Confirmation · January initialization · FMAM and its months
The screening isolates the amount correction. The confirmation evaluates what the site publishes: each method’s corrected
members go through the full probability pipeline (tercile counts, smoothing and the climatology blend), with every fit and the
blend weight inside the cross-validation folds. Two selection-aware procedures then choose a method for each
left-out year using only the other training years — SEL-P by the lowest inner blended RPS (probabilities),
SEL-A by the lowest inner CRPS (amounts) — so their scores include the effect of choosing among the 14
declared methods. ✓ = better than Mean-Variance Scaling with Holm-adjusted p < 0.05 (methods: across all methods and targets;
SEL-P/SEL-A: across the targets) and not worse over 2017–2025. This is the benchmark’s own decision, as run (Holm); the method selection applies Benjamini–Hochberg to the same p-values (since 17 October 2026). Scope: All Ethiopia.
The season at a glance
FMAM season through the full pipeline (outer leave-one-year-out 1993–2016; test years exploratory)
| Method | Blended RPSS 1993–2016 | Blended RPSS 2017–2025 | BSS below 1993–2016 | BSS above 1993–2016 | Amount CRPSS 1993–2016 | Amount CRPSS 2017–2025 | Mean blend weight λ |
|---|
| Mean-Variance Scaling (operational) | +0.032 | +0.017 | +0.022 | +0.043 | +0.025 | +0.016 | 0.26 |
| Linear Scaling | +0.035 | +0.015 | +0.027 | +0.042 | +0.019 | +0.020 | 0.31 |
| Variance Scaling (unbounded) | +0.033 | +0.016 | +0.023 | +0.043 | +0.025 | +0.015 | 0.25 |
| Square-root-space Mean-Variance Scaling | +0.033 | +0.019 | +0.023 | +0.044 | +0.025 | +0.018 | 0.25 |
| Power Transformation | +0.032 | +0.020 | +0.020 | +0.044 | +0.024 | +0.017 | 0.25 |
| Delta Change | +0.029 | +0.009 | +0.017 | +0.041 | +0.029 | +0.010 | 0.35 |
| Local Intensity Scaling | +0.035 | +0.016 | +0.027 | +0.043 | +0.020 | +0.020 | 0.31 |
| Empirical Quantile Mapping | +0.021 | +0.007 | +0.012 | +0.029 | +0.011 | +0.005 | 0.35 |
| Gamma Quantile Mapping | +0.033 | +0.021 | +0.022 | +0.044 | +0.025 | +0.019 | 0.25 |
| Detrended Quantile Mapping | +0.029 | +0.013 | +0.018 | +0.040 | +0.013 | +0.004 | 0.42 |
| Quantile Delta Mapping | +0.031 | +0.012 | +0.019 | +0.042 | +0.013 | +0.001 | 0.43 |
| Scaled Distribution Mapping | +0.032 | +0.011 | +0.019 | +0.044 | +0.009 | -0.012 | 0.46 |
| CDF-transform | +0.030 | +0.012 | +0.021 | +0.040 | +0.013 | +0.003 | 0.44 |
| MVS with all-zero guard (variant) | +0.032 | +0.017 | +0.022 | +0.043 | +0.025 | +0.016 | 0.26 |
| SEL-P | +0.035 | +0.016 | +0.027 | +0.043 | +0.020 | +0.020 | — |
| SEL-A | +0.027 | +0.009 | +0.017 | +0.037 | +0.020 | +0.010 | — |
Probabilities by target
Blended tercile RPSS by target, outer leave-one-year-out 1993–2016
| Method | Feb | Mar | Apr | May | FMAM |
|---|
| Mean-Variance Scaling (operational) | +0.027 | +0.002 | +0.001 | +0.028 | +0.032 |
| Linear Scaling | +0.041 | +0.003 | +0.001 | +0.029 | +0.035 |
| Variance Scaling (unbounded) | +0.029 | +0.003 | +0.002 | +0.028 | +0.033 |
| Square-root-space Mean-Variance Scaling | +0.073 | +0.006 | -0.000 | +0.031 | +0.033 |
| Power Transformation | +0.062 | +0.004 | -0.003 | +0.031 | +0.032 |
| Delta Change | +0.084 | -0.008 | -0.006 | +0.020 | +0.029 |
| Local Intensity Scaling | +0.040 | +0.002 | +0.002 | +0.028 | +0.035 |
| Empirical Quantile Mapping | +0.074 | -0.003 | -0.006 | +0.018 | +0.021 |
