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PCSDiff: Diffusion-Based Bias Correction and Super Resolution Toward Practical Operational Medium-Term Precipitation Forecast

Yuze Sun, Shiyi Wang, Jiancheng Pan, Die Wang, Andreas F. Prein, Wentao Luo, Linhan Jiang, Jie Wu, Quan Zhang, Xiaomeng Huang

arXiv:2609.06942v1cs.LGcs.AIphysics.ao-ph

TL;DR

Persistent biases and limited predictability in 10-day precipitation forecasts constrain reliable flood-risk and water-resource assessment. PCSDiff combines dynamic multi-day bias correction with diffusion super-resolution; across 3/5/7/10-day leads, it reduces RMSE by 14.8%–16.1% and improves ACC by 6.4%–13.9% versus raw ECMWF forecasts.

  • Problem

    Persistent precipitation biases and limited predictability in 10-day forecasts make accurate precipitation correction important for flood-risk assessment and water-resource management over China.

    Source: Introduction · p. 1

  • Method

    PCSDiff applies PIMD-based dynamic multi-day bias correction followed by two-phase conditional-diffusion super-resolution, using meteorological and terrain cues.

    Source: Introduction · p. 2

  • Results

    Compared with raw ECMWF outputs, RMSE decreases by 14.8%–16.1% and ACC improves by 6.4%–13.9% across 3/5/7/10-day lead times.

    Source: Quantitative Result · p. 4

  • Takeaways & Limitations

    The streaming inference pipeline supports low-latency deployment in practical operational precipitation forecasting workflows.

    Source: Introduction · p. 2

    The authors identify physically implausible precipitation artifacts as a remaining issue and plan to strengthen physical constraints in diffusion generation.

    Source: Conclusion and Future Work · p. 6

Abstract

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Medium-range precipitation forecasts are impaired by persistent systematic biases, lead-time-dependent error accumulation, and coarse spatial resolution, restricting their reliability for flood-drought risk assessment. Existing AI correction techniques lack dedicated modeling for multi-day dynamic bias evolution and proper meteorological constraints, often generating over-smoothed rainfall structures, and cannot meet operational deployment demands. This work introduces PCSDiff, a cascaded task-decoupled diffusion framework targeting 10-day precipitation bias correction and downscaling. To jointly counteract temporal error drifts and reconstruct physically plausible local precipitation details, PCSDiff integrates the Precipitation Intensity-aware Multi-branch Decoder (PIMD) module for dynamic multi-day error mitigation using synoptic-temporal features, followed by a two-phase conditional diffusion super-resolution module to restore fine-scale precipitation patterns. Evaluated against CMA-CRA observations over China after global-data training, PCSDiff cuts RMSE by 16.1% and lifts ACC by 13.9% relative to raw ECMWF forecasts at 3-10-day lead times, and consistently outperforms mainstream deep-learning baselines on both general and extreme-precipitation metrics. Benefiting from a streaming inference pipeline, our method achieves low-latency rolling forecasting for practical meteorological operations.

Introduction

PCSDiff targets 10-day precipitation bias correction and spatial downscaling over China with a cascaded, task-decoupled diffusion framework. It combines dynamic multi-day correction, fine-scale reconstruction, global-data training with Chinese regional validation, and an operational streaming inference pipeline.

Introduction

  • Prior precipitation-correction approaches include static CNNs, spatiotemporal models, GANs, and diffusion models for spatial refinement, temporal evolution, and rainfall-texture reconstruction.The passage cites U-Net (Ronneberger, Fischer, and Brox 2015), U²-Net, and other examples across these model families.Source: Introduction · p. 1
  • Existing methods often miss daily rainband evolution, over-smooth rainfall without meteorological constraints, and lack continuous 10-day operational evaluation or feasible deployment pipelines.Static statistical correction also cannot model continuous spatiotemporal precipitation evolution, contributing to cumulative forecast errors.Source: Introduction · pp. 1–2
  • PCSDiff cascades a PIMD-based module for dynamic multi-day precipitation bias correction with conditional diffusion super-resolution to reconstruct fine-scale precipitation patterns.The correction module handles varied atmospheric and precipitation-intensity conditions.Source: Introduction · p. 2
  • Global meteorological-data training, meteorological and terrain cues, and Chinese regional validation target generalizable performance on conventional and extreme precipitation.The paper describes these choices as intended to mitigate overfitting and stabilize performance.Source: Introduction · p. 2
  • An optimized streaming inference scheme enables low-latency deployment for practical operational precipitation forecasting workflows.The framework is presented as supporting efficient forecasting in real operational scenarios.Source: Introduction · p. 2

Method: PCSDiff

PCSDiff separates 10-day precipitation bias correction from super-resolution, using synoptic and terrain priors to constrain both stages and a deployment-oriented inference pipeline. Its first stage corrects lead-time-dependent biases, while the second reconstructs high-resolution precipitation details.

