Feng et al. (2025) Research on Optimizing Rainfall Interpolation Methods for Distributed Hydrological Models in Sparsely Networked Rainfall Stations of Watershed

Identification

• Journal: Water
• Year: 2025
• Date: 2025-11-13
• Authors: Dinggen Feng, Yangbo Chen, Ping Jiang, Jinren Ni
• DOI: 10.3390/w17223237

Research Groups

• School of Geography and Planning, Sun Yat-sen University, Guangzhou, China
• Meizhou Branch, Bureau of Hydrology of Guangdong Province, Meizhou, China
• Anhui & Huaihe River Institute of Hydraulic Research, Bengbu, China

Short Summary

This study optimizes rainfall interpolation methods for distributed hydrological models in sparsely networked rainfall stations of watersheds. It found that the Inverse Distance Weighting (IDW) method significantly outperforms Thiessen Polygon Interpolation (THI) and Trend Surface Interpolation (TSI) for flood forecasting in such conditions, demonstrating superior stability and accuracy.

Objective

• To analyze the distribution characteristics of rainfall stations and the interpolation effectiveness of the original Thiessen Polygon Interpolation (THI) method in the Liuxihe model for the Hezikou basin.
• To compare the applicability of THI, Inverse Distance Weighting (IDW), and Trend Surface Interpolation (TSI) methods in flood forecasting under various rainfall station sparsity scenarios.
• To provide an optimized rainfall interpolation scheme for the Liuxihe Model and similar distributed hydrological models in small and medium-sized basins with sparse rainfall stations.

Study Configuration

• Spatial Scale: Hezikou basin, approximately 1033 square kilometers. Model spatial resolution was set to 90 meters. Rainfall station density was approximately 0.0068 stations per square kilometer (one station per 150 square kilometers).
• Temporal Scale: Rainfall-flood process data collected from 2005 to 2019. Model temporal resolution and calculation time step were set to 1 hour.

Methodology and Data

• Models used: Liuxihe Model (a physically based distributed hydrological model), Particle Swarm Optimization (PSO) algorithm for parameter optimization. Rainfall spatial interpolation methods compared: Thiessen Polygon Interpolation (THI), Inverse Distance Weighting (IDW) with a distance power of 2, and Trend Surface Interpolation (TSI) using a quadratic polynomial.
• Data sources:
  • Digital Elevation Model (DEM) data: Aster GDEM.
  • Land use type data: China Land Use Data from the Joint Research Centre of the European Commission.
  • Soil type data: SOTER (Soil and Terrain) China Soil Database.
  • Rainfall-flood process data: Collected from the Hezikou Watershed for five typical flood events between 2005 and 2019.
  • Rainfall stations: Seven stations within the Hezikou Watershed.
  • Rainfall station distribution scenarios: Full coverage (All), upstream-only (Up), downstream-only (Down), and single station (One).

Main Results

• Under sparse rainfall station conditions (0.0068 stations per square kilometer), the Inverse Distance Weighting (IDW) method yielded the best flood forecasting results.
• For IDW, model Nash–Sutcliffe Efficiency (NSE) values were consistently above 0.85, Kling–Gupta Efficiency (KGE) values exceeded 0.78, and the Peak Relative Error (PRE) was controlled within 0.09.
• IDW significantly outperformed Thiessen Polygon Interpolation (THI) and Trend Surface Interpolation (TSI), with an average NSE of 0.9304 (compared to 0.8706 for THI and 0.8976 for TSI) and an average PRE of 5.28% (compared to 10.8% for THI and 7.06% for TSI).
• As rainfall station sparsity increased, IDW exhibited the smallest decline in performance, demonstrating stronger adaptability to sparse scenarios with a weak negative correlation (p ≤ 0.05) between prediction performance and rainfall station sparsity.
• In single-station scenarios, IDW maintained NSE above 0.85, KGE around 0.78, and PRE at 0.09, while THI and TSI performance deteriorated sharply (e.g., THI NSE dropped below 0.75, TSI KGE dropped below 0.7).
• THI interpolation results showed discrete polygon blocks, failing to reflect gradual spatial rainfall characteristics, especially in sparse scenarios. IDW produced continuous and smooth spatial gradients consistent with terrain-driven rainfall patterns. TSI's global trend fitting led to "false gradients" and rapid deterioration in sparse conditions.

Contributions

• Systematically analyzes the inherent limitations of the Thiessen Polygon Interpolation (THI) method within the Liuxihe Model when applied to watersheds with sparse rainfall station networks.
• Provides a comprehensive comparative study of THI, Inverse Distance Weighting (IDW), and Trend Surface Interpolation (TSI) methods for flood forecasting, specifically addressing the challenges of sparsely gauged small and medium-sized river basins.
• Demonstrates and quantifies the superior adaptability and stability of the IDW method across various rainfall station sparsity scenarios, including extremely sparse conditions (e.g., single station coverage).
• Offers an optimized and validated rainfall interpolation scheme (IDW) for the Liuxihe Model and similar physically based distributed hydrological models, significantly enhancing flood forecasting accuracy in data-scarce regions.
• Enriches the understanding of interpolation method performance by quantifying differences across four typical scenarios (full coverage, upstream-only, downstream-only, single-station), confirming the generalizability of findings with prior research.

Funding

• Open Research Fund of Anhui Provincial Key Laboratory of Water Conservancy and Water Resources (Grant No. 2023SKJ04)
• Natural Science Foundation of China (Grant No. U2243227)

Citation

@article{Feng2025Research,
  author = {Feng, Dinggen and Chen, Yangbo and Jiang, Ping and Ni, Jinren},
  title = {Research on Optimizing Rainfall Interpolation Methods for Distributed Hydrological Models in Sparsely Networked Rainfall Stations of Watershed},
  journal = {Water},
  year = {2025},
  doi = {10.3390/w17223237},
  url = {https://doi.org/10.3390/w17223237}
}