Nowcast3D: Reliable precipitation nowcasting via gray-box learning (2511.04659v1)

Abstract: Extreme precipitation nowcasting demands high spatiotemporal fidelity and extended lead times, yet existing approaches remain limited. Numerical Weather Prediction (NWP) and its deep-learning emulations are too slow and coarse for rapidly evolving convection, while extrapolation and purely data-driven models suffer from error accumulation and excessive smoothing. Hybrid 2D radar-based methods discard crucial vertical information, preventing accurate reconstruction of height-dependent dynamics. We introduce a gray-box, fully three-dimensional nowcasting framework that directly processes volumetric radar reflectivity and couples physically constrained neural operators with datadriven learning. The model learns vertically varying 3D advection fields under a conservative advection operator, parameterizes spatially varying diffusion, and introduces a Brownian-motion--inspired stochastic term to represent unresolved motions. A residual branch captures small-scale convective initiation and microphysical variability, while a diffusion-based stochastic module estimates uncertainty. The framework achieves more accurate forecasts up to three-hour lead time across precipitation regimes and ranked first in 57\% of cases in a blind evaluation by 160 meteorologists. By restoring full 3D dynamics with physical consistency, it offers a scalable and robust pathway for skillful and reliable nowcasting of extreme precipitation.

• The paper introduces a hybrid physics-guided deep learning model integrating 3D radar data with explicit advection, diffusion, and microphysical decomposition for improved precipitation nowcasting.
• It utilizes a dual-branch conditional diffusion ensemble to refine deterministic forecasts with statistically calibrated probabilistic uncertainties.
• Evaluation using metrics like CSI, PSD, and LPIPS shows significant improvements over traditional methods, demonstrating both accuracy and operational viability.

Technical Summary of "Nowcast3D: Reliable precipitation nowcasting via gray-box learning"

Conceptual Framework

"Nowcast3D" presents a hybrid, physics-guided deep learning architecture for precipitation nowcasting, utilizing volumetric (3D) radar reflectivity data to address limitations in both numerical weather prediction (NWP) and purely data-driven approaches. The model achieves spatiotemporal high fidelity and extended lead times through an explicit decomposition of reflectivity evolution into three physically interpretable processes: advection by 3D wind fields, local stochastic diffusion, and microphysical tendencies. A deterministic physics-informed neural operator predicts these contributions, which are then further refined and ensembled using a dual-branch conditional diffusion model. This architecture enables statistically calibrated probabilistic forecasts while maintaining strict physical consistency throughout the forecast horizon.

Figure 1: Schematic decomposition and system architecture; advection, diffusion, and microphysical effects are dynamically predicted, forming a physically constrained core which conditions ensemble generation via a diffusion model.

Physical Decomposition and Neural Operator Design

At the core, Nowcast3D employs an advection-diffusion-source PDE:

$$\frac{\partial R}{\partial t} = -\boldsymbol{v}\cdot\nabla R + \boldsymbol{\kappa}\nabla^2 R + s$$

where $R$ is radar reflectivity, $\boldsymbol{v}$ is the velocity field reconstructed via Helmholtz decomposition (scalar potential $\varphi$, vector potential $\psi$), $\boldsymbol{\kappa}$ is a spatially varying, anisotropic diffusivity tensor inferred from input sequences, and $s$ is a residual source term modeling unresolved microphysical effects. The model uses a shared encoder with parallel U-Net and Transformer branches to extract latent spatiotemporal features, followed by specialized decoders for each physical field.

Figure 2: Model architecture overview; shared encoder, parallel branches, and decoders for latent motion, diffusion, and source fields.

Forward integration is performed using operator splitting, with semi-Lagrangian advection and Monte Carlo stochastic diffusion steps, as per:

$$R_{t+1}(x) \approx \frac{1}{M}\sum_{m=1}^M R_t(x-\boldsymbol{v}_t(x)\Delta t+\eta^{(m)}_t(x)) + s_t(x)\Delta t$$

where $$\eta^{(m)}_t(x) \sim \mathcal{N}(0, 2\boldsymbol{\kappa}_t(x)\Delta t)$$, echoing Brownian-inspired hydrometeor dispersion.

