Confirmation · February 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) | +0.021 | +0.059 | +0.017 | +0.025 | -0.007 | +0.071 | 0.49 |
| Linear Scaling | +0.021 | +0.057 | +0.018 | +0.024 | -0.023 | +0.086 | 0.52 |
| Variance Scaling (unbounded) | +0.021 | +0.058 | +0.017 | +0.025 | -0.007 | +0.070 | 0.49 |
| Square-root-space Mean-Variance Scaling | +0.021 | +0.062 | +0.018 | +0.025 | -0.005 | +0.073 | 0.49 |
| Power Transformation | +0.021 | +0.062 | +0.016 | +0.025 | -0.008 | +0.074 | 0.50 |
| Delta Change | +0.017 | +0.049 | +0.015 | +0.020 | -0.010 | +0.075 | 0.55 |
| Local Intensity Scaling | +0.021 | +0.057 | +0.018 | +0.024 | -0.022 | +0.086 | 0.52 |
| Empirical Quantile Mapping | +0.012 | +0.044 | +0.008 | +0.015 | -0.018 | +0.059 | 0.56 |
| Gamma Quantile Mapping | +0.022 | +0.063 | +0.019 | +0.025 | -0.005 | +0.073 | 0.49 |
| Detrended Quantile Mapping | +0.017 | +0.054 | +0.012 | +0.022 | -0.035 | +0.072 | 0.61 |
| Quantile Delta Mapping | +0.018 | +0.060 | +0.014 | +0.022 | -0.048 | +0.075 | 0.63 |
| Scaled Distribution Mapping | +0.019 | +0.058 | +0.015 | +0.023 | -0.059 | +0.063 | 0.65 |
| CDF-transform | +0.016 | +0.054 | +0.010 | +0.021 | -0.041 | +0.072 | 0.61 |
| MVS with all-zero guard (variant) | +0.021 | +0.059 | +0.017 | +0.025 | -0.007 | +0.071 | 0.49 |
| SEL-P | +0.020 | +0.063 | +0.015 | +0.025 | -0.017 | +0.073 | — |
| SEL-A | +0.019 | +0.063 | +0.015 | +0.023 | -0.011 | +0.073 | — |
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) | +0.126 | +0.011 | +0.009 | +0.008 | +0.021 |
| Linear Scaling | +0.140 | +0.016 | +0.011 | +0.010 | +0.021 |
| Variance Scaling (unbounded) | +0.124 | +0.012 | +0.010 | +0.008 | +0.021 |
| Square-root-space Mean-Variance Scaling | +0.207 ✓ | +0.025 | +0.007 | +0.008 | +0.021 |
| Power Transformation | +0.193 | +0.020 | +0.004 | +0.007 | +0.021 |
| Delta Change | +0.155 | +0.014 | +0.004 | +0.006 | +0.017 |
| Local Intensity Scaling | +0.138 | +0.015 | +0.011 | +0.009 | +0.021 |
| Empirical Quantile Mapping | +0.190 | +0.011 | -0.002 | -0.007 | +0.012 |
| Gamma Quantile Mapping | +0.160 | +0.018 | +0.007 | +0.007 | +0.022 |
| Detrended Quantile Mapping | +0.166 | +0.016 | +0.001 | -0.000 | +0.017 |
| Quantile Delta Mapping | +0.135 | +0.016 | +0.002 | +0.001 | +0.018 |
| Scaled Distribution Mapping | +0.124 | +0.010 | +0.005 | +0.002 | +0.019 |
| CDF-transform | +0.165 | +0.021 | +0.000 | +0.000 | +0.016 |
| MVS with all-zero guard (variant) | +0.126 | +0.011 | +0.009 | +0.008 | +0.021 |
| SEL-P | +0.207 ✓ | +0.019 | +0.006 | -0.003 | +0.020 |
| SEL-A | +0.207 | +0.025 | +0.001 | -0.002 | +0.019 |
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) | +0.240 | -0.034 | -0.001 | -0.005 | -0.007 |
| Linear Scaling | -0.031 | -0.091 | -0.011 | -0.013 | -0.023 |
| Variance Scaling (unbounded) | +0.246 | -0.032 | -0.000 | -0.005 | -0.007 |
| Square-root-space Mean-Variance Scaling | +0.267 | -0.017 | +0.001 | -0.002 | -0.005 |
| Power Transformation | +0.202 | -0.020 | -0.001 | +0.000 | -0.008 |
| Delta Change | +0.091 | -0.055 | +0.001 | +0.004 | -0.010 |
| Local Intensity Scaling | +0.040 | -0.082 | -0.011 | -0.012 | -0.022 |
| Empirical Quantile Mapping | +0.248 | -0.028 | -0.012 | -0.011 | -0.018 |
| Gamma Quantile Mapping | +0.245 | -0.018 | +0.001 | -0.002 | -0.005 |
| Detrended Quantile Mapping | -0.016 | -0.089 | -0.024 | -0.017 | -0.035 |
| Quantile Delta Mapping | +0.158 | -0.113 | -0.035 | -0.019 | -0.048 |
| Scaled Distribution Mapping | -0.077 | -0.105 | -0.037 | -0.023 | -0.059 |
| CDF-transform | -0.367 | -0.112 | -0.030 | -0.021 | -0.041 |
| MVS with all-zero guard (variant) | +0.240 | -0.034 | -0.001 | -0.005 | -0.007 |
| SEL-P | +0.267 | -0.034 | -0.014 | -0.007 | -0.017 |
| SEL-A | +0.267 ✓ | -0.017 ✓ | -0.011 | -0.002 | -0.011 |
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 | Square-root-space Mean-Variance Scaling 24 | Square-root-space Mean-Variance Scaling | -0.0367 | 0.0022 | -0.0066 | yes |
| SEL-P | Mar | Square-root-space Mean-Variance Scaling 21, CDF-transform 3 | Square-root-space Mean-Variance Scaling | -0.0035 | 1.0000 | -0.0103 | no |
| SEL-P | Apr | Linear Scaling 23, Delta Change 1 | Linear Scaling | +0.0016 | 1.0000 | +0.0003 | no |
| SEL-P | May | Square-root-space Mean-Variance Scaling 14, Delta Change 8, Linear Scaling 1, Power Transformation 1 | Square-root-space Mean-Variance Scaling | +0.0050 | 1.0000 | +0.0012 | no |
| SEL-P | FMAM | Local Intensity Scaling 21, Linear Scaling 1, Delta Change 1, Gamma Quantile Mapping 1 | Gamma Quantile Mapping | +0.0005 | 1.0000 | -0.0018 | no |
| SEL-A | Feb | Square-root-space Mean-Variance Scaling 24 | Square-root-space Mean-Variance Scaling | -0.1842 | 0.0132 | -0.0956 | yes |
| SEL-A | Mar | Square-root-space Mean-Variance Scaling 24 | Square-root-space Mean-Variance Scaling | -0.3411 | 0.0448 | -0.4562 | yes |
| SEL-A | Apr | Square-root-space Mean-Variance Scaling 19, Delta Change 5 | Square-root-space Mean-Variance Scaling | +0.3048 | 1.0000 | -0.1520 | no |
| SEL-A | May | Delta Change 22, Power Transformation 2 | Delta Change | -0.0732 | 0.9399 | -0.2111 | no |
| SEL-A | FMAM | Gamma Quantile Mapping 20, Square-root-space Mean-Variance Scaling 3, Delta Change 1 | Gamma Quantile Mapping | +0.2314 | 1.0000 | -0.1436 | no |