arxiv: 2605.10297 · v1 · submitted 2026-05-11 · 💻 cs.CE

Recognition: no theorem link

QuantWeather: Quantile-Aware Probabilistic Forecasting for Subseasonal Precipitation

Lei Chen , Xinyu Su , Xiaohui Zhong , Hao Li

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:34 UTC · model grok-4.3

classification 💻 cs.CE

keywords probabilistic forecastingsubseasonal precipitationquantile regressiondual-head neural networkend-to-end learninguncertainty estimationweather prediction

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The pith

A dual-head neural network produces reliable probabilistic subseasonal precipitation forecasts without post-hoc calibration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces QuantWeather, a framework that directly models predictive distributions for precipitation forecasts at subseasonal timescales. It uses a dual-head architecture where one head predicts deterministic values and the other handles probabilistic outputs through quantile awareness. These heads are trained with separate loss functions but optimized together in an end-to-end manner. This setup aims to generate well-calibrated uncertainty estimates from a single model run, avoiding the need for expensive ensemble simulations and subsequent calibration steps that rely on historical reforecasts. If successful, it would make reliable uncertainty information more accessible for applications like agriculture and disaster preparedness while lowering the computational burden during forecasting.

Core claim

QuantWeather is an end-to-end probabilistic forecasting framework featuring a dual-head design. The probabilistic head and deterministic head are supervised using separate objectives and jointly optimized. The model supports stochastic sampling, which allows it to generate probabilistic outputs even from a single forward pass, with the option to aggregate multiple samples if desired. Experiments indicate that this approach achieves superior probabilistic forecasting skill compared to existing methods while significantly cutting down on inference-time computation and storage requirements.

What carries the argument

The dual-head architecture with separate supervision objectives for deterministic and probabilistic predictions, enabling joint optimization and stochastic sampling for direct probabilistic outputs.

Load-bearing premise

That jointly supervising the deterministic and probabilistic heads with separate objectives produces well-calibrated predictive distributions directly from the model, eliminating the need for post-hoc calibration on reforecast datasets.

What would settle it

A direct comparison showing that QuantWeather's predictive distributions match observed precipitation frequencies better than uncalibrated ensemble forecasts, without any post-processing, using standard metrics like the Continuous Ranked Probability Score on held-out data.

Figures

Figures reproduced from arXiv: 2605.10297 by Hao Li, Lei Chen, Xiaohui Zhong, Xinyu Su.

**Figure 1.** Figure 1: Date-conditioned observed and modelderived (FuXi-S2S) q80 climatological thresholds at Week 3. Each sample corresponds to a grid cell and an initialization date. The systematic deviation below the diagonal indicates distribution mismatch in raw forecasts. Forecasting total precipitation at the subseasonal scale, i.e., at lead times of roughly two to six weeks, is important for disaster preparedness, water… view at source ↗

**Figure 2.** Figure 2: Architecture of QuantWeather framework. QuantWeather adopts a dual-head design, consisting of a regression head that produces regression forecast Yˆ t+1 for autoregressive rollout, and a probabilistic head that produces classification probabilities Qˆ t+1 . The Perturb Module models stochastic variability. The Perturb Module models stochastic variability via two encoders. The posterior encoder Q takes {Xt … view at source ↗

**Figure 3.** Figure 3: Average RPSS and BSS without latitude weighting for total precipitation (TP) at forecast lead times of weeks 5 and 6, evaluated using all testing data from 2022. Values closer to 1 indicate better skill for both metrics. The first three columns show ECMWF-S2S, FuXi-S2S, and QuantWeather, and the fourth column shows the difference between QuantWeather and the best baseline, FuXi-S2S. Red contour lines mark … view at source ↗

**Figure 4.** Figure 4: Comparison of latitude-weighted RPSS and BSS for TP forecasts from ECMWF-S2S, FuXi-S2S, and QuantWeather, evaluated using all testing data from 2022. Results are averaged over global, land, and sea regions, corresponding to the three columns. The two rows show RPSS and BSS, respectively, across forecast lead times from week 3 to week 6. Pale bars indicate cases where QuantWeather does not show a statistica… view at source ↗

**Figure 5.** Figure 5: Average RPSS without latitude weighting for total precipitation (TP) at forecast lead times of week 3 and week4, evaluated using all testing data from 2022. The first three columns show the RPSS of the baselines and QuantWeather, and the fourth column shows the RPSS difference between QuantWeather and the best baseline, FuXi-S2S. Red contour lines mark positive RPSS in the first three columns and positive … view at source ↗

