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%.

It is particularly important for users to appreciate from the outset that the "probabilities", as portrayed should not, generally, be portrayed as probabilities to customers.  This is because the reliability of probabilities in seasonal forecasts is rather poor in most areas and for most parameters.  So in the subsequent discussion of seasonal forecast products we will generally refer to the "proportion of members showing...", rather than the "probability that...".  Product construction is based upon a comparison of Cumulative Distribution Functions (CDF).

Each product is labelled with:

  • the start date of the forecast,
  • the period for which it is valid (e.g. DJF 2017/18 is the three-month period December 2017-February 2018),
  • the number of model integrations in the forecast ensemble,
  • the number of model integrations used to define the climate and the years for which re-forecasts are produced.

Products for lead-times of 1, 2, 3 and 4 months are produced each month, and can be selected using the arrows and time-line below the maps.

The colour scale depends on the field plotted; in most cases blue is used for lower values and red for higher values of a field or probability, but for precipitation brown is used for drier and green for wetter conditions.  For individual tercile and outer quintile (20%ile) categories, high probabilities are in red regardless of the field or category being plotted.

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:

  • the lower tercile, which is the value below which the outcome occurs in 1 out of 3 cases in the model climate.  Assuming a stationary climate and without other information, the probability of a future value being less than the lower tercile (i.e. lying within the lower tercile category) may be expected to be 1/3.
  • the upper tercile, which is the value above which the outcome occurs in 1 out of 3 cases in the model climate.  Assuming a stationary climate and without other information, the probability of a future value being greater than the upper tercile (i.e. lying within the upper tercile category) may be expected to be 1/3.

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:

  • the lower quintile, which is the value below which the outcome occurs in 1 out of 5 cases in the model climate.  Assuming a stationary climate and without other information, the probability of a future value being less than the lower quintile (i.e. lying within the lower tercile category) may be expected to be 1/5.
  • the upper quintile, which is the value above which the outcome occurs in 1 out of 5 cases in the model climate.  Assuming a stationary climate and without other information, the probability of a future value being greater than the upper quintile (i.e. lying within the upper tercile category) may be expected to be 1/5.

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.    


                               

Fig8.3.1-1: The chart shows the probability that precipitation will lie in the upper tercile category of the shorter S-M-climate over the three months Oct-Dec 2023, DT September 2023 run.

The probabilities are shown by colours according to the scale.     Precipitation higher than model climatology is:

  • very likely wetter than S-M-climate over the Arctic, north Siberia, and equatorial Pacific and Indian Oceans (dark red; 70%-100% ENS members). 
  • likely wetter than S-M-climate over central Africa, Middle East, and British Isles and Northeast Europe (orange, light red; 50%-70% ENS members).
  • very unlikely wetter than S-M-climate northeast and far south of South America, Australia, western Indian Ocean, tropical Pacific (dark blue, light blue; 0%-20%).

 

Fig8.3.1-2: The chart shows the probability that precipitation will lie in the lower tercile category of the shorter S-M-climate over the three months Oct-Dec 2023, DT September 2023 run.

The probabilities are shown by colours according to the scale.     Precipitation lower than model climatology is:

  • 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.

Fig8.3.1-3: The chart shows the probability that precipitation will lie in the upper quintile category of the shorter S-M-climate over the three months Oct-Dec 2023, DT September 2023 run.

The probabilities are shown by colours according to the scale (intervals different from tercile charts).     Precipitation much higher than model climatology is:

  • very likely much wetter than S-M-climate over equatorial Pacific and Indian Oceans (dark red; 70%-100% ENS members). 
  • moderately likely much wetter than S-M-climate over central Africa, Middle East, and British Isles and Northeast Europe (orange, light red; 40%-70% ENS members).
  • very unlikely much wetter than S-M-climate northeast and far south of South America, Australia, western Indian Ocean, tropical Pacific (light blue; 0%-10% ENS members).


Fig8.3.1-4: The chart shows the probability that precipitation will lie in the lower tercile category of the shorter S-M-climate over the three months Oct-Dec 2023, DT September 2023 run.

The probabilities are shown by colours according to the scale (intervals different from tercile charts).     Precipitation much lower than model climatology is:

  • 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 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).

Fig8.3.1-5: The chart shows a summary of the probabilities (proportion of ENS members) that precipitation will lie in the higher or lower tercile category of the shorter S-M-climate over the three months Oct-Dec 2023, DT September 2023 run.

The probabilities are shown by colours according to the scale.    The chart shows probabilities that precipitation will be:

  • 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.

Fig8.3.1-6: The chart shows a summary of the probabilities (proportion of ENS members) that precipitation will be greater than the median of the shorter S-M-climateover the three months Oct-Dec 2023, DT September 2023 run.

The probabilities are shown by colours according to the scale.    The chart shows probabilities that precipitation will be above the median of the S-M-climate:

  • 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.

Fig8.3.1-7:  The chart shows the probabilities (proportion of ENS members) of the magnitude of the anomaly of precipitation totals from the shorter S-M-climate over the three months Oct-Dec 2023, DT September 2023 run.

The mean magnitude of the anomalies are shown by colours according to the scale.    The chart shows forecast precipitation to be:

  • >100 and >200mm above S-M-climate east Africa and equatorial Pacific and Indian Oceans (dark greens).
  • 50-100mm above S-M-climate tropical Atlantic Ocean and central Africa (turquoise).
  • 0-50mm above S-M-climate Antarctic, Arctic, north Siberia, Middle East, and British Isles and Northeast Europe (light green).
  • 0-50mm below S-M-climate Australia, tropical Pacific (light yellow).
  • 50-100mm below S-M-climate far south of South America, Australia (orange).
  • >100 and >200mm below S-M-climate over western Indian Ocean, tropical Pacific (brown, dark brown).

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

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.

Consider precipitation. In predominantly arid regions the “usual” amounts of precipitation can be quite small or zero.  However, on rare occasions precipitation can be extreme.  Consequently the S-M-Climate mean is raised to a value larger than experienced for the large majority of the time.  So when non-extreme precipitation is forecast in the arid region, it can occur that the mean of the forecast is drier than the mean of the S-M-Climate even though precipitation of any kind is an unusual event.

Inspection of the distribution of probabilities within the S-M-Climate for the region will allow assessment of the probability that dry conditions will occur.  The median value (at 50%) often gives a much better indication of ‘usual’ conditions.

Anomaly charts of rainfall or temperature are based upon anomalies between the forecast seasonal ensemble mean values and the S-M-Climate mean values.  Users should beware misrepresentation of anomalies on the charts in arid regions.  In these cases it is wise to compare the forecast mean precipitation with the median of the S-M-Climate.  See Fig8.3.1-8 for an illustration.


Fig8.3.1-8: Illustration of the effect of rare occurrence of extreme precipitation upon the climate mean value of precipitation at a hypothetical location in an arid region.  The rare but extreme precipitation (100mm) skews the climatological distribution (red) to such an extent that the mean of the distribution is raised away from the "usual" conditions of near 0mm. If the ensemble forecast (blue) shows precipitation is probable (though not high) the mean may lie on the dry side of the climate mean.  This is misleading as even moderate precipitation may be a significant event in an arid location. Comparing the ensemble forecast against the median value of the climate distribution can give a better assessment.