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In order to compress the amount of information being produced by the ensemble and highlight the most predictable parts, individual ensemble members that are "similar" according to some measure (or norm) can be grouped together.   This process is known as clustering.  

Fig811.AFig8.1.1-1: A example of postage stamps showing PMSL forecasts from ensemble control, and all 50 ensemble members, DT 00UTC 19 May 2017, VT T+120hr at 00UTC 24 May 2017.  Some large differences in the pressure pattern can be seen on individual ensemble members.  Each member has been allocated to a cluster, shown in a different colour above each frame for lead-times T+120 and above only.  The representative member of each cluster is here shown by arrows. The clusters are shown in Fig811.BFig8.1.1-2.

Fig811.BFig8.1.1-2: Clustering or the case shown in Fig811.AFig8.1.1-1.  The three clusters for T+120hr are in the left column.  Clustering is based on 500hPa geopotential height pattern.  

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Spaghetti diagrams are available on ecCharts.  The charts display isolines from each ensemble member for MSLP, or 500hPa geopotential height, or 850hPa temperature.  The isoline values are selected by the user (e.g. 1015hPa, or 546dam, or 0°C).  The isolines are drawn for each member.  At short lead times the isolines are very tightly packed for forecasts because the spread of the ensembles is quite limited.  As the forecast progress they become increasingly spread showing the flow-dependent increase in forecast uncertainty.   Spaghetti diagrams are sensitive to gradients; in areas of weak gradient they can show a large spread of the isolines, even if the situation is highly predictable.  Conversely, in areas of strong gradient they can display a small spread of the isolines, even if there are important forecast variations.

Fig811.CFig8.1.1-3: Spaghetti Plot 500hPa geopotential height plotted at 560dam DT 12UTC 26 May 2017, VT T+30hr at 18UTC 27 May 2017.  The ensemble members (grey) are quite tightly packed except at about 20°W  where gradients are slack and there is some uncertainty in the trough disruption.  The control ensemble member is shown in red.

Fig811.DFig8.1.1-4: Spaghetti Plot 500hPa geopotential height plotted at 560dam DT 12Z 26 May 2017, VT T+144hr at 01 June 2017.  The ensemble members (grey) have become more spread out, but retain the general pattern of an upper ridge over the northwest Atlantic and another over the North Sea but there are differences in position (or speed of movement eastwards) and amplitude.  The control ensemble member is shown in red.

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The ensemble mean is less suitable for wind speeds and precipitation because these have skewed distributions.  For these the ensemble median might be more useful.  The ensemble median is defined as the value of the middle ensemble member where the members have been ranked by value. 

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Fig811.EFig8.1.1-5: Ensemble mean PMSL (red) and Spaghetti Plot of 990hPa isobars (grey) from ensemble DT 00UTC 10 June 2017 T+120 hr VT 00UTC 15 June 2017.  There is a wide diversity amongst ensemble members in the location and shape of the depressions.  The ensemble mean depression is smooth by comparison and less deep (the inner isobar has a value of 995hPa).   Because of averaging of the ensemble members, the pressure gradients and associated winds will generally be less strong in the ensemble mean field than in the ensemble members themselves.  Chart taken from ecCharts.

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Fig811.FFig8.1.1-6: As Fig811.EFig8.1.1-5 but with the spread of mean sea level pressure (PMSL) by ensemble members (coloured - orange: high spread, blue: low spread).  Highest spread of PMSL is on the eastern side of the depression indicating greater uncertainty in the strength of a southerly wind.  There is lower spread to the west where most members suggest a fairly low pressure and higher probability of a northerly flow.  The smallest spread is near the centre of the depression indicated by the ensemble mean but wind direction is very uncertain here; it depends upon the positioning of the low in the of individual ensemble members.  Chart taken from ecCharts.

Probabilities

The most consistent way to convey forecast uncertainty information is by the probability of the occurrence of an event.  The event can be general or user-specific regarding probability of exceeding an event threshold.  The event threshold may correspond to the point at which the user has to take some action to mitigate potential damage from a significant weather event.   Probabilities can be:

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Probabilities for extreme wind gusts are computed as probabilities over 24 hours because it is considered more important to know that an extreme wind gust might occur than to know the precise time.

Fig811.GFig8.1.1-7: As Fig811.E with Fig8.1.1-5bwith the probability of wind ≥10m/s.  There is a higher probability (dark blue) in the area west of Ireland where the pressure gradient is uncertain although the direction is fairly certain.  The ensemble mean (Fig811.EFig8.1.1-5) would not suggest such strong winds.  There is very low probability (white) south of Greenland where the gradient is generally light but the direction is uncertain.   Chart taken from ecCharts.  Light blue >25%, Blue >50%, Dark blue >75% probability.

Additionally, ecCharts can display the probability of a combination of events occurring together.  For example:

• strong wind gusts and heavy snowfall (for assessment of drifting snow),
• precipitation and surface temperature (to aid rain/snow forecasting),
• strong winds and significant wave height (to help forecast dangerous conditions at sea).

Fig811.HFig8.1.1-8: As Fig811.G Fig8.1.1-7 with the probability of significant wave height ≥4m. Chart taken from ecCharts.  Yellow >25%, Orange >50% probability.

Fig811.IFig8.1.1-9: As Fig811.G Fig8.1.1-7 with the probability of significant wave height ≥4m AND wind ≥10m/s.  Chart taken from ecCharts.  Light blue >10%, Green >20%, Yellow >30% probability.

Forecast expressed in terms of intervals

Forecast intervals (e.g. “temperatures between 2°C and 5°C”, or “precipitation between 5 and 8mm/24hr”) can be used as a hybrid between categorical and probabilistic forecasts.  ecCharts provide a simple way of displaying probabilities above or below thresholds and by intercomparison can give a indication of probability of a parameter lying between the thresholds.   For example for maximum temperatures at Vilnius, (see Fig811.JFig8.1.1-10) there is a 20% probability of being ≥20°C, and from Fig811.J Fig8.1.1-10 there is a 25% probability of being ≤15°C.  Therefore there is a 55% probability that the maximum temperature will lie between these two values.  Combinations of parameters are possible (e.g. the probability of combined events of wind gust and total snowfall is available on ecCharts as an aid to forecasting drifting of snow).

Fig811.JFig8.1.1-10: Chart taken from ecCharts showing ensemble probability of maximum 2m temperature ≥20°C (ecCharts colour bands for this scheme denote 5%-20%-40%-60%-80%-95%-100%).  There is a 20% probability of maximum temperatures ≥20°C at Vilnius (shown in the box).  The location of Vilnius is shown by the pin.

Fig811.KFig8.1.1-11: Chart taken from ecCharts showing ensemble probability of maximum 2m temperature ≤15°C (ecCharts colour bands for this scheme denote 5%-20%-40%-60%-80%-95%-100%).  There is a 25% probability of maximum temperatures ≤15°C at Vilnius (shown in the box).  The location of Vilnius is shown by the pin.

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• 2m temperature and total precipitation,
• wind speed and total precipitation,
• wind gust and total snowfall,
• 10m wind speed and significant wave height.

Fig811.LFig8.1.1-12: Chart taken from ecCharts showing ensemble probability of wind gust ≥10m/s and ≥2mm/12hr (ecCharts colour bands for this scheme denote Light blue 5-35%, Blue 35-65%, Dark blue 65-95%, Purple >95%).  There is a 31% probability of exceeding the thresholds at Munich (shown in the box).  The location of Munich is shown by the pin.

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