Ma et al. (2026) Deep learning based multi-temporal scale precipitation modeling for spring discharge prediction, Shentou springs, China

Identification

• Journal: Journal of Hydrology Regional Studies
• Year: 2026
• Date: 2026-01-06
• Authors: Chunmei Ma, Shilei Ma, Yonghong Hao, Junfeng Zhu, Qinghua Lei, Jitao Sang, Huiqing Hao
• DOI: 10.1016/j.ejrh.2025.103097

Research Groups

• School of Computer and Information Engineering, Tianjin Normal University, Tianjin, China
• Tianjin Key Laboratory of Water Resources and Environment, Tianjin Normal University, Tianjin, China
• Kentucky Geological Survey, University of Kentucky, Lexington, KY, USA
• Department of Earth Science, Uppsala University, Uppsala, Sweden

Short Summary

This study proposes a Multi-scale Convolutional Transformer (MCT) deep learning framework for accurate karst spring discharge prediction at Shentou springs, China, by integrating an adaptive denoising method with multi-temporal and spatial precipitation features. The model reveals a significant 6-month lag in precipitation's effect on spring discharge and spatially heterogeneous influences that challenge simple distance-based assumptions.

Objective

• To develop a more accurate and adaptive precipitation-driven karst spring discharge prediction model by capturing both multi-temporal scale features and spatial characteristics of precipitation.
• To propose an adaptive denoising method for precipitation data to enhance data quality and improve prediction accuracy.
• To analyze the multi-temporal scale relationships and spatial contributions of precipitation to spring discharge in the Shentou springs catchment.

Study Configuration

• Spatial Scale: Shentou springs catchment, Shanxi Province, China, covering an area of 4756 km². Precipitation data from ten gauge stations within the catchment were used.
• Temporal Scale: Monthly spring discharge and precipitation data spanning 63 years (January 1958 to December 2020), totaling 756 months. The optimal input data length for the model was determined to be 24 months.

Methodology and Data

• Models used:
  • Multi-scale Convolutional Transformer (MCT) model, coupling Multi-scale Convolutional Neural Networks (CNNs) with a Transformer network.
  • Adaptive denoising method based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and cosine similarity.
  • Convolutional kernels of sizes [1 × 1], [1 × 6], [1 × 12], and [2 × 1] for multi-temporal scale feature extraction.
  • Transformer encoder-decoder architecture for spatial feature fusion and prediction.
• Data sources:
  • Monthly discharge records of Shentou Springs.
  • Monthly precipitation data from ten observation stations (Kelan, Ningwu, Pingguan, Pinglu, Shanyin, Shenchi, Shuozhou, Yingxian, Youyu, Zuoyun) within the Shentou Springs catchment.

Main Results

• The proposed adaptive denoising method significantly improved spring discharge prediction accuracy, increasing the Nash–Sutcliffe Efficiency (NSE) from 0.61 to 0.75 and reducing the Mean Absolute Error (MAE) from 0.11 m³/s to 0.09 m³/s on the test set.
• Precipitation and spring discharge exhibit clear multi-temporal scale relationships (monthly, semi-annual, annual, and inter-annual), with precipitation typically affecting spring discharge after a lag of approximately 6 months. Precipitation also has a temporally persistent influence.
• The MCT model achieved high prediction accuracy on the test set, with an NSE of 0.75, MAE of 0.09 m³/s, Root Mean Square Error (RMSE) of 0.11 m³/s, and Mean Absolute Percentage Error (MAPE) of 4.23%.
• Spatial analysis using Transformer attention weights revealed that precipitation in areas closer to the spring has a strong impact, but distant areas located in topographic depressions (e.g., Zuoyun, Shenchi, Ningwu, Kelan) also exert a significant volume-driven influence due to efficient deep water-conducting channels and hydraulic controls, challenging simple geographical distance assumptions.
• The optimal input data length for the model was determined to be 24 months, corresponding to two complete hydrological annual cycles.
• The MCT model outperformed traditional statistical models (ARIMA, MLR) and other deep learning models (GRU, LSTM, GCN) in spring discharge prediction.

Contributions

• Introduction of MCT, a novel deep learning framework that effectively couples multi-scale CNNs and a Transformer network to simultaneously capture multi-temporal scale features and spatial characteristics of precipitation for karst spring discharge prediction.
• Development of an adaptive denoising method for precipitation data based on CEEMDAN and cosine similarity, which objectively identifies and removes noise components, leading to improved data quality and prediction accuracy.
• Comprehensive analysis and visualization of the multi-temporal scale relationships between precipitation and spring discharge, explicitly identifying a 6-month lag effect and cumulative influence in the Shentou Springs catchment.
• Demonstration of the Transformer's ability to implicitly learn complex hydrogeological connectivity and spatial heterogeneity of precipitation influence, providing new insights into karst recharge mechanisms beyond simple geographical distance.
• Validation of the model's robustness and generalization ability through extensive comparative experiments and ablation studies, highlighting the critical role of both multi-temporal and spatial features.

Funding

• National Natural Science Foundation of China, Grant No. U2244214
• National Natural Science Foundation of China, Grant No. 42577059
• National Natural Science Foundation of China, Grant No. 42072277
• National Natural Science Foundation of China, Grant No. 41272245
• National Natural Science Foundation of China, Grant No. 40972165
• National Natural Science Foundation of China, Grant No. 42307088
• National Natural Science Foundation of China, Grant No. 40572150

Citation

@article{Ma2026Deep,
  author = {Ma, Chunmei and Ma, Shilei and Hao, Yonghong and Zhu, Junfeng and Lei, Qinghua and Sang, Jitao and Hao, Huiqing},
  title = {Deep learning based multi-temporal scale precipitation modeling for spring discharge prediction, Shentou springs, China},
  journal = {Journal of Hydrology Regional Studies},
  year = {2026},
  doi = {10.1016/j.ejrh.2025.103097},
  url = {https://doi.org/10.1016/j.ejrh.2025.103097}
}