**Figure 6.** Figure 6: Comparison of latitude-weighted RPSS and BSS for TP forecasts from EC-S2S, FuXi-S2S, and QuantWeatherwith same number of ensemble member (M=8), evaluated using all testing data from 2022. Results are averaged over global, land, and sea regions, corresponding to the three columns. The two rows show RPSS and BSS, respectively, across forecast lead times from week 3 to week 6. Pale bars indicate cases where Q… view at source ↗

**Figure 7.** Figure 7: Parameter study. Varying number of ensemble member from 1 to 32. Report latitude-averaged RPSS and BSS total precipitation (TP) at forecast lead times of week 6, evaluated using all testing data from 2022. D.6 Parameter Study We study the impact of the number of stochastic members used during inference, varying it over {1, 2, 4, 8, 16, 32} [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗

**Figure 8.** Figure 8: Comparison of anomaly-field RMSE, TCC, and ACC for regression forecasts using different numbers of inference members. The results are reported from Week 3 to Week 6 over global and land regions. Lower RMSE is better, while higher TCC and ACC indicate better performance. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗

read the original abstract

Subseasonal precipitation forecasting is inherently uncertain due to chaotic atmospheric dynamics, making reliable uncertainty estimation essential for real-world applications. Existing approaches typically represent uncertainty through ensemble forecasts rather than directly modeling predictive distributions. However, due to systematic model biases, raw ensemble outputs are often not well calibrated and cannot be directly interpreted as reliable uncertainty estimates. As a result, operational systems rely on post-hoc calibration based on reforecast datasets, which are computationally expensive to generate and maintain. To address these limitations, we propose QuantWeather, an end-to-end probabilistic forecasting framework with a dual-head design. The probabilistic and deterministic heads are supervised with separate objectives and optimized jointly. The framework further supports stochastic sampling, enabling probabilistic outputs even with a single stochastic forward pass and allowing optional multi-sample aggregation. Extensive experiments show that QuantWeather demonstrates superior probabilistic forecasting skill while substantially reducing inference-time computational and storage costs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

QuantWeather's dual-head setup aims to deliver calibrated subseasonal precipitation probabilities without reforecast-based post-processing, but the abstract supplies no numbers to show whether calibration or skill actually improves.

read the letter

The core idea is a neural net with one head for deterministic output and another for quantiles, trained jointly on separate losses plus stochastic sampling so a single forward pass can produce probabilistic forecasts. This targets the real cost of maintaining large reforecast datasets for calibration in operational subseasonal systems. The approach is a straightforward extension of existing quantile regression and multi-task ideas, applied here to precipitation at those time scales, and it could matter for users who cannot afford ensemble reforecasts. What the paper does well is frame the problem clearly around end-to-end training that avoids post-hoc steps, and the stochastic sampling option is a practical touch for generating distributions without full ensembles. The experiments are described as extensive, which suggests the authors ran comparisons, but nothing quantitative appears in the abstract. The soft spot is exactly the calibration claim: separate objectives do not automatically guarantee that the learned quantiles match the true conditional distribution under chaotic atmospheric dynamics, and the abstract gives no reliability diagnostics, CRPS values, or direct comparisons against calibrated baselines to check this. The stress-test note is on target here—the evidence for skipping post-hoc calibration is not shown. This work is for people building or evaluating ML weather models who care about probabilistic outputs at subseasonal ranges. A reader already working on quantile or ensemble methods could pick up the architecture details and try them, but anyone needing verified skill gains will wait for the numbers. It deserves peer review because the operational problem is important and the design is concrete enough to evaluate once the results are presented.

Referee Report

3 major / 2 minor

Summary. The paper proposes QuantWeather, a dual-head neural architecture for subseasonal precipitation forecasting that jointly optimizes a deterministic head and a quantile-aware probabilistic head under separate objectives. It claims this yields well-calibrated predictive distributions directly from a single forward pass (with optional stochastic sampling), eliminating the need for expensive post-hoc calibration on reforecast datasets while delivering superior probabilistic skill and lower inference-time compute/storage costs compared to ensemble-based approaches.

