Gorgij et al. (2026) Metaheuristic-optimized neuro-fuzzy models for meteorological drought prediction

Identification

• Journal: Environmental Earth Sciences
• Year: 2026
• Date: 2026-03-30
• Authors: Alireza Docheshmeh Gorgij, Ozgur Kisi, Salim Heddam, Dinesh Kumar Vishwakarma, Hakan Ergun, Christoph Külls
• DOI: 10.1007/s12665-026-12910-8

Research Groups

• Faculty of Industry and Mining, University of Sistan and Baluchestan, Iran
• Department of Civil Engineering, Lübeck University of Applied Sciences, Germany
• Department of Civil Engineering, Ilia State University, Georgia
• School of Civil, Environmental and Architectural Engineering, Korea University, South Korea
• Faculty of Science, Agronomy Department, Hydraulics Division, University 20 Août 1955 Skikda, Algeria
• Department of Irrigation and Drainage Engineering, College of Technology, Govind Ballabh Pant University of Agriculture and Technology, India
• Division of Irrigation and Drainage Engineering, College of Technology, Sher-e-Kashmir University of Agricultural Sciences and Technology of Kashmir, India
• Department of Computer Engineering, International Black Sea University, Georgia

Short Summary

This study develops and evaluates hybrid neuro-fuzzy models, optimized by metaheuristic algorithms, for meteorological drought prediction using the Standardized Precipitation Index (SPI) in Baden-Württemberg, Germany. The ANFIS-MVO model consistently demonstrated superior predictive accuracy, particularly for longer SPI time scales (SPI12), outperforming other hybrid variants and benchmark models.

Objective

• To assess the predictive capability of ANFIS–HHO, ANFIS–MFO, and ANFIS–MVO models in forecasting drought severity and duration using multiple SPI time scales (SPI3, SPI6, SPI9, SPI12) and lagged SPI inputs.
• To optimize ANFIS model structure and membership function parameters through Harris Hawks Optimization (HHO), Moth-Flame Optimization (MFO), and Multi-Verse Optimization (MVO) algorithms to enhance convergence efficiency and avoid local minima.
• To conduct a comprehensive comparative analysis of the proposed hybrid models against other soft computing techniques (ANFIS-PSO, SVR) and statistical benchmarks (ARIMA).

Study Configuration

• Spatial Scale: Regional scale, specifically the federal state of Baden-Württemberg, Germany. Data from four meteorological stations: Freudenstadt-Kniebis, Gundelsheim, Kaisersbach-Cronhütte, and Öhringen.
• Temporal Scale: Prediction of Standardized Precipitation Index (SPI) at multiple time scales: 3-month (SPI3), 6-month (SPI6), 9-month (SPI9), and 12-month (SPI12). Lagged SPI values were used as inputs.

Methodology and Data

• Models used:
  • Hybrid Adaptive Neuro-Fuzzy Inference System (ANFIS) models optimized by metaheuristic algorithms:
    • ANFIS–Harris Hawks Optimization (HHO)
    • ANFIS–Moth-Flame Optimization (MFO)
    • ANFIS–Multi-Verse Optimization (MVO)
  • Zero-order Sugeno-type Fuzzy Inference System (FIS) with Gaussian membership functions.
  • Benchmark models for comparison: Autoregressive Integrated Moving Average (ARIMA), Support Vector Regression (SVR), and ANFIS–Particle Swarm Optimization (PSO).
• Data sources:
  • Standardized Precipitation Index (SPI) values derived from precipitation data.
  • Precipitation data collected from four meteorological stations operated by the Deutscher Wetterdienst (DWD) in Baden-Württemberg, Germany.
  • Lagged SPI values were used as input features for the models.
  • Data split: 70% for training, 30% for testing.
  • Model evaluation metrics: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Coefficient of Determination (R²), and Nash-Sutcliffe Efficiency (NSE).

Main Results

• Model performance generally improved with increasing SPI time scales, with SPI12 exhibiting the most robust and accurate predictions.
• For SPI3, all hybrid models showed poor performance (mean R² ≈ 0.439, NSE ≈ 0.419), indicating challenges in short-term drought prediction.
• For SPI6, moderate improvements were observed (mean RMSE ≈ 0.111, MAE ≈ 0.087), with ANFIS-MFO generally showing better accuracy.
• For SPI9, significant performance enhancements were achieved, with ANFIS-MVO often outperforming ANFIS-MFO and ANFIS-HHO.
• For SPI12, the ANFIS-MVO hybrid model consistently achieved the highest prediction accuracy across all stations. For example, at Kaisersbach-Cronhütte, it yielded RMSE ≈ 0.079, MAE ≈ 0.063, R² ≈ 0.841, and NSE ≈ 0.840.
• Comparative analysis confirmed that ANFIS-MVO consistently outperformed traditional statistical (ARIMA) and machine learning (SVR, ANFIS-PSO) benchmark models, especially for the SPI12 time scale.
• The ANFIS-HHO model generally demonstrated the lowest performance among the proposed hybrid models across most time scales and stations.

Contributions

• Introduced a novel hybrid modeling framework integrating ANFIS with HHO, MFO, and MVO metaheuristic algorithms for meteorological drought prediction in Baden-Württemberg, Germany.
• Provided a comprehensive assessment of the predictive capabilities of these hybrid models across multiple SPI time scales (SPI3–SPI12), demonstrating their effectiveness in capturing nonlinear drought dynamics.
• Optimized ANFIS parameters (membership function centers and widths) using metaheuristic algorithms, leading to enhanced model convergence and reduced risk of local minima.
• Conducted an extensive comparative analysis, establishing the superior performance of the ANFIS-MVO model over classical statistical (ARIMA) and widely used machine learning (SVR, ANFIS-PSO) approaches, particularly for long-term drought forecasting.
• Offered a promising tool for early warning systems and water resource management in climate-sensitive regions by improving the accuracy, robustness, and interpretability of regional drought forecasting models.

Funding

Open Access funding enabled and organized by Projekt DEAL. No direct external funding for the research itself was reported.

Citation

@article{Gorgij2026Metaheuristicoptimized,
  author = {Gorgij, Alireza Docheshmeh and Kisi, Ozgur and Heddam, Salim and Vishwakarma, Dinesh Kumar and Ergun, Hakan and Külls, Christoph},
  title = {Metaheuristic-optimized neuro-fuzzy models for meteorological drought prediction},
  journal = {Environmental Earth Sciences},
  year = {2026},
  doi = {10.1007/s12665-026-12910-8},
  url = {https://doi.org/10.1007/s12665-026-12910-8}
}