Seasonal Rainfall Outlook Platform
Phase 2 · Probability calibration · January initialization · FMAM and its months

Phase 2 · January initialization · FMAM 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
MethodFebMarAprMayFMAM
Climatology blend (incumbent)+0.027+0.002+0.001+0.028+0.032
Platt (sigmoid) calibration, one-vs-rest + normalization+0.032+0.001+0.003+0.026+0.032
Beta calibration, one-vs-rest + normalization+0.064+0.001-0.000+0.031+0.029
Isotonic regression, one-vs-rest + normalization-0.032-0.033-0.004+0.033+0.028
SEL (chosen each year)+0.064+0.005+0.001+0.028+0.032
Tercile RPSS, fit 1993–2016, scored 2017–2025 (exploratory)
MethodFebMarAprMayFMAM
Climatology blend (incumbent)+0.022+0.008+0.002+0.004+0.017
Platt (sigmoid) calibration, one-vs-rest + normalization-0.013+0.005+0.006-0.006+0.019
Beta calibration, one-vs-rest + normalization-0.012+0.008+0.006-0.013+0.019
Isotonic regression, one-vs-rest + normalization-0.091-0.064-0.001-0.019+0.017
SEL (chosen each year)-0.012+0.008+0.002+0.004+0.017

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 (FMAM).

Tercile probabilities

Tercile RPSS, outer leave-one-year-out 1993–2016
MethodFebMarAprMayFMAM
Published probabilities (incumbent)+0.033+0.002+0.001+0.028+0.032
EMOS, censored shifted gamma+0.043-0.065-0.001+0.026+0.037
Heteroscedastic extended logistic regression+0.065-0.065-0.000+0.027+0.031
Regularized quantile regression+0.039-0.052-0.001+0.028+0.030

Rainfall amounts

Amount CRPSS against the CHIRPS climatology, 1993–2016
MethodFebMarAprMayFMAM
MVS-corrected ensemble+0.074-0.044-0.016+0.007+0.025
EMOS, censored shifted gamma+0.074-0.026+0.005+0.014+0.039 ✓
Heteroscedastic extended logistic regression+0.072-0.076-0.005-0.004+0.032
Regularized quantile regression+0.104-0.018+0.004+0.012+0.033

Intervals and quantiles

Share of observations inside the 10–90% interval, 1993–2016 (80% is calibrated)
MethodFebMarAprMayFMAM
MVS-corrected ensemble56%54%68%69%72%
EMOS, censored shifted gamma82%81%77%78%78%
Heteroscedastic extended logistic regression89%92%84%85%83%
Regularized quantile regression78%77%77%77%77%
Pinball loss of the median (mm), 1993–2016 (lower is better)
MethodFebMarAprMayFMAM
MVS-corrected ensemble5.0914.0920.4720.4433.73
EMOS, censored shifted gamma5.1514.3620.2320.5133.87
Heteroscedastic extended logistic regression5.1214.6320.2220.6534.06
Regularized quantile regression5.0514.1320.1520.5233.97

Test years

Fit 1993–2016, scored 2017–2025 (exploratory)
MethodFebMarAprMayFMAM
Published probabilities / MVS ensemble+0.020 / +0.002+0.008 / +0.005+0.002 / -0.006+0.004 / -0.007+0.017 / +0.016
EMOS, censored shifted gamma (RPSS / CRPSS)+0.014 / +0.028+0.011 / +0.022-0.009 / +0.006+0.003 / +0.007+0.019 / +0.029
Heteroscedastic extended logistic regression (RPSS / CRPSS)-0.031 / +0.007-0.003 / -0.015+0.005 / +0.005+0.010 / -0.006+0.017 / +0.033
Regularized quantile regression (RPSS / CRPSS)-0.055 / +0.029-0.000 / +0.006+0.002 / +0.010+0.002 / +0.007+0.014 / +0.034

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 1.8% 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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