...
In these examples, for simplicity reason, a fixed portion of the climatological and/or ensemble forecast distribution is 0, while the non-zero ensemble members have just one or few more groups that have other rank for the very dry cases and 5 for the non-zero cases, with members having the same rank in each group. This way, the computation methodology can be demonstrated in a simple way that is easier to interpret.
For example, when the X% of the climatological distribution is 0, then the average rank of the 0-value ensemble members will always be X/2+0.5 with the even rank representation for the 0-value case explained above (e.g. for 10% being 0 in the climate, the average rank of the 0-value case explained above (e.g. for 10% being 0 in the climate, the average rank of the 0-value forecast ensemble members will be 5.5).
...
-value forecast ensemble members will be 5.5).
Example No-1: No zero section in climatology, 5 number/rank groups:
| Number of members in each group | Rank in each group | Rank-mean | Dominant anomaly category | Rank-std | Uncertainty category | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| N1 | N2 | N3 | N4 | N5 | R1 | R2 | R3 | R4 | R5 | ||||
| 10 | 10 | 11 | 10 | 10 | 40 | 45 | 50 | 55 | 60 | 50.0 | Near normal (40-60) | 7.00 | Low uncertainty |
| 10 | 10 | 11 | 10 | 10 | 30 | 40 | 50 | 60 | 70 | 50.0 | Near normal (40-60) | 14.00 | Medium uncertainty |
| 10 | 10 | 11 | 10 | 10 | 10 | 30 | 50 | 70 | 90 | 50.0 | Near normal (40-60) | 28.00 | High uncertainty |
| 10 | 10 | 11 | 10 | 10 | 60 | 65 | 70 | 75 | 80 | 70.0 | Bit high (60-75) | 7.00 | Low uncertainty |
| 10 | 10 | 11 | 10 | 10 | 50 | 60 | 70 | 80 | 90 | 70.0 | Bit high (60-75) | 14.00 | Medium uncertainty |
| 0 | 10 | 31 | 10 | 0 | 45 | 50 | 55 | 50.0 | Near normal (40-60) | 3.13 | Low uncertainty | ||
| 0 | 10 | 31 | 10 | 0 | 40 | 50 | 60 | 50.0 | Near normal (40-60) | 6.26 | Low uncertainty | ||
| 0 | 10 | 31 | 10 | 0 | 30 | 50 | 70 | 50.0 | Near normal (40-60) | 12.52 | Medium uncertainty | ||
| 2 | 10 | 27 | 10 | 2 | 1 | 45 | 50 | 55 | 100 | 50.03 | Near normal (40-60) | 14.21 | Medium uncertainty |
| 2 | 10 | 27 | 10 | 2 | 1 | 40 | 50 | 60 | 100 | 50.03 | Near normal (40-60) | 15.21 | Medium uncertainty |
| 2 | 10 | 27 | 10 | 2 | 1 | 30 | 50 | 70 | 100 | 50.0 | Near normal (40-60) | 18.64 | Medium uncertainty |
| 2 | 10 | 27 | 10 | 2 | 1 | 20 | 50 | 80 | 100 | 50.0 | Near normal (40-60) | 23.34 | High uncertainty |
| 2 | 10 | 27 | 10 | 2 | 1 | 10 | 50 | 90 | 100 | 50.0 | Near normal (40-60) | 28.62 | High uncertainty |
Example No-2: Lowest 10% of the climatology is 0, 2 number/rank groups:
| 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 | Rank-std | Uncertainty 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 | Low uncertainty |
| 0 | 51 | NA | 20 | (0 * 5.5 + 51 * 20)/51 = 20 | Low (10-25) | 0 | Low uncertainty |
| 0 | 51 | NA | 50 | (0 * 5.5 + 51 * 50)/51 = 50 | Near normal (40-60) | 0 | Low uncertainty |
