Interpretation · May initialization · JJAS and its months
Interpretation — national aggregate (All Ethiopia)
- All tested corrections improve national JJAS rainfall-amount CRPSS over raw ECMWF in 1993–2016 (raw -1.311; corrected -0.078 to -0.025). Performance varies for monthly tercile probabilities: 0 method–month combinations score below the raw model on RPSS.
- Accounting for the whole search. With Holm adjustment across all 60 method–target comparisons, the amount (CRPS) screening passes are Variance Scaling (unbounded) (Jul, Aug), Square-root-space Mean-Variance Scaling (Aug), Power Transformation (Aug) and Gamma Quantile Mapping (Aug), and the tercile (RPS) passes are none. Within-method passes that do not survive this check: Gamma Quantile Mapping Jun, Gamma Quantile Mapping Sep, Power Transformation Jul, Power Transformation Jun, Square-root-space Mean-Variance Scaling JJAS, Square-root-space Mean-Variance Scaling Jul, Square-root-space Mean-Variance Scaling Jun, Square-root-space Mean-Variance Scaling Sep and Variance Scaling (unbounded) Sep.
- Variance Scaling (unbounded) is at least as good as Mean-Variance Scaling in the national aggregate for every tested target and period, on amounts and unblended terciles (JJAS CRPSS -0.027 vs -0.028 in 1993–2016, -0.016 vs -0.018 in 2017–2025). Its JJAS amount screening pass does not survive the family-wide correction. Members clipped to 0 mm in the months: 1.3%–9.9% with Mean-Variance Scaling, 0.2%–1.4% with this method. This need not hold in each region; see the tables for the JJAS R1+R2 rainfall domain.
- Empirical Quantile Mapping reproduces the CHIRPS distribution and, with the dry policy, its dry share (totals ≤ 1 mm: —); it passes the screening for none, but its JJAS amount skill is lower than Mean-Variance Scaling (-0.040 vs -0.028). A possible explanation is sampling noise in an empirical quantile function built from 23 CHIRPS values per fold; the results do not isolate it.
- The methods that use the forecast’s own distribution (Detrended Quantile Mapping, Quantile Delta Mapping, Scaled Distribution Mapping, CDF-transform) score lower on JJAS terciles (-0.080 to -0.044 vs -0.017) and none passes the season screening. A possible explanation is that the distribution of a single forecast’s 25–51 members is a noisy estimate of the “future” distribution these methods were designed for; the results do not isolate the cause.
- Jun and Sep remain hard: every method has negative amount skill over 2017–2025.
- No tested method demonstrates a statistically significant improvement over Mean-Variance Scaling for the published tercile probabilities under this validation protocol, although several have slightly higher point estimates. Choosing the method each year from training-only scores, the probability procedure (SEL-P) scores JJAS blended RPSS +0.025 against +0.027, confirmed for none. Amounts: the amount procedure (SEL-A) scores CRPSS -0.036 against -0.028, confirmed for Jun, Aug and Sep; fixed methods confirmed against the family of all declared methods and targets: Variance Scaling (unbounded) (Jul, Aug), Square-root-space Mean-Variance Scaling (Aug), Power Transformation (Aug) and Gamma Quantile Mapping (Aug).
- The climatology blend narrows the differences. Across the methods, JJAS RPSS (1993–2016) spans 0.010 after the blend against 0.066 for the unblended screening counts. A better amount correction is trusted more by the blend: in Jun the fitted weight on climatology is 0.75 with Square-root-space Mean-Variance Scaling against 0.80 with Mean-Variance Scaling.
- Choosing by training scores can backfire. For Jul, SEL-A chose Delta Change from the 1993–2016 scores; over 2017–2025 it has a worse mean CRPS (Δ +0.194 mm, 95% interval -0.094 to +0.517 mm; better than Mean-Variance Scaling in 3 of 9 years, with the largest losses in 2020 and 2024); for Sep, SEL-P chose Scaled Distribution Mapping from the 1993–2016 scores; over 2017–2025 it has a worse mean RPS (Δ +0.001, 95% interval -0.001 to +0.003; better than Mean-Variance Scaling in 5 of 9 years, with the largest losses in 2018 and 2024); for JJAS, SEL-P chose Delta Change from the 1993–2016 scores; over 2017–2025 it has a worse mean RPS (Δ +0.004, 95% interval -0.000 to +0.009; better than Mean-Variance Scaling in 2 of 9 years, with the largest losses in 2018 and 2023). These choices fail the no-harm rule; where the interval includes 0 they do not establish a significant deterioration. A method that ranks first on the training years is not, on that alone, a replacement.
- Where the confirmed amount gains come from (climate groups from each fold’s training years; contributions add up to the national difference from Mean-Variance Scaling): Variance Scaling (unbounded) in Jul (Δ CRPS -0.139 mm): all ≤ 1 mm -0.014 mm (10%; 4% of the area), mixed -0.042 mm (30%; 9% of the area), always wet -0.083 mm (60%; 88% of the area); Variance Scaling (unbounded) in Aug (Δ CRPS -0.129 mm): all ≤ 1 mm -0.008 mm (6%; 2% of the area), mixed -0.018 mm (14%; 3% of the area), always wet -0.103 mm (80%; 95% of the area); Square-root-space Mean-Variance Scaling in Aug (Δ CRPS -0.096 mm): all ≤ 1 mm -0.004 mm (5%; 2% of the area), mixed -0.012 mm (13%; 3% of the area), always wet -0.079 mm (83%; 95% of the area); Power Transformation in Aug (Δ CRPS -0.124 mm): all ≤ 1 mm -0.008 mm (6%; 2% of the area), mixed -0.017 mm (14%; 3% of the area), always wet -0.099 mm (80%; 95% of the area); Gamma Quantile Mapping in Aug (Δ CRPS -0.128 mm): all ≤ 1 mm +0.000 mm (-0%; 2% of the area), mixed -0.012 mm (9%; 3% of the area), always wet -0.116 mm (91%; 95% of the area).
- No cell of All Ethiopia has exactly 0 mm in every training year, for any target, at 0.25° with CHIRPS. The all-zero guard (a separate MVS variant, outside the declared family) therefore never acts and equals Mean-Variance Scaling: the non-zero totals that Mean-Variance Scaling gives where every training year is 0 mm (its spread ratio cannot fall below 0.5) do not arise in these data. The guard remains a documented option; a finite history of zero rainfall does not make rain impossible.
4 of the 15 interpretation statements do not hold for this cycle’s results and are not shown (each is checked against the numbers before it is displayed).
Caveats
- Screening skill is from 1993–2016 leave-one-year-out (clean) and 2017–2025 (exploratory: these years were seen while the operational method was chosen).
- Screening tercile scores use smoothed member counts without the climatology blend; the confirmation scores the blended product.
- Two multiplicity families are shown: within one method across its targets (✓) and across all methods and targets (✓✓). The confirmation’s selection-aware procedures include the method choice in the evaluation itself.
- Scores are area-weighted over many correlated cells but tested year by year, so each year counts once.
- The ordinary CRPS scores the delivered ensemble; the fair CRPS is a diagnostic under a sampling interpretation that DC’s rescaled years and methods tied to the forecast mean or ranks only approximate.
- Results are national aggregates unless a table says otherwise; a method can rank differently in a region (see the regional tables).