Shu et al. (2026) Physics-Constrained Deep Learning with Adaptive Z-R Relationship for Accurate and Interpretable Quantitative Precipitation Estimation

⚠️ Warning: This summary was generated from the abstract only, as the full text was not available.

Identification

• Journal: Remote Sensing
• Year: 2026
• Date: 2026-01-03
• Authors: Ting Ting Shu, Huan Zhao, Kanglong Cai, Zexuan Zhu
• DOI: 10.3390/rs18010156

Research Groups

Not explicitly mentioned in the provided text.

Short Summary

This paper proposes FusionQPE, a novel Physics-Constrained Deep Learning framework that integrates an adaptive Z-R formula to improve quantitative precipitation estimation (QPE) from radar reflectivity, demonstrating superior accuracy, robustness, and interpretability compared to conventional and state-of-the-art deep learning methods.

Objective

• To develop a robust and interpretable deep learning framework for quantitative precipitation estimation (QPE) that overcomes the limitations of empirical Z-R relationships and the lack of physical constraints in existing deep learning models, thereby enhancing estimation accuracy and generalization across different precipitation regimes.

Study Configuration

• Spatial Scale: Regional scale, specifically using radar and rain gauge observations from Guangzhou, China.
• Temporal Scale: Relevant for weather nowcasting, implying continuous, short-term estimation.

Methodology and Data

• Models used: FusionQPE, comprising a DenseNet backbone, a modified Squeeze-and-Excitation (SE) network for adaptive Z-R parameter learning, and a linear combination of their outputs. A physical-based constraint derived from the Z-R branch output is incorporated into the loss function.
• Data sources: Real radar reflectivity data and corresponding rain gauge observations from Guangzhou, China.

Main Results

• FusionQPE consistently outperforms both traditional Z-R formulas and state-of-the-art deep learning-based QPE models across multiple evaluation metrics.
• The adaptive Z-R branch significantly improves both the physical consistency and credibility of the model's precipitation estimation.
• The trained linear weight and Z-R parameters provide interpretable insights into the model’s physical reasoning.

Contributions

• Introduction of FusionQPE, a novel Physics-Constrained Deep Learning framework for QPE that integrates an adaptive Z-R formula.
• Development of a method to adaptively learn Z-R relationship parameters within a deep learning architecture, enhancing generalization and physical consistency.
• Incorporation of a physical-based constraint into the loss function to strengthen physical consistency and robustness.
• Demonstration of superior performance, robustness, and interpretability compared to existing QPE methods on real-world radar and rain gauge data.

Funding

Not explicitly mentioned in the provided text.

Citation

@article{Shu2026PhysicsConstrained,
  author = {Shu, Ting Ting and Zhao, Huan and Cai, Kanglong and Zhu, Zexuan},
  title = {Physics-Constrained Deep Learning with Adaptive Z-R Relationship for Accurate and Interpretable Quantitative Precipitation Estimation},
  journal = {Remote Sensing},
  year = {2026},
  doi = {10.3390/rs18010156},
  url = {https://doi.org/10.3390/rs18010156}
}