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No-1 example: The 1-10 climate percentiles are 0, so the average rank of the 0 ensemble members will always be around 5.5 with the evenly distributed rank representation:
| Number of 0 members | Number of non-0 members | Average rank of 0 members | Average rank of non-0 members | Rank-mean | Dominant anomaly category |
|---|
| 0 | 51 | NA (no member to rank) | 11 (the lowest possible rank for a non-zero member if 1-10 percentiles in the climatology are 0) | (0 * 5.5 + 51 * 11)/51 = 11 | Low (10-25% |
| ) | |||||
| 0 | 51 | NA | 20 | (0 * 5.5 + 51 * 20)/51 = 20 | Low (10-25%) |
| 0 | 51 | NA | 50 | (0 * 5.5 + 51 * 50)/51 = 50 | Near normal (40-60%) |
| 0 | 51 | NA | 70 | (0 * 5.5 + 51 * 70)/51 = 70 | Bit high (60-75%) |
| 0 | 51 | NA | 100 | (0 * 5.5 + 51 * 100)/51 = 100 | Extreme high (90%<) |
| 11 | 40 | 5.5 | 11 | (11 * 5.5 + 40 * 11)/51 = 9.81 | Extreme low (<10%) |
| 11 | 40 | 5.5 | 20 | (11 * 5.5 + 40 * 20)/51 = 16.87 | Low (10-25%) |
| 11 | 40 | 5.5 | 50 | (11 * 5.5 + 40 * 50)/51 = 40.40 | Near normal (40-60%) |
| 11 | 40 | 5.5 | 70 | (11 * 5.5 + 40 * 70)/51 = 56.08 | Near normal (40-60%) |
| 11 | 40 | 5.5 | 100 | (11 * 5.5 + 40 * 100)/51 = 79.61 | High (75-90%) |
| 21 | 30 | 5.5 | 11 | (21 * 5.5 + 30 * 11)/51 = 8.73 | Extreme low (<10%) |
| 21 | 30 | 5.5 | 20 | (21 * 5.5 + 30 * 20)/51 = 14.02 | Low (10-25%) |
| 21 | 30 | 5.5 | 50 | (21 * 5.5 + 30 * 50)/51 = 31.67 | Bit low (25-40%) |
| 21 | 30 | 5.5 | 70 | (21 * 5.5 + 30 * 70)/51 = 43.44 | Near normal (40-60%) |
| 21 | 30 | 5.5 | 100 | (21 * 5.5 + 30 * 50)/51 = 61.08 | Bit high (60-75%) |
| 36 | 15 | 5.5 | 11 | (36 * 5.5 + 15 * 11)/51 = 7.11 | Extreme low (<10%) |
| 36 | 15 | 5.5 | 20 | (36 * 5.5 + 15 * 20)/51 = 9.76 | Extreme low (<10%) |
| 36 | 15 | 5.5 | 50 | (36 * 5.5 + 15 * 50)/51 = 18.58 | Low (10-25%) |
| 36 | 15 | 5.5 | 70 | (36 * 5.5 + 15 * 70)/51 = 24.47 | Low (10-25%) |
| 36 | 15 | 5.5 | 100 | (36 * 5.5 + 15 * 50)/51 = 33.29 | Bit low (25-40%) |
| 51 | 0 | 5.5 | NA (no member to rank) | (51 * 5.5 + 0)/51 = 5.5 | Extreme low (<10%) |
No-2 example: The 1-30 climate percentiles are 0, so the average rank of the 0 ensemble members will always be around 15.5 with the evenly distributed rank representation:
| Number of 0 members | Number of non-0 members | Average rank of 0 members | Average rank of non-0 members | Rank-mean | Dominant anomaly category |
|---|
| 0 | 51 | NA (no member to rank) | 31 (the lowest possible rank for a non-zero member if 1-30 percentiles in the climatology are 0) | (0 * 15.5 + 51 * 31)/51 = 31 | Bit low (25-40%) |
| 0 | 51 | NA | 50 | (0 * 15.5 + 51 * 50)/51 = 50 | Near normal (40-60%) |
| 0 | 51 | NA | 70 | (0 * 15.5 + 51 * 70)/51 = 70 | Bit high (60-75%) |
| 0 | 51 | NA | 100 | (0 * 15.5 + 51 * 100)/51 = 100 | Extreme high (90%<) |
| 11 | 40 | 5.5 | 11 | (11 * 15.5 + 40 * 31)/51 = 27.65 | Bit low (25-40%) |