Stage 1: PIMD-based Dynamic Multi-Day Bias Correction Module

  • The PIMD module combines synoptic context and LSTM-based temporal embeddings with light-, moderate-, and heavy-rain branches to correct evolving multi-day biases.An intensity fusion layer merges the branches into the corrected low-resolution precipitation field.Source: Stage 1: PIMD-based Dynamic Multi-Day… · pp. 2–3

Method: PCSDiff

  • PCSDiff chains PIMD-based low-resolution bias correction with two-phase diffusion super-resolution to produce high-resolution precipitation fields.Synoptic circulation and terrain priors guide both stages toward meteorological plausibility.Source: Method: PCSDiff · p. 2, Figure 1 · p. 3

Stage 2: Regression-DDIM-based Super Resolution Module

  • The super-resolution stage first regresses large-scale precipitation priors, then uses conditional DDIM diffusion to reconstruct residual fine-scale details.Deterministic DDIM sampling with η = 0, a learnable detail gate, and coarse-grid consistency projection help preserve large-scale patterns.Source: Stage 2: Regression-DDIM-based Super… · p. 3

Deployment-Oriented Inference Pipeline.

  • The inference pipeline streams Stage 1 outputs directly to super-resolution without intermediate disk I/O and allows sampling steps to trade generation speed for quality.It supports batch ensemble inference, on-the-fly input normalization, and post-processing that clips negative precipitation while preserving ensemble statistics.Source: Deployment-Oriented Inference Pipeline · pp. 3–4

Data and Experimental Setup

The experiments use global ECMWF forecasts and CMA-CRA precipitation data from 2004–2024, with global training and evaluation over mainland China. Chronological splits, stage-wise optimization, and numerical, temporal, extreme-event, and spatial metrics define the evaluation setup.

Data.

  • The study uses 2004–2024 ECMWF forecasts at 1.5° and 0.25° CMA-CRA precipitation data, training globally and evaluating 10-day heavy-precipitation correction and downscaling over mainland China.Inputs include total precipitation, atmospheric variables, and terrain elevation.Source: Data · p. 4

Training and Inference Configurations.

  • Chronological training and test sets prevent temporal leakage; PCSDiff uses stage-wise optimization with separate loss configurations for PIMD, regression super-resolution, and conditional diffusion.Stage 1 combines MSE, TP losses, and PIMD entropy regularization; Stage 2 uses intensity-weighted Smooth L1 with gradient regularization for regression and a composite diffusion objective.Source: Training and Inference Configurations · p. 4

Evaluation Indicators.

  • Evaluation uses RMSE, MAE, ACC, and TP for numerical accuracy and temporal correlation, plus CSI and FSS for extreme-event detection and fine-scale spatial patterns.The metric definitions and formulas are provided in the Appendix.Source: Evaluation Indicators · p. 4

Experiments and Results

PCSDiff is evaluated for 10-day precipitation bias correction and downscaling over China using quantitative comparisons, heavy-rainfall case visualizations, and ablations. Results show improved skill versus raw ECMWF forecasts, physically plausible high-resolution rainfall reconstruction, and gains from the model’s key design choices.

Quantitative Result.

  • Against raw ECMWF, PCSDiff reduces RMSE by 14.8%–16.1% and improves ACC by 6.4%–13.9% across lead times.It also improves heavy-precipitation CSI and FSS; baselines that lower RMSE over-smooth rainfall and degrade threshold-dependent metrics, especially for extremes. The reported gains are attributed to explicit precipitation-event constraints, PIMD-driven dynamic bias correction, and multi-stage optimization.Source: Quantitative Result · p. 4, Table 1 · p. 5, Figure 2 · p. 5

Qualitative Visualization of Typical Heavy Precipitation Events.

  • Across heavy-rainfall cases and lead times, PCSDiff’s two-phase pipeline reconstructs physically plausible high-resolution precipitation fields that closely match observations.Raw ECMWF forecasts have blurred boundaries, missing small rain centers, and spatial artifacts; low-resolution correction mitigates large-scale biases, while super-resolution restores fine-scale orographic features and localized heavy-rain structures.Source: Qualitative Visualization of Typical… · pp. 4–5

Ablation Study.

  • Ablations show that removing or modifying PIMD, the loss formulation, or input-variable choices reduces numerical accuracy, temporal correlation, and extreme-precipitation detection.The authors conclude these designs jointly support robust medium-range forecasting; further ablations on diffusion sampling steps, training strategies, and hyperparameters are reported in the Appendix.Source: Ablation Study · p. 5

Practical Deployment and Emerging · Application Analysis

PCSDiff is designed to bridge the gap between offline precipitation-model evaluation and operational rolling forecasts through a deployment-oriented pipeline. Its gridded products are presented as useful for disaster-risk, water-management, and public weather-service applications.

