Shen et al. (2026) Regional Calibration of a Statistical Rainfall Retrieval Method for Microwave Links Using Local Probability Distributions

Identification

• Journal: Water
• Year: 2026
• Date: 2026-04-01
• Authors: Leqi Shen, Tao Yang, Yangfan Zhong, Lvfei Zhang, Yvsong Zhang, Jie Tu
• DOI: 10.3390/w18070849

Research Groups

• College of Hydrology and Water Resources, Hohai University, Nanjing, China
• State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Global Change and Water Cycle, Hohai University, Nanjing, China
• China Yangtze Power Co., Ltd. (CYPC), Wuhan, China

Short Summary

This study calibrates a statistical rainfall retrieval method for Commercial Microwave Links (CMLs) in China by incorporating localized Gamma rainfall distribution parameters, demonstrating significantly improved accuracy, especially for high-intensity rainfall events, compared to traditional models.

Objective

• To evaluate and calibrate a probabilistic-statistical rainfall retrieval method for Commercial Microwave Links (CMLs) in the Chinese region by replacing global parameters with a Gamma rainfall distribution derived from local rain gauge observations, aiming to enhance retrieval accuracy, particularly for shorter path lengths and extreme rainfall events.

Study Configuration

• Spatial Scale: Experimental Commercial Microwave Links (CMLs) deployed in Taishun and the Donghu District of Nanchang, China. CML path lengths were 420 m (Taishun), 2.69 km (Nanchang1), and 3.50 km (Nanchang2). Reference rain gauges were located 214 m (Taishun), 3.76 km (Nanchang1), and 4.40 km (Nanchang2) from their respective links. Localized Gamma distribution parameters were derived from 65 meteorological stations across China.
• Temporal Scale: CML signal level measurements were recorded at 10 s sampling intervals. Rain gauge data had a 1 min resolution for Taishun and hourly resolution for Nanchang. The study analyzed 30 rainfall events in Taishun (May 2021) and 14 events for each Nanchang link (2021). Wet antenna attenuation correction used a variation rate parameter of 15 min.

Methodology and Data

• Models used:
  • PL model: Traditional power-law model (Olsen et al., 1978).
  • FM model: Probabilistic model by Moupfouma (1983, 1985) using universal parameters.
  • ITU530 model: Proposed probabilistic model, a calibration of Zheng et al. (2023)'s framework, incorporating localized Gamma rainfall distribution parameters derived by Huang Jie et al. (1991) for China.
  • Wet antenna attenuation (WAA) correction: Dynamic model by Schleiss et al. (2013).
• Data sources:
  • Experimental K-band Commercial Microwave Links (CMLs) in Taishun and Nanchang, China.
  • High-resolution tipping-bucket rain gauges (0.1 mm resolution) as ground truth.
  • Long-term observational data from 65 meteorological stations in China for Gamma distribution parameter derivation.
  • Recommendation ITU-R P.837 for global R0.01 map and mean annual rainfall for R0.01 estimation.

Main Results

• The proposed ITU530 model consistently demonstrated superior performance across all evaluation metrics (Mean Absolute Error (MAE), Normalized Root Mean Square Error (NRMSE), Kling–Gupta Efficiency (KGE), correlation coefficient (R), and coefficient of determination (R^2)).
• The ITU530 model achieved an MAE of 5.07 mm/h, NRMSE of 1.02, KGE of 0.80, and R of 0.85 (R^2 = 0.86).
• Compared to the traditional power-law (PL) model, the ITU530 model reduced MAE by 35%, improved NRMSE by 19%, and more than doubled the KGE, statistically confirming the success of the parameter localization strategy.
• The calibrated method performed particularly well during high-intensity rainfall events, with its advantage diminishing for low-intensity events due to weak signals and noise.
• Retrieval stability was significantly better for the short-path Taishun link (420 m) with high-resolution rain gauge data, highlighting the advantage of short links in addressing the "point-line" scale mismatch.
• An "early peak retrieval" phenomenon was observed in approximately 50% of Taishun events (average lead time of 2.5 min) and 30% of Nanchang2 events (average lead time of approximately 1.3 h, limited by hourly resolution), suggesting CMLs' capability as "line sensors" to capture spatial rainfall dynamics before point gauges.

Contributions

• Calibrated the statistical rainfall retrieval framework proposed by Zheng et al. (2023) for the Chinese region by incorporating localized Gamma rainfall distribution parameters.
• Addressed the critical issue of overestimation in rainfall peak retrieval, with localized parameter calibration achieving a reduction in estimation bias exceeding 30%.
• Introduced an alternative approach for estimating R0.01 from mean annual rainfall, providing a practical solution for regions lacking long-term high-resolution rainfall data.

Funding

• Natural Science Foundation of Tianjin (No. 24JCQNJC00830)
• National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety (524064712)

Citation

@article{Shen2026Regional,
  author = {Shen, Leqi and Yang, Tao and Zhong, Yangfan and Zhang, Lvfei and Zhang, Yvsong and Tu, Jie},
  title = {Regional Calibration of a Statistical Rainfall Retrieval Method for Microwave Links Using Local Probability Distributions},
  journal = {Water},
  year = {2026},
  doi = {10.3390/w18070849},
  url = {https://doi.org/10.3390/w18070849}
}