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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).
Figure 2 shows the process of determining the ranks for each ensemble member. In this example, the lowest member gets the rank of 54 (red r54 on the graph in Figure 2) by moving vertically until crossing the climatological distribution and then moving horizontally to the y-axis to determine the two bounding percentiles and thus the right percentile bin. In this case, the lowest ensemble member value is between the 53rd and 54th percentile, which results in bin54bin-54. Then all ensemble members, similarly, get a bin number, the 2nd lowest values with bin60 bin-60 and so on until the largest ensemble member value getting bin97bin-97, as the river discharge value is between the 96th and 97th percentiles.
Figure 2. Schematic of the forecast extremity ranking of the 51 ensemble members and the 7 anomaly categories in the context of the climatological distribution.
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 normalNormal' 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. For ease of interpretation, the 7 categories are displayed here with different colours. 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 three high flow categories have each 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%). In addition, the extended 'Near normal' category would have 15 members with 31.4% probability, which is lower than the climatological probability of 50%.
Extremity rank computation for ensemble members with 0 values
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