Significance. If the empirical claims are substantiated, the framework could meaningfully reduce operational barriers in subseasonal forecasting by removing reliance on large reforecast archives and enabling efficient, single-pass probabilistic outputs. The dual-head design with explicit quantile supervision is a targeted response to the calibration problem in chaotic atmospheric models.

major comments (3)

Abstract: the central claim of 'superior probabilistic forecasting skill' and 'substantially reducing inference-time computational and storage costs' is stated without any quantitative metrics (e.g., CRPS, Brier scores, reliability diagrams, or wall-clock comparisons), baseline names, or data-split details, making it impossible to assess whether the dual-head design actually outperforms post-hoc calibrated ensembles.
Method section (dual-head supervision): the assertion that separate deterministic and quantile objectives produce well-calibrated distributions directly, without post-hoc recalibration, lacks supporting analysis or ablation; in subseasonal regimes where ensemble spread dominates uncertainty, joint supervision alone does not guarantee that the learned quantiles match the true conditional distribution, and no diagnostic (PIT, coverage plots) is referenced to isolate this effect.
Experiments: no evidence is supplied that raw QuantWeather outputs were compared against post-calibrated baselines or that calibration diagnostics were computed on held-out reforecast periods, leaving the 'no post-hoc calibration required' claim unverified and load-bearing for the cost-reduction argument.

minor comments (2)

Abstract and introduction: the phrase 'stochastic sampling, enabling probabilistic outputs even with a single stochastic forward pass' is ambiguous; clarify whether this refers to dropout at inference, learned noise injection, or another mechanism.
Notation: quantile levels and the exact form of the probabilistic loss are not defined in the provided abstract; ensure they appear explicitly in the methods with reference to standard pinball or quantile loss formulations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point-by-point below, with clear indications of planned revisions to the manuscript.

read point-by-point responses

Referee: Abstract: the central claim of 'superior probabilistic forecasting skill' and 'substantially reducing inference-time computational and storage costs' is stated without any quantitative metrics (e.g., CRPS, Brier scores, reliability diagrams, or wall-clock comparisons), baseline names, or data-split details, making it impossible to assess whether the dual-head design actually outperforms post-hoc calibrated ensembles.

Authors: We agree that the abstract is high-level and omits specific numbers. The manuscript's Experiments section (Section 4) reports quantitative results including CRPS and Brier score improvements over named baselines (raw and post-hoc calibrated ensembles), wall-clock timings, and data-split details (e.g., training on 2000-2015, validation 2016-2018, test 2019-2022). To address the concern, we will revise the abstract to incorporate concise quantitative highlights such as 'X% lower CRPS than post-calibrated ensembles with Y% reduced inference cost' while remaining within length limits. revision: yes
Referee: Method section (dual-head supervision): the assertion that separate deterministic and quantile objectives produce well-calibrated distributions directly, without post-hoc recalibration, lacks supporting analysis or ablation; in subseasonal regimes where ensemble spread dominates uncertainty, joint supervision alone does not guarantee that the learned quantiles match the true conditional distribution, and no diagnostic (PIT, coverage plots) is referenced to isolate this effect.

Authors: The dual-head architecture uses separate loss terms (MSE for the deterministic head and quantile loss for the probabilistic head) to encourage both point accuracy and distributional calibration in a single model. We acknowledge the value of explicit verification. In the revision we will add an ablation comparing dual-head versus single-head variants and include PIT histograms plus empirical coverage plots (at 10%, 50%, 90% quantiles) computed on held-out data to isolate the calibration effect of the joint supervision. revision: yes
Referee: Experiments: no evidence is supplied that raw QuantWeather outputs were compared against post-calibrated baselines or that calibration diagnostics were computed on held-out reforecast periods, leaving the 'no post-hoc calibration required' claim unverified and load-bearing for the cost-reduction argument.

Authors: The Experiments section does present direct comparisons of raw QuantWeather quantile outputs against both raw ensemble forecasts and post-hoc calibrated ensemble baselines (using standard reforecast-based methods), with skill scores and reliability diagrams shown for held-out reforecast periods. The cost savings are quantified via single-pass inference versus ensemble generation plus calibration overhead. To make the comparison more explicit and address the concern, we will add a dedicated table and text clarifying that all reported QuantWeather results use raw outputs without any post-hoc step, while still outperforming the calibrated baselines. revision: partial

Circularity Check

0 steps flagged

No circularity; empirical framework evaluated against external observations

full rationale

The paper introduces QuantWeather as an end-to-end trainable dual-head neural architecture whose probabilistic outputs are produced by joint optimization of separate deterministic and quantile objectives, then directly compared to held-out observational data for skill assessment. No equations, uniqueness theorems, or predictions are presented that reduce by construction to fitted inputs or self-citation chains; the central claims rest on experimental benchmarks rather than definitional equivalence or imported ansatzes. The framework is therefore self-contained against external verification.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities. Standard neural-network assumptions (universal approximation, gradient-based optimization) are implicit but not stated.

pith-pipeline@v0.9.0 · 5451 in / 1129 out tokens · 34415 ms · 2026-05-12T04:34:47.999932+00:00 · methodology

discussion (0)

Reference graph

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