| Gamma Quantile Mapping | +0.054 | +0.003 | -0.001 | +0.031 | +0.033 |
| Detrended Quantile Mapping | +0.091 | -0.005 | -0.006 | +0.019 | +0.029 |
| Quantile Delta Mapping | +0.082 | -0.003 | -0.007 | +0.022 | +0.031 |
| Scaled Distribution Mapping | +0.047 | -0.002 | -0.004 | +0.020 | +0.032 |
| CDF-transform | +0.088 | +0.003 | -0.005 | +0.022 | +0.030 |
| MVS with all-zero guard (variant) | +0.027 | +0.002 | +0.001 | +0.028 | +0.032 |
| SEL-P | +0.073 | +0.004 | +0.001 | +0.031 | +0.035 |
| SEL-A | +0.073 | +0.001 | -0.002 | +0.031 | +0.027 |
Amounts by target and the selection-aware procedures
Amount CRPSS by target, outer leave-one-year-out 1993–2016
| Method | Feb | Mar | Apr | May | FMAM |
|---|
| Mean-Variance Scaling (operational) | +0.070 | -0.044 | -0.016 | +0.007 | +0.025 |
| Linear Scaling | -0.084 | -0.083 | -0.030 | +0.004 | +0.019 |
| Variance Scaling (unbounded) | +0.076 | -0.040 | -0.016 | +0.007 | +0.025 |
| Square-root-space Mean-Variance Scaling | +0.110 | -0.019 | -0.014 | +0.011 | +0.025 |
| Power Transformation | +0.064 | -0.020 | -0.017 | +0.012 | +0.024 |
| Delta Change | +0.051 | -0.062 | -0.021 | +0.010 | +0.029 |
| Local Intensity Scaling | -0.049 | -0.076 | -0.029 | +0.004 | +0.020 |
| Empirical Quantile Mapping | +0.099 | -0.028 | -0.026 | +0.000 | +0.011 |
| Gamma Quantile Mapping | +0.084 | -0.021 | -0.014 | +0.011 | +0.025 |
| Detrended Quantile Mapping | +0.033 | -0.074 | -0.037 | -0.004 | +0.013 |
| Quantile Delta Mapping | +0.082 | -0.084 | -0.046 | -0.000 | +0.013 |
| Scaled Distribution Mapping | -0.111 | -0.101 | -0.050 | -0.007 | +0.009 |
| CDF-transform | -0.085 | -0.085 | -0.041 | -0.001 | +0.013 |
| MVS with all-zero guard (variant) | +0.070 | -0.044 | -0.016 | +0.007 | +0.025 |
| SEL-P | -0.076 | -0.047 | -0.030 | +0.011 | +0.020 |
| SEL-A | +0.110 ✓ | -0.030 | -0.015 | +0.012 | +0.020 |
Selection-aware procedures against the operational method (Δ: RPS for SEL-P, CRPS for SEL-A; negative favours the procedure)
| Procedure | Target | Methods chosen (1993–2016, years) | Chosen for 2017–2025 | Δ score vs MVS | Holm p (targets) | Δ 2017–2025 | Confirmed |
|---|
| SEL-P | Feb | CDF-transform 17, Detrended Quantile Mapping 7 | CDF-transform | -0.0211 | 0.5477 | +0.0204 | no |
| SEL-P | Mar | Square-root-space Mean-Variance Scaling 23, CDF-transform 1 | Square-root-space Mean-Variance Scaling | -0.0009 | 1.0000 | -0.0057 | no |
| SEL-P | Apr | Linear Scaling 19, Local Intensity Scaling 5 | Local Intensity Scaling | +0.0001 | 1.0000 | +0.0014 | no |
| SEL-P | May | Square-root-space Mean-Variance Scaling 24 | Square-root-space Mean-Variance Scaling | -0.0014 | 1.0000 | +0.0066 | no |
| SEL-P | FMAM | Local Intensity Scaling 13, Linear Scaling 11 | Local Intensity Scaling | -0.0010 | 1.0000 | +0.0006 | no |
| SEL-A | Feb | Square-root-space Mean-Variance Scaling 24 | Square-root-space Mean-Variance Scaling | -0.2752 | 0.0223 | -0.1094 | yes |
| SEL-A | Mar | Square-root-space Mean-Variance Scaling 14, Power Transformation 10 | Square-root-space Mean-Variance Scaling | -0.2756 | 0.2927 | -0.5804 | no |
| SEL-A | Apr | Square-root-space Mean-Variance Scaling 22, Gamma Quantile Mapping 2 | Square-root-space Mean-Variance Scaling | -0.0537 | 0.4779 | -0.1713 | no |
| SEL-A | May | Power Transformation 24 | Power Transformation | -0.1462 | 0.0716 | -0.0901 | no |
| SEL-A | FMAM | Delta Change 21, Square-root-space Mean-Variance Scaling 3 | Delta Change | +0.2278 | 0.7559 | +0.3446 | no |