| 0 | 51 | NA | 70 | (0 * 5.5 + 51 * 70)/51 = 70 | Bit high (60-75) | 0 | Low uncertainty |
| 0 | 51 | NA | 100 | (0 * 5.5 + 51 * 100)/51 = 100 | Extreme high (90<) | 0 | Low uncertainty |
| 11 | 40 | 5.5 | 11 | (11 * 5.5 + 40 * 11)/51 = 9.81 | Extreme low (<10) | 2.26 | Low uncertainty |
| 11 | 40 | 5.5 | 20 | (11 * 5.5 + 40 * 20)/51 = 16.87 | Low (10-25) | 5.96 | Low uncertainty |
| 11 | 40 | 5.5 | 50 | (11 * 5.5 + 40 * 50)/51 = 40.40 | Near normal (40-60) | 18.3 | Medium uncertainty |
| 11 | 40 | 5.5 | 70 | (11 * 5.5 + 40 * 70)/51 = 56.08 | Near normal (40-60) | 26.52 | High uncertainty |
| 11 | 40 | 5.5 | 100 | (11 * 5.5 + 40 * 100)/51 = 79.61 | High (75-90) | 38.86 | High uncertainty |
| 21 | 30 | 5.5 | 11 | (21 * 5.5 + 30 * 11)/51 = 8.73 | Extreme low (<10) | 2.70 | Low uncertainty |
| 21 | 30 | 5.5 | 20 | (21 * 5.5 + 30 * 20)/51 = 14.02 | Low (10-25) | 7.13 | Low uncertainty |
| 21 | 30 | 5.5 | 50 | (21 * 5.5 + 30 * 50)/51 = 31.67 | Bit low (25-40) | 21.90 | High uncertainty |
| 21 | 30 | 5.5 | 70 | (21 * 5.5 + 30 * 70)/51 = 43.44 | Near normal (40-60) | 31.74 | High uncertainty |
| 21 | 30 | 5.5 | 100 | (21 * 5.5 + 30 * 50)/51 = 61.08 | Bit high (60-75) | 46.50 | High uncertainty |
| 36 | 15 | 5.5 | 11 | (36 * 5.5 + 15 * 11)/51 = 7.11 | Extreme low (<10) | 2.50 | Low uncertainty |
| 36 | 15 | 5.5 | 20 | (36 * 5.5 + 15 * 20)/51 = 9.76 | Extreme low (<10) | 6.60 | Low uncertainty |
| 36 | 15 | 5.5 | 50 | (36 * 5.5 + 15 * 50)/51 = 18.58 | Low (10-25) | 20.27 | High uncertainty |
| 36 | 15 | 5.5 | 70 | (36 * 5.5 + 15 * 70)/51 = 24.47 | Low (10-25) | 29.38 | High uncertainty |
| 36 | 15 | 5.5 | 100 | (36 * 5.5 + 15 * 50)/51 = 33.29 | Bit low (25-40) | 43.05 | High uncertainty |
| 51 | 0 | 5.5 | NA (no member to rank) | (51 * 5.5 + 0)/51 = 5.5 | Extreme low (<10) | 0 | Low uncertainty |
Example No-
...
3: Lowest 30% of the climatology is 0, 2 number/rank groups:
| 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 | Rank-std | Uncertainty 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 | Low uncertainty |
| 0 | 51 | NA | 50 | (0 * 15.5 + 51 * 50)/51 = 50 | Near normal (40-60) | 0 | Low uncertainty |
| 0 | 51 | NA | 70 | (0 * 15.5 + 51 * 70)/51 = 70 | Bit high (60-75) | 0 | Low uncertainty |
| 0 | 51 | NA | 100 | (0 * 15.5 + 51 * 100)/51 = 100 | Extreme high (90<) | 0 | Low uncertainty |
| 11 | 40 | 15.5 | 31 | (11 * 15.5 + 40 * 31)/51 = 27.65 | Bit low (25-40) | 6.37 | Low uncertainty |
| 11 | 40 | 15.5 | 50 | (11 * 15.5 + 40 * 50)/51 = 42.55 | Near normal (40-60) | 14.18 | Medium uncertainty |
| 11 | 40 | 15.5 | 70 | (11 * 15.5 + 40 * 70)/51 = 58.24 | Near normal (40-60) | 22.41 | High uncertainty |
| 11 | 40 | 15.5 | 100 | (11 * 15.5 + 40 * 100)/51 = 81.77 | High (75-90) | 34.75 | High uncertainty |
| 21 | 30 | 15.5 | 31 | (21 * 15.5 + 30 * 31)/51 = 24.61 | Low (10-25) | 7.62 | Low uncertainty |