Application Analysis.

  • Most existing precipitation-correction models emphasize offline evaluation and case studies, leaving a gap between academic prototypes and operational meteorological services.Figure 3 presents three heavy-rainfall cases, showing raw ECMWF forecasts, low-resolution bias-corrected output, super-resolution results, and CMA-CRA ground truth.Source: Application Analysis · p. 5, Figure 3 · p. 6
  • The section frames PCSDiff’s deployability and practical strengths as responses to operational engineering requirements for continuous rolling medium-range forecasting.Source: Application Analysis · p. 5

Practical Deployment Barriers of Current Forecasting Models.

  • Current AI precipitation methods face incompatibility with 10-day rolling workflows, inefficient inference from non-decoupled architectures, and incomplete offline-to-operational porting workflows.Source: Practical Deployment Barriers of… · p. 6

Deployment-Oriented Pipeline of PCSDiff.

  • PCSDiff’s lightweight, portable cascaded architecture supports offline training through rolling batch inference, using in-memory tensor streaming to remove intermediate disk I/O.Decoupled modules require one-time pre-training and support low-cost parallel inference for stable continuous precipitation product generation.Source: Deployment-Oriented Pipeline of PCSDiff · p. 6
  • PCSDiff is tailored for operational medium-range precipitation forecasting, using a lightweight, portable cascaded architecture and supporting an engineering workflow from offline training through rolling batch inference.Its in-memory tensor-streaming design removes intermediate disk I/O overhead; decoupled modules enable one-time pre-training and low-cost parallel inference for stable continuous precipitation product generation.Source: Deployment-Oriented Pipeline of PCSDiff · p. 6

Practical Application Value and Representative Use-Cases.

  • PCSDiff’s high-precision gridded precipitation products are proposed for flood-drought early warning, water-resource management, and public-oriented weather services.Examples include basin-scale flood assessment, flash-flood pre-warning, seasonal drought monitoring, reservoir scheduling, and cross-basin allocation.Source: Practical Application Value and… · p. 6

Conclusion and Future Work

PCSDiff combines multi-day precipitation bias correction with diffusion-based spatial downscaling, achieving competitive precipitation metrics and enabling low-latency operational forecasting. Future work targets more physically constrained generation, broader forecasting tasks, and practical deployment.

Conclusion

  • PCSDiff achieves competitive general- and extreme-precipitation performance against raw forecasts and mainstream AI baselines after global-dataset training and validation on CMA-CRA observations.The framework targets 10-day medium-range precipitation bias correction and spatial downscaling over China.Source: Conclusion and Future Work · p. 6
  • Its PIMD-based dynamic multi-day bias correction and two-phase super-resolution diffusion modules mitigate cumulative forecast errors and reconstruct physically consistent fine-scale precipitation patterns.Source: Conclusion and Future Work · p. 6
  • An optimized streaming inference pipeline enables low-latency migration to operational forecasting systems for drought-flood disaster prevention applications.Source: Conclusion and Future Work · p. 6

Future Work

  • Future work will add stronger physical constraints to diffusion generation, extend forecasting jointly to temperature, humidity, and wind, and develop compressed lightweight variants with accelerated sampling.Source: Conclusion and Future Work · p. 6
  • Planned deployment work includes domain-adaptive fine-tuning for rare extreme weather and real-time offline trial runs with meteorological agencies.Source: Conclusion and Future Work · p. 6

Appendix · Table

The appendix tables document baseline comparisons, component ablations, ECMWF input variables, and implementation configurations for PCSDiff. The captions specify the forecast leads and regions covered but do not provide metric values or identify a winning method.

Appendix · Table

  • Table S1 compares baseline methods at 7- and 10-day forecast lead times over China.Source: Table S1 · p. 8
  • The appendix lists ECMWF ensemble input meteorological variables and dataset and hardware configurations.Source: Table S2 · p. 8, Table S7 · p. 11
  • Table S3 reports ablations of PCSDiff key components over China at 3- and 5-day lead times.Source: Table S3 · p. 8
  • Table S4 reports ablations of PCSDiff key components over China at 7- and 10-day lead times.Source: Table S4 · p. 9
  • Table S5 specifies the training hyperparameters for Stage 1.Source: Table S5 · p. 9
  • Table S6 specifies the training hyperparameters for Stage 2.Source: Table S6 · p. 10

Evaluation Metrics

The evaluation metrics assess precipitation magnitude errors, anomaly consistency, categorical event skill, and spatial pattern realism. Metrics are computed at individual grid points and aggregated over the Chinese mainland domain.