| 11 | 40 | 5.5 | 50 | (11 * 15.5 + 40 * 50)/51 = 42.55 | Near normal (40-60%) |
| 11 | 40 | 5.5 | 70 | (11 * 15.5 + 40 * 70)/51 = 58.24 | Near normal (40-60%) |
| 11 | 40 | 5.5 | 100 | (11 * 15.5 + 40 * 100)/51 = 81.77 | High (75-90%) |
| 21 | 30 | 5.5 | 11 | (21 * 15.5 + 30 * 31)/51 = 24.61 | Low (10-25%) |
| 21 | 30 | 5.5 | 50 | (21 * 15.5 + 30 * 50)/51 = 35.79 | Bit low (25-40%) |
| 21 | 30 | 5.5 | 70 | (21 * 15.5 + 30 * 70)/51 = 47.55 | Near normal (40-60%) |
| 21 | 30 | 5.5 | 100 | (21 * 15.5 + 30 * 100)/51 = 65.20 | Bit high (60-75%) |
| 36 | 15 | 5.5 | 11 | (36 * 15.5 + 15 * 11)/51 = 20.05 | Low (10-25%) |
| 36 | 15 | 5.5 | 50 | (36 * 15.5 + 15 * 50)/51 = 25.64 | Bit low (25-40%) |
| 36 | 15 | 5.5 | 70 | (36 * 15.5 + 15 * 70)/51 = 31.52 | Bit low (25-40%) |
| 36 | 15 | 5.5 | 100 | (36 * 15.5 + 15 * 100)/51 = 40.35 | Near normal (40-60%) |
| 51 | 0 | 5.5 | NA (no member to rank) | (51 * 15.5 + 0)/51 = 15.5 | Low (10-25%) |
No-3 example: The 1-70 climate percentiles are 0, so the average rank of the 0 ensemble members will always be around 35.5 with the evenly distributed rank representation:
| Number of 0 members | Number of non-0 members | Average rank of 0 members | Average rank of non-0 members | Rank-mean | Dominant anomaly category |
|---|---|---|---|---|---|
| 0 | 51 | NA (no member to rank) | 71 (the lowest possible rank for a non-zero member if 1-30 percentiles in the climatology are 0) | (0 * 15.5 + 51 * 31)/51 = 31 | Bit low (25-40% |
| ) | |||||
| 0 | 51 | NA | 50 | (0 * 15.5 + 51 * 50)/51 = 50 | Near normal (40-60%) |
| 0 | 51 | NA | 70 | (0 * 15.5 + 51 * 70)/51 = 70 | Bit high (60-75%) |
| 0 | 51 | NA | 100 | (0 * 15.5 + 51 * 100)/51 = 100 | Extreme high (90%<) |
| 11 | 40 | 5.5 | 11 | (11 * 15.5 + 40 * 31)/51 = 27.65 | Bit low (25-40%) |
| 11 | 40 | 5.5 | 50 | (11 * 15.5 + 40 * 50)/51 = 42.55 | Near normal (40-60%) |
| 11 | 40 | 5.5 | 70 | (11 * 15.5 + 40 * 70)/51 = 58.24 | Near normal (40-60%) |
| 11 | 40 | 5.5 | 100 | (11 * 15.5 + 40 * 100)/51 = 81.77 | High (75-90%) |
| 21 | 30 | 5.5 | 11 | (21 * 15.5 + 30 * 31)/51 = 24.61 | Low (10-25%) |
| 21 | 30 | 5.5 | 50 | (21 * 15.5 + 30 * 50)/51 = 35.79 | Bit low (25-40%) |
| 21 | 30 | 5.5 | 70 | (21 * 15.5 + 30 * 70)/51 = 47.55 | Near normal (40-60%) |
| 21 | 30 | 5.5 | 100 | (21 * 15.5 + 30 * 100)/51 = 65.20 | Bit high (60-75%) |
| 36 | 15 | 5.5 | 11 | (36 * 15.5 + 15 * 11)/51 = 20.05 | Low (10-25%) |
| 36 | 15 | 5.5 | 50 | (36 * 15.5 + 15 * 50)/51 = 25.64 | Bit low (25-40%) |
| 36 | 15 | 5.5 | 70 | (36 * 15.5 + 15 * 70)/51 = 31.52 | Bit low (25-40%) |
| 36 | 15 | 5.5 | 100 | (36 * 15.5 + 15 * 100)/51 = 40.35 | Near normal (40-60%) |
| 51 | 0 | 5.5 | NA (no member to rank) | (51 * 15.5 + 0)/51 = 15.5 | Low (10-25%) |
- If all ensemble members are 0, then the ranks will spread evenly from 1 to 10 and the rank-mean will be around 5.5, so in the Extreme low category.
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