Conditional Diffusion Ensemble Generator

The deterministic forecast is refined probabilistically using a conditional diffusion model with a dual output: one branch generates the structural field, and another models residual error relative to the physics-consistent prediction. Contextual features are extracted by ContextNet from both historical data and the deterministic prediction, guiding the denoising process in the Condition GenNet U-Net.

Figure 3: Architectural details of the dual-branch conditional diffusion model for ensemble forecast generation.

Each ensemble member is computed by independently sampling the noise process, with three meaningful forecast types constructed:

1. Direct structural field output,
2. Physics-corrected field (adding residual to deterministic prediction),
3. Hybrid linear combination.

This allows calibrated probabilistic uncertainty representation while remaining physically constrained.

Forecast Evaluation and Quantitative Results

The system was evaluated on both coarse (0.04°) and fine (0.01°) resolution datasets covering diverse convective regimes in China, against pySTEPS (physics-based extrapolation), NowcastNet (2D hybrid/generative baseline), and SimVP (video prediction). Evaluation metrics included CSI at multiple thresholds for event localization, PSD for scale fidelity, LPIPS for perceptual similarity, and direct wind field validation with radar profiler data.

Notable results:

• Nowcast3D consistently achieved the highest CSI across lead times and reflectivity thresholds, outperforming all baselines, especially in tracking intense events.
• PSD and LPIPS analyses show Nowcast3D forecasts preserve both physical scale variance and visual realism more accurately than competing models (Figures 2, 3, 4).
• Ensemble calibration assessed via CRPS demonstrates superior reliability versus other diffusion-based approaches.
• Wind field reconstruction closely matches profiler radar observations within precipitating volumes, validating the physical interpretability of the learned dynamics (Figure 4).
• Blind evaluation by 160 meteorologists preferred Nowcast3D in 57% of post-hoc and 51% of prior tests, with strong preference robustness across regions.

  Figure 5: Forecast performance for a severe Beijing mesoscale convective event; Nowcast3D maintains morphological integrity and intensity, improving CSI, LPIPS, and scale accuracy.

  

  Figure 6: Finer-scale generalization in Maoming event; Nowcast3D tracks rapid convective expansion and translation, outperforming baselines on all metrics and ensemble calibration.

  

  Figure 7: Aggregate skill evaluation; Nowcast3D demonstrates superiority across CSI, PSD, and LPIPS at both resolutions, with expert meteorologist preference.

  

  Figure 4: Wind field calculation methodology and evaluation; predicted velocities validated vs profiler observations using spatiotemporal averaging.

Implementation and Computational Considerations

Training was performed on 4 × NVIDIA A800 GPUs using Adam optimizer and deep supervision across operator-split stages. Inference and ensemble generation leverage parallelized Monte Carlo sampling for stochastic diffusion, and U-Net/Transformer component architectures are structured for scalable volumetric data processing. The pipeline generalizes across resolutions (provincial to urban), with transfer/fine-tuning procedures shown feasible for new domains.

The primary computational bottleneck is ensemble sampling in the dual-branch diffusion model, which can be mitigated by limiting ensemble size or distributed rollout. Real-time deployment in operational nowcasting centers is tractable given recent advances in GPU inference and radar data streaming, and the model architecture is amendable to multi-modal augmentation (e.g., adding Doppler velocity or satellite inputs).

Discussion and Future Directions

Nowcast3D advances reliable precipitation nowcasting by restoring full 3D physical dynamics in deep learning models, combining interpretable deterministic core evolution with calibrated probabilistic generation. The architecture maintains physical consistency via direct parameterization of advection, diffusion, and microphysical processes, facilitating expert trust and scientifically meaningful uncertainty quantification.

Limitations include dependence on radar scan quality/coverage, residual underdetermination in inferring velocity fields from reflectivity alone (especially in microphysical dominance scenarios), and error propagation under beam attenuation/anomalous propagation. Future progress lies in multi-modal data integration, especially Doppler velocity and satellite imagery, finer coupling with NWP through data assimilation, and extension to multivariate hazard nowcasting (e.g., hail, wind, lightning).

Conclusion

Nowcast3D establishes a robust paradigm for volumetric radar-based precipitation nowcasting, unifying physics-guided operator learning and probabilistic ensemble generation. Strong empirical results, physical interpretability, and operational scalability underscore its value for high-impact weather forecasting. Further integrations with complementary sensor modalities and NWP-driven assimilation strategies will be pivotal to close the predictive gap for extreme convective events.