| 21 | 30 | 15.5 | 50 | (21 * 15.5 + 30 * 50)/51 = 35.79 | Bit low (25-40) | 16.97 | Medium uncertainty |
| 21 | 30 | 15.5 | 70 | (21 * 15.5 + 30 * 70)/51 = 47.55 | Near normal (40-60) | 26.82 | High uncertainty |
| 21 | 30 | 15.5 | 100 | (21 * 15.5 + 30 * 100)/51 = 65.20 | Bit high (60-75) | 41.58 | High uncertainty |
| 36 | 15 | 15.5 | 31 | (36 * 15.5 + 15 * 31)/51 = 20.05 | Low (10-25) | 7.06 | Low uncertainty |
| 36 | 15 | 15.5 | 50 | (36 * 15.5 + 15 * 50)/51 = 25.64 | Bit low (25-40) | 15.71 | Medium uncertainty |
| 36 | 15 | 15.5 | 70 | (36 * 15.5 + 15 * 70)/51 = 31.52 | Bit low (25-40) | 24.83 | High uncertainty |
| 36 | 15 | 15.5 | 100 | (36 * 15.5 + 15 * 100)/51 = 40.35 | Near normal (40-60) | 38.50 | High uncertainty |
| 51 | 0 | 15.5 | NA (no member to rank) | (51 * 15.5 + 0)/51 = 15.5 | Low (10-25) | 0 | Low uncertainty |
Example No-
...
4: Lowest 70% of the climatology is 0, 2 number/rank groups:
| 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 | Rank-std | Uncertainty category |
|---|---|---|---|---|---|---|---|
| 0 | 51 | NA (no member to rank) | 71 (the lowest possible rank for a non-zero member if 1-70 percentiles in the climatology are 0) | (0 * 35.5 + 51 * 71)/51 = 71 | Bit high (60-75) | 0 | Low uncertainty |
| 0 | 51 | NA | 100 | (0 * 35.5 + 51 * 100)/51 = 100 | Extreme high (90<) | 0 | Low uncertainty |
| 11 | 40 | 35.5 | 71 | (11 * 35.5 + 40 * 71)/51 = 63.34 | Bit high (60-75) | 14.60 | Medium uncertainty |
| 11 | 40 | 35.5 | 100 | (11 * 35.5 + 40 * 100)/51 = 86.08 | High (75-90) | 26.52 | High uncertainty |
| 21 | 30 | 35.5 | 71 | (21 * 35.5 + 30 * 71)/51 = 56.38 | Near normal (40-60) | 17.47 | Medium uncertainty |
| 21 | 30 | 35.5 | 100 | (21 * 35.5 + 30 * 100)/51 = 73.44 | Bit high (60-75) | 31.74 | High uncertainty |
| 36 | 15 | 35.5 | 71 | (36 * 35.5 + 15 * 71)/51 = 45.94 | Near normal (40-60) | 16.17 | Medium uncertainty |
| 36 | 15 | 35.5 | 100 | (36 * 35.5 + 15 * 100)/51 = 54.47 | Near normal (40-60) | 29.38 | High uncertainty |
| 51 | 0 | 35.5 | NA (no member to rank) | (51 * 35.5 + 0)/51 = 35.5 | Bit low (25-40) | 0 | Low uncertainty |
Example No-
...
5: All percentiles of the climatology (1-99) are 0, 2 number/rank groups:
| 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 | Rank-std | Uncertainty category |
|---|---|---|---|---|---|---|---|
| 0 | 51 | NA (no member to rank) | 100 (the lowest possible rank for a non-zero member if 1-99 percentiles in the climatology are 0) | (0 * 50.5 + 51 * 100)/51 = 100 | Extreme high (90<) | 0 | Low uncertainty |
| 11 | 40 | 50.5 | 100 | (11 * 50.5 + 40 * 100)/51 = 89.32 | High (75-90) | 20.35 | High uncertainty |
| 21 | 30 | 35.5 | 100 | (21 * 50.5 + 30 * 100)/51 = 79.61 | High (75-90) | 24.36 | High uncertainty |
| 36 | 15 | 35.5 | 100 | (36 * 50.5 + 15 * 100)/51 = 65.05 | Bit high (60-75) | 22.55 | High uncertainty |
| 51 | 0 | 35.5 | NA (no member to rank) | (51 * 50.5 + 0)/51 = 50.5 | Near normal (40-60) | 0 | Low uncertainty |
...