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Long range output - chart format

The long-range graphical products do not show absolute values, but instead highlight differences between the forecasts and the Seasonal climate (S-M-climate).  When "probabilities" are provided, these denote the proportion of ensemble members that predict a certain type of outcome.  Thus if 35 members of a 50 member ensemble predict the 2m temperature to exceed the mean in the S-M-Climate, then the "probability" is taken as 70%.

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Charts cover global or regional (including European) areas.  Precipitation anomaly charts are used as examples, but anomaly charts for 2m temperature, 500hPa geopotential, 850hPa temperature, mean sea level pressure, and sea surface temperature may be interpreted in a similar way to that described.

Probabilistic Charts

Explanation of Terciles and Quintiles

In SEAS5, anomalies are evaluated relative to 1993-2016 model climate (shorter S-M-climate), both for consistency with Copernicus C3S and because anomalies relative to a more recent “past” are likely to be more relevant to most users.  However, the re-forecasts are also produced from 1981-2016 (longer S-M-climate). This period is the basis of the verification charts provided online, and also allows users to explore the choice of different reference and calibration periods.

Terciles

For each forecast parameter, forecast lead-time, calendar start date (the 1st of each month) and location, the 600 re-forecasts of the shorter S-M-climate are analysed to determine the median and terciles of the model climate distribution.  The terciles are:

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Using the forecast we can calculate the fraction of ensemble members that predict values to be above the upper tercile or below the lower tercile of the model climate distribution, or indeed lie in between.  The predicted "probabilities" can be very different from 1/3 within each tercile category.  These situations are of particular interest because they indicate a departure from the distribution of results in the re-forecasts making up the shorter S-M-climate.

Quintiles

For each forecast parameter, forecast lead-time, calendar start date (the 1st of each month) and location, the 600 re-forecasts of the shorter S-M-climate are analysed to determine the median and quintiles of the model climate distribution. The quintiles are:

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Using the forecast we can calculate the fraction of ensemble members that predict values to be above the upper quintile or below the lower quintile of the model climate distribution, or indeed lie in between.  The predicted "probabilities" can be very different from 1/5 within each tercile category.  These situations are of particular interest because they indicate a large departure from the distribution of results in the re-forecasts making up the shorter S-M-climate.

Probabilities (tercile category) charts

These show the proportion of ensemble members lying within each tercile category (i.e. below the lower tercile, between the lower and upper tercile, or above the upper tercile) of the shorter S-M-climate. Contour intervals are chosen to show both where there is an unusually high chance of a particular category occurring and also where there is an unusually low chance of a particular category occurring.    

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• very unlikely drier than S-M-climate over the Arctic, north Siberia, and equatorial Pacific and Indian Oceans, central Africa, Middle East, and British Isles and Northeast Europe (dark blue, light blue; 0%-20% ENS members). 
• very likely drier than S-M-climate northeast and far south of South America, Australia, western Indian Ocean, tropical Pacific (dark red; 70%-100% ENS members)).

Probability (quintile category) charts

These charts show where predicted values lie within the upper and lower 20th percentiles (i.e. the value above or below which the outcome occurs in 1 out of 5 cases in the model climate).  These are useful for highlighting regions in which the distribution of likely outcomes is shifted substantially from the climatological average.

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• very unlikely much drier than S-M-climate over the Arctic, north Siberia, and equatorial Pacific and Indian Oceans, central Africa, Middle East, and British Isles and Northeast Europe (light blue; 0%-10% ENS members). 
• moderately likely much drier than S-M-climate far south of South America and Australia (30%-50% ENS members)
• very likely much drier than S-M-climate northeast south of South America, western Indian Ocean, tropical Pacific (dark red; 70%-100% ENS members).

Tercile summary

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charts

These charts show the probability (proportion of ENS members) being above the upper tercile (shades of green, wetter) or below the lower tercile (shades of brown, drier) of the shorter S-M-climate.  This plot gives a convenient, simple overview of a seasonal forecast.  Darker colours imply greater confidence in anomalously high precipitation (green) or low precipitation (brown).

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• above the upper tercile of the S-M-climate over the Arctic, north Siberia, and equatorial Pacific and Indian Oceans (light to dark greens). 
• below the lower tercile of the S-M-climate over northeast and far south of South America, Australia, western Indian Ocean, tropical Pacific (yellow to brown).

Probability (> median) charts

These charts show the probability (proportion of ENS members) being greater than the median of the shorter S-M-climate over the three months Oct-Dec 2023, DT September 2023 run.   The probabilities are shaded symmetrically above 60% and below 40%.  Contours are used to show where the S-M-climate and the forecast are significantly different at the 1% level, based on a Wilcoxon rank-sum test which is efficient at detecting shifts in the distribution.  See the implications of using mean values of the S-M-Climate below.

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• likely (light to dark greens, 60%-100% ENS members). 
• unlikely (yellow to brown), 0% to 40% ENS members).

Anomaly magnitude charts

These charts show in absolute terms the difference between the mean value in the forecasts and the mean value in the corresponding model climate (shorter S-M-climate).  This type of product goes some way towards quantifying the differences between the forecast and the re-forecasts.  Shading shows where the forecast distribution is significantly different from the S-M-climate at the 10% level. Contours show regions significant at the 1% level.   Significance is assessed using a Wilcoxon rank-sum test, which will detect a shift in the distribution.  See the implications of using mean values of the S-M-Climate below.

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Shading shows where the forecast distribution is significantly different from the S-M-climate at the 10% level.  Contours show regions significant at the 1% level.  

Using Probability and Anomaly charts

Tercile and other percentile category probability plots give information on what the model is predicting relative to the typical amplitude of variation of the quantity concerned - for example, the proportion of members showing it to be "unusually" warm.  The ensemble mean plots give information on what the model is predicting in absolute terms - °C, or mm of rainfall.  However, it cannot be emphasised too much that it is inappropriate to give precise values to what is, after all, a probable or "most likely" forecast.  Other solutions are of course also possible, particularly given the innate low reliability of seasonal forecasts, for most areas, for most parameters.

The major forecast signals are usually (but not always) fairly stable.   Weaker signals are subject to appreciable sampling error, and even if the model signal remains unchanged, plots from different start times can vary just because of the sampling.  It is good practice to compare the forecast charts for a given target period at different lead times as they become available.

Implications of using mean values on the anomaly charts

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In regions with very skewed S-M-Climate distributions, it is possible for the extreme but rare observations to cause the mean value of the whole distribution to be shifted from a value that would describe the climate more realistically.  The problem predominantly affects evaluation of anomalies of precipitation, but on rare occasions can theoretically also affect temperature.

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