Interpretation · Bias correction · May initialization · JJAS and its months

Interpretation · May initialization · JJAS and its months

Interpretation — national aggregate (All Ethiopia)

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Jun and Sep remain hard: every method has negative amount skill over 2017–2025.
  7. 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).
  8. 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.
  9. 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.
  10. 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).
  11. 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).

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