extreme temperature anomaly (below the 1st M-climate percentile) though less extreme than the ERSUBS-M-climate Climate anomaly.   This suggests the temperature anomalies are similar to the ERSUBS-M-climate Climate anomaly distribution (small positive/negative EFI), and a cold anomaly, if it occurs, will  be unexceptional compared with ERSUBS-M-climate Climate (SOT –1.7) - but nevertheless one member does suggest an exceptional cold anomaly is possible.

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Fig8.2.4-10: The large negative EFI shows the frequencies of ensemble temperature anomaly distribution is for colder anomalies well below the ERSUBS-M-climate Climate anomaly distribution.  The positive lower tail SOT (quantile 10)  indicates there are several ensemble members predicting extreme cold temperature anomalies (below the 1st ERSUBS-M-climate Climate percentile shown by the dashed green line).   This suggests a cold temperature anomaly may be confidently forecast (large negative EFI), exceptional and probably extreme (SOT +0.95).  Confidence in extreme temperatures rises as SOT values increase - users should focus on SOT values >0.5.

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Fig8.2.4-11: An example CDF for snowfall - snowfall is just considered as equivalent rainfall.   Moderately large positive EFI shows the equivalent rainfall anomaly distribution is above the ERSUBS-M-climate Climate anomaly distribution.  The positive upper tail SOT (quantile 90) indicates there are several ensemble members predicting extreme equivalent rainfall anomalies (above the 99th ERSUBS-M-climate Climate percentile shown by the dashed green line).  This suggests uncertainty that a significant equivalent rainfall anomaly is forecast (moderate EFI.  Note: 50% of ensemble members forecast less than about 1mm precipitation (the lower part of the ERSUBS-M-climate Climate only just above 0mm), but equally 25% of ensemble members forecast more than about 2mm precipitation (significantly above ERSUBS-M-climate Climate where about 97% of precipitation less than 2mm). If a significant rainfall occurs it could be an exceptional rainfall equivalent (SOT 0.8).  Confidence in extreme rainfall rises as SOT values increase - users should focus on SOT values >0.5.

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Fig8.2.4-12: The moderate positive EFI suggests the ensemble rainfall anomaly distribution is slightly above the ERSUBS-M-climate Climate anomaly distribution.  The negative upper tail SOT (quantile 90) indicates there are very few if any ensemble members predicting extreme equivalent rainfall anomalies anomalies (above the 99th ERSUBS-M-climate Climate percentile shown by the dashed green line).  This suggests uncertainty that larger than normal rainfall anomaly may be forecast (moderate EFI - but note 70% of ensemble members forecast less than about 1mm precipitation, equally 15% of ensemble members forecast more than about 2mm precipitation), but it is unlikely there will be an exceptional rainfall event (SOT -0.6).

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Fig8.2.4-13: An example of a rainfall CDF most frequently encountered where very few ensemble members forecast any rain at all.  The small negative EFI shows the ensemble rainfall anomaly distribution is lower than the ERSUBS-M-climate Climate anomaly distribution.  The negative upper tail SOT (quantile 90) indicates there are very few if any ensemble members (and in this case none of them) predict extreme equivalent rainfall anomalies (above the 99th ERSUBS-M-climate Climate percentile shown by the dashed green line).  This suggests confidence that larger than normal rainfall anomaly will not occur (small EFI) and an exceptional rainfall an exceptional rainfall event will not occur(SOT -1.2).

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