Quantile-based weekly guidance maps

Information on the mid-range solution, and the range of possibilities in accessible map-format

Assessment of confidence in the ensemble mean anomaly from climatology

The sub-seasonal ensemble of 100 members runs once per day giving users an early indication of a forecast signal.

The Weekly Mean Anomaly charts show 7-day mean anomalies from the sub-seasonal climate of several forecast parameters.  Currently the forecast parameters are 2m air temperature, surface temperature, precipitation and mean sea level pressure.  The background colour shading in Fig8.2.9.3 shows the anomaly of the forecast median from the mean of the model sub-seasonal climate (SUBS-M-climate).  These are shown in units of the variable displayed.  

However, the Weekly Mean Anomaly charts do not give information on the confidence that may be placed upon the anomaly that is presented.  Some assessment of this can be made by comparing the spread of the forecast variable against the spread of the model sub-seasonal climate (SUBS-M-climate).

By definition of a median, there is a 50/50 chance of the forecast value of an individual ensemble member being greater or less than the median of the ensemble forecast values.  Some of these forecast values may lie within the sub-seasonal climate (SUBS-M-climate), some may lie outside.

Relative spread of ensemble and climatology

It is useful to assess the relative spread of the ensemble forecast against the spread of the sub-seasonal climatology.  The inter-decile range (the separation of the 10% and 90% quantiles) is used as this represents the more extreme solutions without considering outliers where sampling maybe an issue. 

The relative spread is represented as the ratio of the ensemble forecast inter-decile range divided by the model climate inter-decile range (Fig8.2.9.1). 

Fig8.2.9.1: Definition of terms used in deriving a quantile based product.  The diagram shows a schematic extract from a meteogram for "Weekly Mean Anomaly of precipitation from Subs-M-climate".  Letters denote:

• A is the anomaly of the forecast median from the mean of the Subs-M-climate (positive or negative).  This anomaly is shown as colour shading on the new product (e.g. red for warmer, blue for colder in the temperature anomaly charts). 
• B is the inter-decile spread (10% to 90%) of the sub-seasonal ensemble results (positive).
• C is the inter-decile spread (10% to 90%) of the sub-seasonal climate (positive).

The ratio of the inter-decile spreads of ensemble and climate (B divided by C) gives the inter-decile range ratio, or ‘spread metric’.   This is shown as contours and transparent grey shading on the new product charts.

For a given location:

• if the spread in the sub-seasonal climate is:
  • small, then there is small variability found during the reanalysis process and the values at that location are reasonably stable.  One can be fairly confident that variables will usually lie within that narrow range and probably near the mean climate value.
  • large, then there is large variability found during the reanalysis process and the values at that location vary quite a lot.  One can only have confidence that variables will probably lie within that broad range but not necessarily near the mean climate value.
• if the spread of the ensemble forecast is:
  • small then there is high confidence in the median ensemble forecast value.  
  • large then there is low confidence in the median ensemble forecast value.
• if the spread of the ensemble forecast is:
  • greater than the spread of the sub-seasonal climate then the ensemble values vary more widely than the climatological range.  There is decreased confidence in the forecast.  Contours are coloured purple on charts. 
  • similar to the spread of the sub-seasonal climate then confidence is much as for climatological range.  Grey shading on charts.
  • less than the spread of the sub-seasonal climate then the ensemble values vary less widely than the climatological range.  There is higher confidence in the forecast.  Contours are coloured green on charts.

The spread of the climate and the spread of the ensemble normally, but not necessarily, overlap.  If they do not overlap and:

• the spread of the ensemble forecast is small, then the user must consider whether such a confident departure from climatology is reasonable and, if so, be given a moderate probability.
• the spread of the ensemble forecast is large, then the user must consider the result as unreliable or be given a very low probability.

It is important to note, however, that all members of an ensemble are equally probable and no result should be discarded out of hand.

Fig8.2.9.2(A,B,C): Three examples of the distribution of sub-seasonal ensemble members compared with the sub-seasonal model climate. The shaded colours show range and probabilities of anomalies from the mean in the sub-seasonal model climate.  The  box and whisker plots show the range and probabilities of anomalies of the sub-seasonal ensemble members from their median.  Cumulative distribution functions are shown to help visualisation.  If the spread of the ensemble forecast is:

• greater than the spread of the sub-seasonal climate then the ensemble values vary more widely than the climatological range.  There is decreased confidence in the forecast.  Contours are coloured purple on charts. 
• similar to the spread of the sub-seasonal climate then confidence is much as for climatological range.  Grey shading on charts.
• less than the spread of the sub-seasonal climate then the ensemble values vary less widely than the climatological range.  There is higher confidence in the forecast.  Contours are coloured green on charts.

If the spread of the sub-seasonal model climate and spread of the ensemble forecast do not overlap and:

• the spread of the ensemble forecast is small, then the user must consider whether such a confident departure from climatology is reasonable and, if so, be given a moderate probability.
• the spread of the ensemble forecast is large, then the user must consider the result as unreliable or be given a very low probability.

It is important to note, however, that all members of an ensemble are equally probable and no result should be discarded out of hand.

Examples and usage

Fig8.2.9.3 shows a forecast chart for mean 2m temperature for a period about 3 weeks into the future. In the figure:

• At Catania (CA) the forecast is very similar to the model climate, so we get grey shading to denote ‘climatological spread’ and white underneath to signify the forecast median has a very small anomaly; in other words, this could be described as a ‘no signal’ forecast.
• At the Atlantic point (AT), the anomaly is also about zero, but the green contours signify an inter-decile range ratio that is very small (0.5), so we can say quite confidently that temperatures will be very close to normal here.
• At N'Guigmi (NG), the forecast shows a cold anomaly, the anomaly has a relatively high confidence level (0.7).
• At Faya-Largeau (FA), the forecast favours a cold anomaly, there is unusually large uncertainty in what the anomaly will be (2.0).

Typically, on these charts the anomaly magnitudes reduce, as lead time advances.  Charts become less colourful, and spread increases.  Thus green contours tend to get replaced by black, with increasingly large areas of transparent grey shading.

Purple contours (denoting a forecast spread larger than the climatological spread) are relatively uncommon.  When present the user should be particularly cautious and be careful not to over-interpret a forecast.  Purple contours can appear, for example, as a result of climate-change-related shifts in the cryosphere, or with forecasts of very wet conditions or with a case of severe drought. 

Fig8.2.9.3: A forecast chart for mean 2m temperature for a period about 3 weeks into the future. 

The contours show the forecast spread, relative to the model climatology.  Contours are coloured:

• thick purple when the forecast spread is larger than the climatological spread (B divided by C > 1). There is decreased confidence in the forecast.  These are uncommon.  Users should be particularly cautious and be careful not to over-interpret a forecast.  Purple contours can appear, for example, as a result of climate-change-related shifts in the cryosphere, or with forecasts of very wet conditions or with a case of severe drought.   
• thin green when the forecast spread is smaller than the climatological spread (B divided by C < 1). There is increased confidence in the forecast.  These are more common.
• transparent grey shading shows where model and climatological spread are similar (B divided by C ≈ 1).

The inset boxes are extracts from sub-seasonal meteograms; each illustrates a different type of forecast behaviour.

It might be argued that forecast quantiles should be compared with a climatological median rather than a climatological mean.  However, there are benefits, and this approach has parallels with an older-style product class; ECMWF’s pre-existing 'anomaly>0' products perform a similar comparison, but display probabilities instead of a dimensioned quantity.