DIAL: Dynamic and Informed Adjustment of the Native Stochastic Law for Reliable Weather Ensembles

Yucheng Wang; Haonan Guo; Tianhao Zhao; Di Wang; Yu Wu; Zengmao Wang; Bo Du

cs.CVOct 15, 2026

DIAL: Dynamic and Informed Adjustment of the Native Stochastic Law for Reliable Weather Ensembles

Authors: Yucheng Wang, Haonan Guo, Tianhao Zhao, Di Wang, Yu Wu, Zengmao Wang, Bo Du

Organizations: Wuhan University · Zhongguancun Academy

Abstract

Ensemble weather forecasts can look reliable in global averages while hiding too little spread in some cases and too much in others. These errors vary across variables, spatial scales, lead times, and weather states. Adapting randomness during forecasting can correct these errors, but training fixes stochastic behavior beforehand and output calibration acts afterward. Inference guidance also acts during forecasting, but typically scores ensemble members separately rather than the ensemble as a whole. Reliability feedback arrives at the end, and tracing it backward through many chaotic forecast steps is expensive and unstable. We therefore introduce Dynamic and Informed Adjustment of the Native Stochastic Law (DIAL), which controls a frozen model's native stochasticity. DIAL learns from past forecasts to predict whether each variable and scale needs more or less spread. As a forecast develops, it estimates how possible noise changes will affect later forecast accuracy and reliability. It combines these predictions to make small noise updates at each step. This loop avoids retraining the weather model and full backpropagation through the forecast. We evaluate DIAL on FourCastNet 3 (FCN3) using later ERA5 years unseen during training. DIAL provides better scale-resolved reliability than learned postprocessing and reward-based control baselines. Relative to the unmodified Native FCN3 reference, DIAL achieves an 8.27% improvement in the primary multiscale continuous ranked probability score (CRPS).

Figures & tables

Figure 1: Why pooled reliability is insufficient. (a) Aggregation can cancel signed SSR gaps across variables, scales, and leads. (b) Unlike training-time stochasticity or output post-processing, DIAL uses signed reliability demand and forecast-state feedback to adjust the native noise during ensemble generation.

Figure 2: DIAL learns where reliability needs correction and controls native noise as the forecast evolves. (a) Training forecasts and verifying weather reveal signed reliability errors, which define a fixed set of reliability modes. (b) The ideal path law gives more weight to ensemble paths with lower combined forecast and reliability cost. (c) The frozen Estimator uses recent weather history for each variable and scale to predict signed reliability demand for the current case. (d) During forecasting, the Pilot provides the live rollout state and the Q-Critic scores possible native-noise changes. The Controller sends an allowed action to the native-noise Actuator within the remaining KL budget.

Figure 3: Scale- and lead-resolved nMS-afCRPS. (a) DIAL’s relative reduction over KL-PG across the reported fields, bands B1–B8 (largest to smallest), and three lead windows; positive values favor DIAL and $\times$ marks nonpositive cells. (b) Native-relative skill across 28 six-hour leads for DIAL and the strongest output-side and reward-control baselines, shown for Z500, T850, U850, and V850. Lead curves for all reported fields appear in the supplement.

Figure 4: Budget robustness. DIAL and the reward-control baselines use the same validation-frozen ex-ante Path-KL grid. Panels report (a) nMS-afCRPS, (b) pooled reliability

J_{\mathrm{2nd}}/\epsilon_{\rm rel}

, and (c) Native-relative fixed-pair variogram skill. Dotted and dashed lines mark the registered budget and point reliability threshold, respectively.

Method	nMS- afCRPS $\downarrow$	fCRPSS (%) $\uparrow$	RMSE gain (%) $\uparrow$	RMS( $C$ ) $\downarrow$
Native FCN3	1.0000	0.000	0.000	0.4353
Cond-SP	0.9681	2.737	0.018	0.3207
PoET	0.9453	4.824	1.274	0.2491
Gen. postproc.	0.9370	5.913	2.413	0.2278
DRaFT-K-style	0.9345	5.663	1.537	0.2436
KL-PG	0.9320	6.050	1.780	0.2310

Table 1: Aggregate equal-weight ensemble performance. DIAL applies native-noise control across all FCN3 variables, while scores aggregate all eight evaluated fields (

Z

T

U

, and

V

at 500 and 850 hPa). nMS-afCRPS uses

\alpha=0.95

and Native normalization; fCRPSS and RMSE improvement are relative to Native FCN3; RMS(

C

)=0 is ideal.

(A) Forecast-visible information
Variant	nMS- afCRPS $\downarrow$	RMSE gain (%) $\uparrow$	$J_{\mathrm{2nd}}/$ $\epsilon_{\rm rel}$ $\downarrow$	Realized Path-KL
No Estimator	0.9449	1.084	0.874	0.0238
Matched stale-weather	0.9283	1.736	0.719	0.0269
Full DIAL	0.9173	2.117	0.591	0.0259
(B) Control-mechanism failures
Myopic future cost	0.9286	1.423	0.772	0.0246

Table 2: Ablations at the registered Path-KL budget. Panel A tests forecast-visible information; Panel B tests control mechanisms. Ratios are point estimates;

\dagger

marks values above

1

. Formal feasibility uses a one-sided 95% upper confidence bound. Metrics use each row’s final executed kernel.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1: Native-relative nMS-afCRPS skill across all eight fields and 28 six-hour leads. DIAL has the highest lead-averaged skill in every field, while its margin varies with lead. Static-SP is a training-frozen output correction; generative postprocessing has the lowest aggregate nMS-afCRPS among output-side comparators, and KL-PG has the lowest aggregate nMS-afCRPS among generation-time baselines. Positive values favor the displayed method over Native FCN3.

$\beta_{\rm path}$	Realized KL	nMS-afCRPS	$J_{\mathrm{2nd}}/\epsilon_{\rm rel}$	Variogram skill (%)
0.000	0.0000	1.0000	1.480	0.000
0.006	0.0048	0.9603	1.193	0.158
0.012	0.0098	0.9415	0.951	0.361
0.020	0.0165	0.9267	0.728	0.579
0.030	0.0259	0.9173	0.591	0.728
0.045	0.0387	0.9201	0.566	0.214

Appendix

Table S5: DIAL sensitivity across the validation-frozen ex-ante Path-KL grid. The pre-specified

\beta_{\rm path}=0.030

gives the lowest nMS-afCRPS and the highest variogram skill; raising the budget to

0.045

only lowers

J_{\mathrm{2nd}}/\epsilon_{\rm rel}

while degrading both metrics. Other rows are sensitivity points around this registered operating point.

Table 9

Weather Forecasting

Weather forecasting predicts future atmospheric conditions, from local storms to global patterns, using physical models, observations, and machine learning.

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