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The characterisation of the forecast signal in both the sub-seasonal and seasonal is based on the ensemble member's extremity in the context of the model climatological distribution.
Climatological percentiles and forecast anomaly categories
Currently, the sub-seasonal climate sample uses 660 reforecast values, while the seasonal uses 500 values. From the climate sample 99 climate percentiles are determined, which represent equally likely (1% chance) segments of the river discharge value range that occurred in the 20-year climatological sample (both sub-seasonal and seasonal is currently based on 20 years). Figure 1 shows an example idealised generic climate distribution, either based on weekly means or monthly means, with the percentiles represented along the y-axis. Only the deciles (every 10%), the quartiles (25%, 50% and 75%), of which the middle (50%) is also called median, and few of the extreme percentiles are indicated near the minimum and maximum of the climatological range indicated by black crosses. Each of these percentiles have an equivalent river discharge value along the x-axis. From one percentile to the next, the river discharge value range is divided into 100 equally likely bins (separated by the percentiles), some of which is indicated in Figure 1, such as bin1 of values below the 1st percentile, bin2 of values between the 1st and 2nd percentiles or bin 100 of river discharge values above the 99th percentiles, etc.
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Table 1: Definition and description of the 7 anomaly categories. The possible value ranges in the 'Ranks column' are inclusive at the start and exclusive at the end, so for example for Cat-1 the possible ranks are 1, 2, 3, ... and 10. Depending on the products, sometimes the middle three categories (Cat3, Cat-4 and Cat-5) are combined into one extended 'Near normal' category.
Extremity rank computation for ensemble members
The forecast has 51 ensemble members, again for both EFAS/GloFAS and both sub-seasonal or seasonal, regardless. The members are all checked for climatological extremity and placed in one of the 100 climate bins. This will be the anomaly or extremity level of the ensemble members, which can be called hereafter rank, as one of the values from 1 to 100. For example, 1 will mean the forecast value is below the 1st climate percentile (i.e. extremely anomalously low, less than the value that happened in the climatological period only 1% of the time), then 2 will mean the value is between the 1st and 2nd climate percentiles (i.e. slightly less extremely low), etc., and finally 100 will mean the forecast value is above the 99th climate percentile (i.e. extremely high as higher than 99% of all the considered reforecasts (representing the model climate conditions for this time of year, location and lead time).
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The probability of the 7 anomaly categories is calculated by counting of the ensemble members in each category and then dividing by 51, the total number of members. In the example of Figure 2, there is no member in the 3 low anomaly categories, while the 'Near normal' category has 2, resulting in 3.9% probability, the 'Bit high' category 13, with 27.5%, the 'High' category 17, as 33.3%, and finally the 'Extreme high' category has 18 ensemble members, with 35.3% probability. The inset table in Figure 2 shows the numbers and the probabilities, but also shows the size (in terms of probabilities) of the 7 categories. This highlights, e.g., that the normal flow category's 3.9% probability is much lower than the climatologically expected probability of 20%, however, the 3 high flow categories have much higher probabilities than the climatological reference probability, especially the extreme high category, where the forecast probability (35.3%) is more than double the corresponding climatological probability (15%).
Extremity rank computation for ensemble members with 0 values
The forecast extremity rank computation can be done for any value above 0 m3/s. However, it becomes undefined when the values drop to 0, as there is no way to differentiate amongst the same values. The hydrological simulations of EFAS and GloFAS are less reliable and more prone to any random noise when we approach 0, so everything below 0.1 m3/s will be considered as 0 for the sub-seasonal and seasonal products. This problem can also happen for non-zero values, but normally the simulation should not produce a lot of identical non-zero values, unless there is some specific process, like reservoir operation rule, etc., which might generate such signal. There is no indication that the non-zero constant value is an issue at all in CEMS-flood, but it is clear that the 0 value is actually a major problem, as large parts of the world has dry enough areas often combined with small enough catchments to have near zero or totally 0 river discharge values.
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In the extreme case of all climate percentiles being 0, which happen over river pixels of the driest places of the world, such as the Sahara, the ensemble forecast member ranks can either be 100 for any non-zero value, regardless of the magnitude of the river discharge, or the evenly spread ranks from 1 to 100, as a representation of the totally 0 climatology. In the absolute most extreme case of all 99 climate percentiles being 0 and all 51 members being 0 in the forecast, the ranks of the forecast will be from 1 to 100 in equal representation. This means, this forecast will be a perfect representation of the climatological distribution, or with another word a perfectly 'normal' condition.
Dominant anomaly category computation for the ensemble forecast
The ensemble forecasts have 51 members, which will be assigned an extremity rank each. Using these 51 ranks the forecasts will be put in one of the 7 anomaly categories (as described in Table 1). This is done based on the arithmetic mean of the 51 ensemble member rank values (rank-mean). This rank-mean will also be a number between 1 and 100, but this time a real (not integer) number. If the anomaly is 50.5, that is exactly the normal (median) condition, i.e. no anomaly whatsoever. If the anomaly is below 50.5, then drier than normal conditions are forecast, if above 50.5, then wetter than normal. The lower/higher the anomaly value is below/above 50.5, the drier/wetter the conditions are predicted to be. The lowest/highest possible value is 1/100, if all ensemble members are 1/100 (the most extremely dry/wet). Then, based on this rank-mean, we define the dominant anomaly category (one of the 7 categories in Table 1) for the ensemble forecast, by placing the rank-mean into the right categories, as defined in Table 1 above. For example, all rank-mean values from 40.0 to 60.0, interpreted as 40.0<= <60.0, will be assigned to 'Near normal', or category-4.
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Figure 2. Schematic of the forecast extremity ranking of the 51 ensemble members and the calculation of the dominant anomaly category.
Forecast uncertainty category computation for the ensemble forecast
In addition to the dominant forecast anomaly computation, as one of 7 predefined categories, the forecast uncertainty is also represented in the sub-seasonal and seasonal products, namely on the new river network and basin summary products. The forecast uncertainty is defined by the standard deviation (std) of the ensemble member ranks (rank-std). If the ensemble member ranks cluster well, and the spread of the ranks is low, then the forecast uncertainty will be low and conversely the confidence will be high.
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Table 2: Uncertainty categories defined by the standard deviation of the ensemble member ranks.
Examples to help interpret the methodology of the rank computation and the selection of the dominant anomaly and the uncertainty categories
Below, there are examples with simplified rank distributions and specific cases of very dry rivers (0 values) that will demonstrate how the dominant anomaly category and uncertainty category computation work.
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