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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.
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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 bin-54. Then all ensemble members, similarly, get a bin number, the 2nd lowest values with bin-60 and so on until the largest ensemble member value getting bin-97, as the river discharge value is between the 96th and 97th percentiles.
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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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For the forecast rank computation in the 0-value singularity case, a special solution was developed. All the 0 ensemble member values (all below 0.1 m3/s) get an evenly-representing rank assigned from any of the percentiles that have 0 values (i.e. below 0.1 m3/s) in the model climatology. In practice, this will mean, the 'rank-undefined' section of the ensemble forecast is going to be spread evenly across the 'rank-undefined' section of the climatology during the rank computation.
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