Jiang et al. (2026) Comparative analysis of spatial interpolation methods for daily rainfall data in complex terrain

Identification

• Journal: Theoretical and Applied Climatology
• Year: 2026
• Date: 2026-02-10
• Authors: Lu Jiang, Qinggaozi Zhu, Xihua Yang, Genghong Wu, Jonathan K. Webb, Jiaojiao Tan, Qiang Yu
• DOI: 10.1007/s00704-026-06041-0

Research Groups

• State Key Laboratory of Soil and Water Conservation and Desertification Control, College of Soil and Water Conservation Science and Engineering, Northwest A&F University, Yangling, Shaanxi, China
• State Key Laboratory of Soil and Water Conservation and Desertification Control, Institute of Soil and Water Conservation, Northwest A&F University, Yangling, Shaanxi, China
• New South Wales Department of Climate Change, Energy, the Environment and Water, Parramatta, NSW, Australia
• School of Life Sciences, Faculty of Science, University of Technology Sydney, Broadway, NSW, Australia
• School of Agriculture and Food Sciences, The University of Queensland, Brisbane, QLD, Australia

Short Summary

This study systematically evaluated six spatial interpolation methods for daily rainfall in China's Loess Plateau from 1980-2020. It found that Thin Plate Spline (TPS) and Inverse Distance Weighting (IDW) provided the best overall accuracy and stability, outperforming machine learning methods and Co-kriging, especially in complex terrain and during extreme events.

Objective

• To compare six spatial interpolation methods for daily rainfall estimation on the Loess Plateau.
• To assess the accuracy of these methods across seasons and ecological zones.
• To identify optimal methods for improved rainfall mapping in the region.

Study Configuration

• Spatial Scale: The Loess Plateau in north-central China, spanning approximately 640,000 square kilometres (33°N to 41°N latitude and 100°E to 114°E longitude), with an elevation gradient from 100 to 5,000 metres. A 50 km buffer zone around the plateau was included. Interpolation results were simulated at a spatial resolution of 0.001°.
• Temporal Scale: Daily rainfall data from 1980 to 2020 (41 years), with analysis of interannual, seasonal (monthly), and daily extreme events.

Methodology and Data

• Models used:
  • Thin Plate Spline Interpolation (TPS)
  • Inverse Distance Weighting (IDW)
  • Co-kriging (using elevation as a covariate)
  • Random Forest (RF)
  • Support Vector Machine (SVM)
  • Gaussian Process Regression (GPR)
• Data sources:
  • Daily rainfall observations from 384 meteorological stations (299 within the Loess Plateau, 85 in the buffer zone) provided by the National Meteorological Science Data Center (https://data.cma.cn/).
  • Digital Elevation Model (DEM) data from the Shuttle Radar Topography Mission (SRTM) with a spatial resolution of 90 metres, obtained from the Resource and Environment Data Center of the Chinese Academy of Sciences (http://www.resdc.cn/).
  • Loess Plateau ecological zoning data from the National Earth System Science Data Center, China (http://www.geodata.cn).
  • Covariates for some models included longitude, latitude, and elevation.

Main Results

• TPS (RMSE = 2.76 mm/d, R² = 0.71) and IDW (RMSE = 2.75 mm/d, R² = 0.71) demonstrated the best overall accuracy and stability for daily rainfall interpolation.
• Machine learning methods (RF, SVM, GPR) generally underperformed compared to traditional methods (R² ranging from 0.61 to 0.67) and systematically underestimated extreme rainfall events (e.g., 13% to 51% underestimation for a 111.9 mm event).
• Co-kriging (R² = 0.52) showed notably compromised accuracy, particularly in areas with significant elevation changes, and exhibited severe overestimation (up to 416.99 mm/d above measured maximum) in terrain mutation areas.
• Interpolation errors exhibited seasonal variation, peaking during the summer months (July–August, mean RMSE = 5.98 mm/d), which is attributed to intense convective rainfall and high frequency of extreme events.
• Spatial accuracy varied across ecological zones: highest in sandy and irrigated agricultural areas (Zone C, average MAE = 0.49 mm/d, RMSE = 2.23 mm/d) and lowest in gully-dominated regions (Zone A1, average MAE = 0.87 mm/d, RMSE = 3.25 mm/d).
• TPS and IDW consistently provided superior performance across most ecological zones (A1, A2, B1, C, D), with TPS being particularly suitable for the B2 sub-region. Co-kriging is not recommended for rocky mountain and valley plain regions (D area).
• All interpolation methods showed non-significant spatial autocorrelation in their errors (global Moran's I: 0.012–0.106, P > 0.25), indicating spatially random error distributions.

Contributions

• Provided a systematic comparison of six spatial interpolation methods for daily rainfall data, specifically focusing on the Loess Plateau's complex terrain.
• Assessed interpolation accuracy across different seasons and ecological zones, highlighting the spatiotemporal heterogeneity of errors.
• Analyzed the error behavior of interpolation methods under elevation gradients, particularly identifying limitations of Co-kriging and underestimation by machine learning for extreme rainfall.
• Offered a robust basis for selecting appropriate rainfall spatial interpolation methods for improved hydrological simulations and ecological management in complex terrain.

Funding

Not explicitly stated in the provided text, but data providers are acknowledged: National Meteorological Science Data Center of China, Resource and Environment Data Center of Chinese Academy of Sciences, and National Earth System Science Data Center, China.

Citation

@article{Jiang2026Comparative,
  author = {Jiang, Lu and Zhu, Qinggaozi and Yang, Xihua and Wu, Genghong and Webb, Jonathan K. and Tan, Jiaojiao and Yu, Qiang},
  title = {Comparative analysis of spatial interpolation methods for daily rainfall data in complex terrain},
  journal = {Theoretical and Applied Climatology},
  year = {2026},
  doi = {10.1007/s00704-026-06041-0},
  url = {https://doi.org/10.1007/s00704-026-06041-0}
}