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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.

Figure 3 demonstrates the process on an idealised example, where the lowest 77 percentiles are 0 in the climatology and 23 out of 51 ensemble members are also 0 (see Figure 3a). The 23 ensemble members with 0 value then are spread across the 0-value range of the climatology from 1 to 77 (see Figure 3b). This way the ranks of the 23 members will be assigned from 1 to 77 with equal as possible spacing in between (see Figure 3c). Finally, the remaining non-zero ensemble members also get their ranks in the usual way, as described above in Figure 2. Finally, the schematic of ranks of all 51 members are provided in Figure 3d.

Figure 3. Schematic of the forecast extremity ranking calculation for areas with 0 river discharge values.

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.