Merufinia et al. (2026) Long term stream flow for enhanced accuracy prediction through machine learning models (Ali Baba and the forty thieves vs. Fire Hawk Optimizer)

Identification

• Journal: Modeling Earth Systems and Environment
• Year: 2026
• Date: 2026-02-09
• Authors: Edris Merufinia, Ahmad Sharafati, Hirad Abghari, Yousef Hassanzadeh
• DOI: 10.1007/s40808-025-02710-7

Research Groups

• Department of Civil Engineering, SR.C., Islamic Azad University, Tehran, Iran
• Department of Range and Watershed Management, Urmia University, Urmia, Iran
• Department of Water Engineering, Center of Excellence in Hydroinformatics, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran
• Farazab Co. (Consulting Engineers), Research and Writing Capacity, Tabriz, Iran

Short Summary

This study developed and evaluated novel hybrid machine learning models, integrating Artificial Neural Networks (ANN) and Support Vector Regression (SVR) with Ali Baba and the Forty Thieves (AFT) and Fire Hawk Optimizer (FHO) metaheuristic algorithms, for long-term streamflow prediction in the Kurkursar River basin. The hybrid SVR-AFT model demonstrated superior performance, improving prediction accuracy by approximately 47% compared to standalone models, achieving an R² of 0.9695 and an RMSE of 0.0813 m³/s.

Objective

• To develop and evaluate hybrid machine learning models (ANN-AFT, ANN-FHO, SVR-AFT, SVR-FHO) for enhanced accuracy in long-term streamflow prediction.
• To compare the performance of these hybrid models against their standalone counterparts (ANN, SVR) to quantify the improvement achieved through optimization.
• To systematically investigate the impact of internal model parameters (e.g., number of neurons, training functions, transfer functions for ANN; hyperparameters C, ε, γ for SVR) and input time lags on prediction accuracy.

Study Configuration

• Spatial Scale: Kurkursar River basin, Nowshahr City, Mazandaran Province, Iran. The basin covers a surface area of 75.495 km², with a river length of 20.3 km. Mean, maximum, and minimum elevations are 860 m, 1944 m, and 24 m above sea level, respectively. Average annual rainfall is 890 mm, and mean discharge is 1.2 m³/s.
• Temporal Scale: 20 years of daily rainfall and discharge data, collected from January 1, 1989, to June 29, 2019. The dataset was split into 70% for training and 30% for testing.

Methodology and Data

• Models used:
  • Standalone Machine Learning Models: Artificial Neural Network (ANN), Support Vector Regression (SVR).
  • Metaheuristic Optimization Algorithms: Ali Baba and the Forty Thieves (AFT), Fire Hawk Optimizer (FHO).
  • Hybrid Models: ANN-AFT, ANN-FHO, SVR-AFT, SVR-FHO.
  • ANN Training Functions: Levenberg-Marquardt backpropagation (trainlm), Gradient Descent backpropagation (traingd), Bayesian Regularization (trainbr), etc.
  • ANN Activation Functions: Sigmoid, Purelin, Softmax, etc.
• Data sources: Daily rainfall and discharge data collected from the regional water company West Azerbaijan.
• Data preprocessing: Missing data reconstruction, outlier elimination, and normalization.
• Input variables: Rainfall (with two lags) and discharge (with three lags). Pearson correlation coefficient was used for optimal input variable selection.

Main Results

• Hybrid models significantly improved the prediction accuracy of standalone models by approximately 47%.
• The SVR-AFT hybrid model achieved the best overall performance with a Coefficient of Determination (R²) of 0.9695 and a Root Mean Square Error (RMSE) of 0.0813 m³/s.
• For ANN models, an optimal number of neurons in the hidden layer was found to be between 10 and 20.
• The Levenberg-Marquardt backpropagation model (trainlm) and the gradient descent backpropagation model (traingd) were identified as the best-performing ANN training functions.
• The softmax-Purelin combination was determined to be the most effective activation function pairing for the regression task.
• Increasing the number of input variables (e.g., scenarios S5 and S6) directly contributed to enhanced accuracy.
• Diagnostic plots revealed systematic biases in the SVR-AFT model, including consistent overestimation (CUSUM plot), a severe systematic bias with errors peaked around +50 (KDE plot), and a saturation issue at a predicted value of -1 (Joint Histogram Heatmap), indicating areas for future model refinement despite high R² and low RMSE.

Contributions

• Introduced and comprehensively evaluated novel hybrid machine learning models (ANN/SVR optimized by AFT/FHO) for long-term streamflow prediction, demonstrating their superior performance over standalone models.
• Identified the SVR-AFT model as the most accurate and reliable approach for the Kurkursar River basin, providing a robust solution for water resource management.
• Conducted a systematic investigation into the optimal configuration of ANN (neuron count, training/transfer functions) and SVR hyperparameters, offering practical guidelines for model development.
• Addressed a research gap in long-term streamflow forecasting for medium-sized rivers by utilizing a substantial 20-year daily dataset.
• Provided in-depth diagnostic analysis using advanced visualization techniques (CUSUM, KDE, Joint Histogram Heatmap) to uncover subtle model biases and limitations, contributing to a more nuanced understanding of model performance beyond standard metrics.

Funding

There is no funding for the present study.

Citation

@article{Merufinia2026Long,
  author = {Merufinia, Edris and Sharafati, Ahmad and Abghari, Hirad and Hassanzadeh, Yousef},
  title = {Long term stream flow for enhanced accuracy prediction through machine learning models (Ali Baba and the forty thieves vs. Fire Hawk Optimizer)},
  journal = {Modeling Earth Systems and Environment},
  year = {2026},
  doi = {10.1007/s40808-025-02710-7},
  url = {https://doi.org/10.1007/s40808-025-02710-7}
}