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| title | Non-zero climatology with 5 rank groups only |
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Few examples are shown here, when there is no zero value in the climatology, so all ensemble forecast members can be ranked without any issue. For simplicity, 5 clusters are used in the forecast only. So, for example in the first row, 10 ensemble members are in the first group, which will all have the rank of 40. Then , again 10 members will be in the 2nd group with the rank of 45, and so on. Then, the rank-mean of this simplified forecast distribution will be very close to 50, as the mean os practically speaking the mean of the rank of the 5 groups with 40, 45, 50, 55 and 60, as the population of the 5 groups is almost exactly the same (other than the middle group with 11). The even distribution is represented first, for which it is shown that by shifting the same rank distribution up or down does not change the standard deviation (and uncertainty). This is true for any variety of rank distributions. Also, after 'narrowing' the rank distribution, the mean does not change, but the uncertainty drops markedly. Moreover, in a similar manner, by adding extreme members (i.e. 1 or 100 or near that), even if only with very few members (2 in this example below), the uncertainty can be increased quite substantially. | Number of ensemble members in each group | Common rank in each group | Rank-mean | Expected forecast anomaly category | Rank-std | Forecast uncertainty category |
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| N1 | N2 | N3 | N4 | N5 | R1 | R2 | R3 | R4 | R5 |
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| 10 | 10 | 11 | 10 | 10 | 40 |
lklk | Number of members in each group | Rank in each group | Rank-mean | Forecast anomaly category | Rank-std | Uncertainty category |
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| 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 | 60 | 50.0 | Near normal (40-60) |
3130310| 30 | 40 | 50 | 60 | 70 | 50.0 | Near normal (40-60) |
626Low 0310| 10 | 30 | 50 | 70 | 90 | 50.0 | Near normal (40-60) |
1252Medium 227214550551005003Near normal 40601421Medium 227214050601005003Near normal 406015212272130 | 10070 | | 55 |
| 50.0 | Near normal (40-60) |
1864Medium 2272120 | 80100 | 23.34 | | 6.26 | Low uncertainty | | 0 | 10 | 31 | 10 | 0 |
| 30 | 50 | 70 |
| 50.0 | Near normal (40-60) | 12.52 | Medium |
High 109002862High uncertainty | |
Example No-1: No zero section in climatology, 5 number/rank groups:
In these simplified examples, a fixed portion of the climatological and/or ensemble forecast distribution is 0, while the non-zero ensemble members have just one 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.
in a Below, there are examples with simplified rank distributions and specific cases of very dry rivers (0 values) that will demonstrate how the forecast anomaly category and uncertainty category generation work.
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 forecast ensemble members will be 5.5).
| 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 |
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Example No-1: No zero section in climatology, 5 number/rank groups:
In these simplified examples, a fixed portion of the climatological and/or ensemble forecast distribution is 0, while the non-zero ensemble members have just one 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.
in a Below, there are examples with simplified rank distributions and specific cases of very dry rivers (0 values) that will demonstrate how the forecast anomaly category and uncertainty category generation work.
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 forecast ensemble members will be 5.5)Example No-1 shows few examples when there is no zero value in the climatology, so all ensemble forecast members can be ranked without any issue. Here 5 clusters are used for simplicity. The even distribution is represented first, for which it is shown that by shifting the same rank distribution up or down does not change the standard deviation (and uncertainty). This is true for any variety of rank distributions. Also, after 'narrowing' the rank distribution, the mean does not change, but the uncertainty drops markedly. Moreover, in a similar manner, by adding extreme members (i.e. 1 or 100 or near that), even if only with very few members (2 in this example below), the uncertainty can be increased quite substantially.
Example No-1: No zero section in climatology, 5 number/rank groups:
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