Evaluation Metrics

  • RMSE measures overall forecast error magnitude and MAE mean absolute deviation; lower values for both indicate more accurate precipitation forecasts.RMSE indicates numerical accuracy, while MAE measures precipitation-magnitude deviation.Source: Evaluation Metrics · p. 12
  • ACC measures temporal correlation of precipitation anomalies relative to climatological means, with higher values indicating more consistent precipitation variation.The reference means are the climatological means of forecast and observed precipitation.Source: Evaluation Metrics · p. 12
  • At the 1 mm/day threshold, TS1 uses hits, false alarms, and misses to measure threat score for general-rain events.The contingency table classifies hits, misses, false alarms, and correct negatives by whether observed and forecast precipitation exceed the threshold.Source: Evaluation Metrics · p. 12, Table S8 · p. 12
  • The heavy-rain threat score uses a local-climatology threshold clamped to 3 mm/day; TP combines general- and heavy-rain skill with categorical accuracy across weighted 1–10-day leads.The heavy-rain score rewards well-predicted heavy-precipitation regions, and larger TP indicates better forecast performance.Source: Evaluation Metrics · pp. 12–13
  • CSI, also called Threat Score, measures categorical precipitation-event skill, with higher values indicating better categorical prediction.Source: Evaluation Metrics · p. 13
  • FSS assesses neighborhood precipitation-pattern similarity, penalizes rainband displacement, and ranges from 0 to 1, with higher values indicating more realistic spatial structures.All metrics are computed on individual grid points and aggregated over the Chinese mainland domain.Source: Evaluation Metrics · p. 13

Implementation Details of the Deployment-Oriented Inference Pipeline … Comparison with Real-World AI-Enhanced Weather Systems

PCSDiff’s deployment pipeline streams bias-corrected forecasts directly into configurable diffusion super-resolution, with post-processing and reusable components for rolling operational forecasts. Reduced-step sampling enables a lower-latency mode with limited spatial-skill degradation, while the framework is positioned as an open alternative to commercial AI-weather services whose internal methods are undisclosed.

Hardware and Software Environment

  • Inference tests use an NVIDIA RTX 4090 / A100 GPU with 40 GB memory, PyTorch 2.1, CUDA 12.1, and FP32 by default, with optional FP16.The appendix reports a single consumer-grade GPU test platform.Source: Hardware and Software Environment · p. 14

Implementation Details of the Deployment-Oriented Inference Pipeline; Inference Pipeline Configuration

  • The four-stage pipeline preprocesses inputs, applies PIMD bias correction, performs two-phase diffusion super-resolution, and physically constrains outputs.Normalization is computed on-the-fly; DDIM uses 50 steps for offline high-fidelity evaluation or 10 for accelerated operations, with η = 0, while post-processing clips negative precipitation and rescales ensemble mean and variance.Source: Inference Pipeline Configuration · p. 14

Performance Test Settings

  • Tests use ECMWF 10-day ensemble forecasts at 1.5° resolution, downscaled to 0.25°, on 2022–2024 samples separated from training.Both single-member and multi-member batch inference are tested.Source: Performance Test Settings · p. 14

Inference Latency and Memory Footprint

  • Reduced-step sampling greatly reduces inference time with limited spatial forecast-skill degradation, while in-memory streaming avoids disk I/O and storage overhead.Table S9 summarizes end-to-end latency and GPU memory use across sampling-step and ensemble-size settings; the reported latency covers raw input through final post-processed output.Source: Table S9 · p. 14, Inference Latency and Memory Footprint · p. 14

Compatibility with NWP operational workflows; Full Workflow of the PCSDiff Deployment-Oriented Pipeline

Additional Details on Model Deployment and Application Analysis; Detailed Analysis of Deployment Bottlenecks; Full Workflow of the PCSDiff Deployment-Oriented Pipeline

  • Existing systems face deployment bottlenecks from discontinuous 10-day validation, coupled correction and downscaling, and missing standardized migration toolchains.PCSDiff’s task-decoupled pipeline streams tensors between bias correction and super-resolution, supports configurable sampling, and applies physical-constrained post-processing.Source: Detailed Analysis of Deployment… · p. 15, Full Workflow of the PCSDiff… · p. 15

Extended Practical and Emerging Application Scenarios

  • High-resolution precipitation products are proposed for hydrological model forcing, agricultural meteorological services, and regional climate-impact research.The listed uses include streamflow simulation for small- and medium-size catchments, fine-scale crop-growth assessment and drought monitoring, and climate-impact and risk research.Source: Extended Practical and Emerging… · p. 15

Comparison with Real-World AI-Enhanced Weather Systems

  • Unlike commercial services such as Google Weather AI, whose internal methods are undisclosed, PCSDiff offers an open, transparent framework for medium-range ensemble precipitation post-processing and secondary development.The paper presents it as an open-source reference for domestically operated high-resolution AI precipitation forecasting systems.Source: Comparison with Real-World AI-Enhanced… · p. 15

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