Seasonal Rainfall Outlook Platform
Phase 2 · Probability calibration · May initialization · JJAS and its months

Phase 2 · May initialization · JJAS and its months

Binary calibrators (one-vs-rest, normalized)

Platt, beta and isotonic calibration of each category against the rest, divided by their sum inside the pipeline, against the incumbent (their own family: Holm across these methods and the targets). Confirmed better: none.

Tercile RPSS, outer leave-one-year-out 1993–2016
MethodJunJulAugSepJJAS
Climatology blend (incumbent)-0.000+0.014+0.012+0.003+0.027
Platt (sigmoid) calibration, one-vs-rest + normalization-0.001+0.012+0.009+0.003+0.026
Beta calibration, one-vs-rest + normalization-0.004+0.010+0.009+0.001+0.024
Isotonic regression, one-vs-rest + normalization-0.014+0.006+0.008+0.000+0.022
SEL (chosen each year)-0.000+0.014+0.012+0.003+0.027
Tercile RPSS, fit 1993–2016, scored 2017–2025 (exploratory)
MethodJunJulAugSepJJAS
Climatology blend (incumbent)+0.010+0.042+0.041+0.008+0.039
Platt (sigmoid) calibration, one-vs-rest + normalization+0.012+0.041+0.041+0.011+0.036
Beta calibration, one-vs-rest + normalization+0.011+0.042+0.040+0.012+0.037
Isotonic regression, one-vs-rest + normalization+0.005+0.043+0.049+0.009+0.037
SEL (chosen each year)+0.010+0.042+0.041+0.008+0.039

Rainfall-distribution models (Pathway B)

Each model predicts a full rainfall distribution from the raw ensemble (pooled over cells in units relative to each cell's climatology); terciles at the training CHIRPS boundaries, quantiles and intervals come from it. References, in the same folds: the published probabilities (tercile RPS) and the MVS-corrected ensemble (CRPS, quantiles). ✓ = better than the reference with Holm-adjusted p < 0.05 across the models and targets, and not worse over 2017–2025. Confirmed better — tercile probabilities: none; rainfall amounts (CRPS): EMOS, censored shifted gamma (Sep) and Regularized quantile regression (Sep).

Tercile probabilities

Tercile RPSS, outer leave-one-year-out 1993–2016
MethodJunJulAugSepJJAS
Published probabilities (incumbent)-0.000+0.015+0.012+0.003+0.027
EMOS, censored shifted gamma-0.045-0.004-0.014-0.013+0.003
Heteroscedastic extended logistic regression-0.052-0.003-0.008-0.018+0.005
Regularized quantile regression-0.052-0.013-0.030-0.020+0.001

Rainfall amounts

Amount CRPSS against the CHIRPS climatology, 1993–2016
MethodJunJulAugSepJJAS
MVS-corrected ensemble-0.096-0.005-0.027-0.060-0.028
EMOS, censored shifted gamma-0.031+0.018-0.004-0.006 ✓+0.017
Heteroscedastic extended logistic regression-0.054+0.013-0.010-0.017+0.007
Regularized quantile regression-0.015+0.014-0.004-0.001 ✓+0.014

Intervals and quantiles

Share of observations inside the 10–90% interval, 1993–2016 (80% is calibrated)
MethodJunJulAugSepJJAS
MVS-corrected ensemble65%73%75%71%70%
EMOS, censored shifted gamma84%81%83%82%81%
Heteroscedastic extended logistic regression90%86%88%87%87%
Regularized quantile regression78%78%78%78%78%
Pinball loss of the median (mm), 1993–2016 (lower is better)
MethodJunJulAugSepJJAS
MVS-corrected ensemble12.4116.9314.7513.2133.54
EMOS, censored shifted gamma11.6216.5414.3912.6132.13
Heteroscedastic extended logistic regression11.6916.5814.4212.6832.22
Regularized quantile regression11.5016.6014.4012.5532.15

Test years

Fit 1993–2016, scored 2017–2025 (exploratory)
MethodJunJulAugSepJJAS
Published probabilities / MVS ensemble+0.010 / -0.030+0.042 / +0.002+0.041 / +0.055+0.008 / -0.034+0.039 / -0.018
EMOS, censored shifted gamma (RPSS / CRPSS)-0.020 / -0.019+0.031 / +0.016+0.053 / +0.038-0.004 / -0.006+0.037 / +0.016
Heteroscedastic extended logistic regression (RPSS / CRPSS)-0.030 / -0.032+0.030 / +0.014+0.047 / +0.032-0.002 / -0.019+0.034 / -0.004
Regularized quantile regression (RPSS / CRPSS)-0.035 / -0.020+0.016 / +0.011+0.019 / +0.007-0.017 / -0.006+0.028 / +0.010

Fits and model definitions

  • EMOS, censored shifted gamma: converged in every fold.
  • Heteroscedastic extended logistic regression: converged in every fold.
  • Regularized quantile regression: converged in every fold; quantile rearrangement needed for at most 0.1% of cells.
Models
ModelEstimatesPredictorsFittingOutputs
EMOS, censored shifted gammarainfall distribution with a probability of zeroensemble mean m' and mean absolute difference md' (relative)maximum likelihood, pooled over cellsCDF, quantiles, tercile probabilities
Heteroscedastic extended logistic regressioncoherent CDF across all thresholdssqrt of the ensemble mean m', log spread s' (relative)log loss over each cell’s CHIRPS deciles, pooledCDF, quantiles, tercile probabilities
Regularized quantile regressionconditional quantiles at 19 levels (5–95%), CDF by interpolationensemble mean m' and spread s' (relative)pinball loss per level (Huber-smoothed), L2 1e-4, pooledCDF, quantiles, tercile probabilities
Tercile RPSS and amount CRPSS of the Phase 2 distribution models against the published pipeline.
Tercile RPSS and amount CRPSS of the Phase 2 distribution models against the published pipeline.

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