Eriskin et al. (2025) A Horizon-Adaptive Benchmarking Framework for Long-Term Reservoir Storage Forecasting Using Physics-Informed Transformers and Machine Learning

Identification

• Journal: Water Resources Management
• Year: 2025
• Date: 2025-12-29
• Authors: Ekinhan Eriskin, Özlem Terzi, Dilek Taylan
• DOI: 10.1007/s11269-025-04399-w

Research Groups

• Department of Property Protection and Security, Suleyman Demirel University, Isparta, Turkey
• Department of Civil Engineering, Faculty of Technology, Isparta University of Applied Sciences, Isparta, Turkey
• Department of Civil Engineering, Faculty of Engineering and Natural Sciences, Suleyman Demirel University, Isparta, Turkey

Short Summary

This study develops a horizon-adaptive benchmarking framework for 12-month reservoir storage forecasting using physics-informed transformers and machine learning models. It demonstrates that optimal model selection varies significantly across different forecast horizons, highlighting the need for a dynamic, horizon-specific approach for robust water management in semi-arid regions.

Objective

• To develop and evaluate a horizon-adaptive benchmarking framework for 12-month-ahead reservoir storage forecasting, identifying the most suitable model (from Physics-Informed Temporal Transformer (PIT-T), Long Short-Term Memory (LSTM), Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX), Multi-Output Perceptron (MLP), and an Ensemble) for different forecast horizons to enhance operational reliability and interpretability in data-scarce semi-arid basins.

Study Configuration

• Spatial Scale: Altınapa Reservoir, Turkey (WWF Ecoregion 415; GRDC Basin 4085), characterized by a cold semi-arid climate (Köppen BSk–s).
• Temporal Scale: Monthly hydrological data from 1975 to 2008 (34 years) used for training and testing. Forecasts generated for 12 months ahead using a 12-month input window.

Methodology and Data

• Models used:
  • Physics-Informed Temporal Transformer (PIT-T)
  • Long Short-Term Memory (LSTM)
  • Multi-Output Regressor (MLP)
  • Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX)
  • Ensemble (arithmetic mean of PIT-T, LSTM, MLP, and SARIMAX)
• Data sources: Monthly observed precipitation (P), inflow (Qin), outflow (Qout), and storage (S) for the Altınapa Reservoir from 1975 to 2008.

Main Results

• No single model consistently outperforms others across all 12 forecast horizons, necessitating horizon-specific model selection.
• PIT-T achieved the lowest 1-month Root Mean Squared Error (RMSE) (≈ 2.0 hm³) and demonstrated the best short-term memory preservation and resilience under extreme input scaling (10x).
• MLP excelled in short- to mid-range forecasts (2–6 months ahead).
• LSTM dominated medium-term predictions (7–10 months ahead) by effectively capturing delayed hydrological dependencies.
• The Ensemble model provided the most stable and reliable performance for long-term horizons (11–12 months ahead), maintaining seasonal persistence and robustness under reduced input richness and noise.
• SARIMAX consistently underperformed due to its limitations in representing nonlinear and long-range processes.
• Robustness tests under reduced complexity and noise confirmed that PIT-T and Ensemble models retained accuracy (RMSE ≈ 5.5–5.8 hm³, Nash–Sutcliffe Efficiency (NSE) ≈ 0.22–0.29).
• Autocorrelation fidelity analysis showed PIT-T and MLP accurately reproduced short-lag dependencies (1–4 months), with PIT-T remaining closest to observed low-lag correlations for longer horizons (9–12 months).

Contributions

• Provides a systematic horizon-adaptive evaluation across 12 forecast horizons, identifying the most effective model for specific operational timeframes in reservoir management.
• Introduces a novel Physics-Informed Temporal Transformer (PIT-T) architecture that embeds hydrological mass-balance consistency through soft constraints, enhancing physical realism without explicit differential equations.
• Includes a comprehensive robustness-oriented validation that tests model stability under various perturbations, including input scaling, noise, and reduced input complexity, crucial for operational deployment.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Citation

@article{Eriskin2025HorizonAdaptive,
  author = {Eriskin, Ekinhan and Terzi, Özlem and Taylan, Dilek},
  title = {A Horizon-Adaptive Benchmarking Framework for Long-Term Reservoir Storage Forecasting Using Physics-Informed Transformers and Machine Learning},
  journal = {Water Resources Management},
  year = {2025},
  doi = {10.1007/s11269-025-04399-w},
  url = {https://doi.org/10.1007/s11269-025-04399-w}
}