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What is the information content?
→ tThere are two key components: a measure of the average (shown with colour-fill), and a measure of the spread of the forecast (shown by contours, and transparent grey shading). In both cases these are defined relative to characteristics of the extended range model climate.
How do we represent these components?
→ tThe underlying philosophy for this product is that we work with quantiles.
- So for the "average" component we plot, using colour fill, the median value of the forecast anomalies delivered by the members of Extended Range ensemble . These anomalies are expressed relative to the model climate mean (for the sites in question, for the time of year in question and for the lead time range in question). "Mean" here implies, for example, average 2m temperature over the week in question, or average accumulated rainfall over the week in question. As we use the ensemble "median" the key point for users is that (according to the ensemble) it is equally likely that the observed anomaly will lie above or below the plotted value.
- For the "spread" component we plot contours of an "interdecile range ratio", or interdecile metric for short. This is the difference between the 10th and 90th percentiles of the forecasts of the members of the Extended Range ensemble, divided by the difference between the 10th and 90th percentiles of the Extended Range model climate (for the sites in question, for the time of year in question and for the lead time range in question). For rainfall a minor adjustment is made to avoid division by zero errors. A value of 1 for this metric means that, in regard to the spread of possible outcomes, there is little information content in the ensemble beyond what one would get from using climatology-based spread. Values <1 mean higher confidence / less uncertainty. Values >1 are rare, and indicate an unusual and curious form of information content, where the spread of possible outcomes is larger than one would get from climatology.
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Colour-fill | Spread Metric <1 | Spread Metric ~1 | Spread Metric >1 |
|---|---|---|---|
| Green contours (lower values mean higher confidence) | Black contours / transparent grey shading | Purple contours (higher values mean lower confidence) | |
Anomaly > 0 | Probably above average, and moderate/high confidence in the forecast anomaly:
| Probably above average, but low confidence in the actual value:
| Probably above average, but confidence in the actual value is very low:
|
Anomaly ~ 0 | Moderate/high confidence in climatologically average conditions:
| No signal of anything. Provide a forecast based on climatology.:
| Very uncertain indeed!
|
Anomaly < 0 | Probably below average, and moderate/high confidence in the forecast anomaly
| Probably below average, but low confidence in the actual value:
| Probably below average, but confidence in the actual value is very low:
|
Table 1: How to interpret different signal combination on the new charts (with a 2m temperature example for each class)
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→ The approach was pragmatic. On the one hand we do not want anomalies that have little or no practical significance for users to show up; on the other we do not want plots that are almost perpetually white at longer leads. For temperature variables anomalies of magnitude <0.5C will not be important for most users. For mean sea level pressure anomalies of 1hPa are admittedly very small in the extratropics, but using this does facilitate signals in the tropics. For rainfall small adjustments to the white range - e.g. between 4mm and 5mm - had a large impact. Using 4mm was a compromise that provided some colour on plots for longer leads, and in temperate climates such a value is not without meaning - equating to about 17mm rainfall per month.
Additional comments regarding precipitation chart interpretation:
For the grey shading why use 1.2 as the upper limit for precipitation, but 1.1 for other variables, when a lower limit of 0.9 is used for all?
→ This was partly pragmatic, because with the value was set to 1.1 for precipitation undesirable noise appears on plots that seems hard to justify on any physical grounds. This noise is much reduced with a value of 1.2. Probably we are seeing sampling sensitivity to the exact value of the 10th wettest member, within the wet tail of the distribution. If that member is drier than the re-forecast 90th percentile, then we are in a portion of the climatological distribution that is more populated (i.e. has a cumulative distribution function with a steeper slope), which seemingly makes the noise less such that we can reasonably use 0.9, as for the other variables, rather than a lower value like 0.8.
For precipitation, we tend to see more "dry" shades than "wet" shades; this is particularly noticeable at longer leads. Why is that?
→ This is because the climatological distribution of 7-day rainfall is skewed in most locations, with the median having a lower value than the mean. So across the world as a whole, for weekly rainfall, below average is ordinarily more likely than above average (where average is referring to the mean). As colour shades represent the (forecast) median minus the (climatological) mean, the default behaviour, if the medians of the forecast and climate distributions are about the same (which is much more likely at longer leads) will be to show a "dry" shade, reflecting the fact that dry is genuinely more likely. This allows the user to correctly put into words a probabilistic outcome, in some absolute sense, even if the forecast signal itself is very muted. Unlike some other forecast products these quantile-based maps are strongly user-oriented, combining in this case two types of information content - local climatological characteristics and forecast signal. A researcher might on the other hand be particularly interested in just identifying where and when there is a probabilistic signal that differs from climatology; although these products do provide a lot of insights into that aspect, for a completely clean view they would need to use something different.
If a "dry" signal can arise on charts because that is climatological behaviour, then how do I know when the forecast has a dry signal on top of that?
→ Look for areas where the spread metric is rather less than 1 - i.e. where green contours are in evidence on top of dry shades. This will mean that wet anomalies are unlikely in those regions.
For precipitation, purple contours can appear in arid areas seemingly quite often. Why is this?
→ This is because in arid periods/locations, when the median is zero, one cannot by definition have a dry signal (in the median) - so dry shades are not possible. There can however still be a low probability of anomalously wet outcomes. So if the 90th percentile in the forecast is notably larger than it is in the climatology, purple contours will appear (noting that the 10th percentile of the forecast and the climatology must both be zero if the respective medians are also both zero).
Tips for users
→ As an aid to learning, and to better comprehend the overall signal shown by the two layers, we recommend that (new) users click on a feature of interest on a product to bring up a meteogram, and then use the drop-down product menu (top left) for that meteogram to select "Sub-seasonal Anomaly meteogram". The medians and the 10th and 90th percentiles can then be compared, between the forecast and the model climate.
→ When "clicking" as above, note that the spread metric on the map (contoured) has been upscaled to lower resolution (144km), whilst this is not the case for the meteogram parameters. This can explain apparent mismatches (although noteworthy mismatches do seem to be very rare).