Kumar et al. (2026) PRRRGN: A Deep Learning Framework for Bias-corrected Satellite Precipitation Estimation in Complex Terrains

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: G. Kalyan Kumar, P.V. Sankar
• DOI: 10.1007/s11269-025-04359-4

Research Groups

• Computer and Communication Engineering, Rajalakshmi Institute of Technology, Chennai, Tamil Nadu, India
• Electronics and Communication Engineering, Hindustan Institute of Technology and Science, Chennai, Tamil Nadu, India

Short Summary

A novel deep learning framework, Preference Relation Recurrent Residual Graph Network (PRRRGN), integrated with a hybrid Dargo Lizard–Fishing Cat Optimizer (DLFCO), was developed to improve bias-corrected satellite precipitation estimation in complex terrains. It achieved superior accuracy in the Peruvian Andes, with an RMSE of 0.10 mm, MAE of 0.07 mm, and NSE of 0.96 in annual assessments.

Objective

• To develop and evaluate a deep learning framework (PRRRGN) with a hybrid optimizer (DLFCO) for enhancing bias-corrected satellite precipitation estimation accuracy in complex terrains by combining spatiotemporal features, optimizing hyperparameters, and improving training convergence.

Study Configuration

• Spatial Scale: Peru, specifically the Andes region (latitude 0° to 17.5° South and longitude 70° to 80° West), including Cajamarca, Madre de Dios, Huánuco, Ica, Iquitos, and Loreto.
• Temporal Scale: January 2015 to December 2024 for satellite precipitation data; daily records for ground-based validation.

Methodology and Data

• Models used:
  • Proposed: Preference Relation Recurrent Residual Graph Network (PRRRGN) composed of Residual Graph Neural Network (Res-GNN) and Preference Relationship with Graph Attention (PRGA), optimized by a hybrid Dargo Lizard–Fishing Cat Optimizer (DLFCO).
  • Compared against: FY4A-AGRI, TMPA v7, TA-UNet, CMIC-NWC-SAF, Wavelet-based Feed-Forward Neural Networks (W-FFNN), Wavelet-based Extreme Learning Machines (W-ELM), Draco Lizard Optimization (DLO), and Fishing Cat Optimization (FCO).
• Data sources:
  • Satellite precipitation: Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network with Cloud Classification System (PERSIANN-CCS).
  • Topographic data: Shuttle Radar Topography Mission (SRTM) and Digital Elevation Model (DEM) from the CHRS dataset.
  • Ground-based validation: Daily precipitation records from 87 meteorological stations of the National Meteorological and Hydrological Service of Peru (SENAMHI).

Main Results

• The PRRRGN framework demonstrated superior performance in annual assessments for the Peruvian region, achieving an RMSE of 0.10 mm, MAE of 0.07 mm, NMAE of 12%, and an NSE of 0.96.
• In daily assessments, PRRRGN showed the lowest error rates (RMSE = 0.12 mm, MAE = 0.08 mm, NMAE = 15%) and highest NSE (0.95) compared to benchmark models.
• The hybrid DLFCO optimizer exhibited faster execution time (6.8 s) and more stable convergence, reaching near-zero fitness in approximately 60 iterations, outperforming DLO (9.5 s) and FCO (13.5 s).
• A Wilcoxon signed-rank test confirmed the statistical superiority of PRRRGN, with p-values less than 1E-06 for RMSE reduction across daily time steps.
• The optimal learning rate for PRRRGN was determined to be 0.0001, yielding a testing accuracy of 99.9921% and minimum loss.

Contributions

• Introduces PRRRGN, a novel deep learning framework that effectively captures spatial and temporal dependencies of precipitation data through residual graph structures and preference relations, enabling the modeling of nonlinear precipitation across large, wet, complex terrains.
• Presents DLFCO, a hybrid optimization algorithm for tuning deep learning parameters, which exhibits superior convergence stability and minimizes local minima more effectively than individual DLO and FCO methods.
• Incorporates in situ environmental monitoring data on ground and topography (i.e., elevation, slope, distance to the coast) into the satellite dataset to build a useful bias-correction framework that enhances the accuracy of satellite measurements in mountainous regions.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Citation

@article{Kumar2026PRRRGN,
  author = {Kumar, G. Kalyan and Sankar, P.V.},
  title = {PRRRGN: A Deep Learning Framework for Bias-corrected Satellite Precipitation Estimation in Complex Terrains},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04359-4},
  url = {https://doi.org/10.1007/s11269-025-04359-4}
}