Predicting the water level of Sefidrood Dam reservoir using an improved neural network along with several meta-heuristic algorithms

Document Type : Full Length Article

Authors

1 MSc. student in Civil Engineering-Hydraulic Structure, Higher-Education Institute of the Academic Center for Education, Culture and Research (ACECR), Rasht, Iran.

2 Assistance Professor, Department of Water Resources Monitoring, Environmental Research Institute of Academic Center for Education, Culture and Research (ACECR), Rasht

3 PhD in Water Engineering, Hydraulic Structures, University of Tabriz

Abstract

Background and Objectives
Reservoir water level prediction plays a critical and strategic role in optimal water resources management, especially in regions facing prolonged droughts and increasing manifestations of climate change. Accurate forecasting of daily reservoir water levels enables better decision-making regarding water allocation, flood control, irrigation scheduling, hydropower generation, and environmental flow maintenance. Traditional physically-based hydrological models often face significant limitations when modeling reservoir level dynamics due to the high complexity, non-linearity, numerous uncertainties, and the lack of comprehensive physical equations capable of fully describing the integrated effects of hydrological, meteorological, operational, and anthropogenic factors.
In recent decades, data-driven artificial intelligence (AI) approaches, particularly Artificial Neural Networks (ANNs), have gained remarkable popularity in hydrological forecasting due to their outstanding ability to capture hidden non-linear relationships without requiring explicit representation of physical processes. However, conventional ANN training methods, mainly gradient-based algorithms such as Levenberg-Marquardt, often suffer from entrapment in local optima, slow convergence, and sensitivity to initial parameter settings. To overcome these drawbacks, hybridization of ANNs with modern metaheuristic optimization algorithms has been increasingly explored. These population-based algorithms provide powerful global search capabilities and significantly enhance the probability of identifying near-global optimum weights and biases of neural networks. The main objective of the present study was to develop and compare four hybrid ANN-metaheuristic models for daily reservoir water level prediction at Sepidroud Dam (Manjil station), which consisted of ANN models optimized using Whale Optimization Algorithm (WOA), Grey Wolf Optimizer (GWO), Harris Hawks Optimization (HHO), and Ant Colony Optimization for Continuous domains (ACOR), in order to identify the most accurate and robust model among them.
Methodology
Daily hydrological time-series data spanning 15 years (2007–2022 / 1386–1401) were collected from Sepidroud Dam (Manjil gauging station). The main variables comprised inflow discharge, outflow discharge, reservoir storage volume, reservoir surface area, and reservoir water level, with water level considered as the target variable. Cross-correlation analysis (CCF) and partial autocorrelation function (PACF) were employed to determine the most influential lagged input variables. The final input structure consisted of five variables, which included inflow discharge of the previous day (QI₋₁), outflow discharge of the previous day (QO₋₁), reservoir surface area of the current day (RA), reservoir volume of the current day (RV), and reservoir water level of the previous day (RL₋₁). All input and output data were normalized to the range [0.1, 0.9], and the dataset was randomly divided into 70% training and 30% testing subsets. The base model consisted of a Multi-Layer Perceptron (MLP) neural network with one hidden layer. Instead of classical gradient-based training, the optimization framework comprised four metaheuristic algorithms, including WOA, GWO, HHO, and ACOR, which were employed to optimize the weights and biases of the MLP.
Model performance evaluation comprised a comprehensive set of statistical indices, which included coefficient of determination (R²), mean absolute error (MAE), normalized root mean square error (NRMSE), scatter index (SI), mean bias error (MBE), Kling-Gupta efficiency (KGE), 95% uncertainty band width, and Global Performance Index (GPI), with GPI considered as the main ranking criterion. All implementations were performed in MATLAB R2018b environment.
Findings
The testing-phase results indicated that the hybrid ANN-WOA model achieved the highest overall performance. Its performance statistics included R² = 0.9991, MAE = 0.4028 m, NRMSE = 0.0101, SI = 0.0101, and the lowest GPI value, corresponding to the best rank. The ranking structure consisted of ANN-WOA as the first model, followed by ANN-GWO, ANN-ACOR, and ANN-HHO. Overall model performance indicators comprised SI values below 0.1 and NRMSE values below 0.03 for all hybrid models, demonstrating very high accuracy for practical engineering applications. Nevertheless, ANN-WOA clearly outperformed the others, as its error distribution included the smallest interquartile range (IQR) in the box-plot analysis, nearly unbiased predictions with a median error of approximately –0.02 m, and the most stable convergence behavior. The comparative analysis of error box-plots and convergence curves showed that the optimization dynamics of WOA consisted of a more effective balance between exploration and exploitation, enabling more robust escape from local optima and improved final solution quality compared to the other metaheuristics. The achieved accuracy substantially exceeded most previously reported results in the literature, which typically consisted of R² values ranging between 0.90 and 0.97.
Conclusion
The hybridization of Artificial Neural Networks with metaheuristic optimization algorithms, particularly the Whale Optimization Algorithm (WOA), significantly enhances the accuracy, stability, and reliability of daily reservoir water level forecasting. The superior performance of the ANN-WOA model in this study demonstrates its strong potential to serve as a reliable operational tool for reservoir management under complex and uncertain hydrological conditions. The results also highlight the importance of global optimization techniques in overcoming the limitations of classical ANN training methods. Considering the very high accuracy achieved, it is recommended to further test the ANN-WOA model under different climatic and operational scenarios, on other reservoirs, and potentially for prediction of other reservoir variables (inflow, outflow, evaporation, etc.). Integration of emerging explainable AI (XAI) techniques and newer metaheuristics are also suggested as promising directions for future research.

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Main Subjects

References

  • Barzegar R, Fijani E, Moghaddam AA, and Tziritis E, 2017. Forecasting of groundwater level fluctuations using ensemble hybrid multi-wavelet neural network-based models, Science of the Total Environment, 599, 20–31, doi:10.1016/j.scitotenv.2017.04.189.

    Behar O, Khellaf A, and Mohammedi K, 2015. Comparison of solar radiation models and their validation under Algerian climate – The case of direct irradiance, Energy Conversion and Management, 98, 236–251, doi:10.1016/j.enconman.2015.03.067.

    Buyukyildiz M, Tezel G, and Yilmaz V, 2014. Estimation of the change in lake water level by artificial intelligence methods, Water Resources Management, 28(13), 4747–4763, doi:10.1007/s11269-014-0773-1.

    Das M, Ghosh SK, Chowdary V, Saikrishnaveni A, and Sharma R, 2016. A probabilistic nonlinear model for forecasting daily water level in reservoir, Water Resources Management, 30(9), 3107–3122, doi:10.1007/s11269-016-1334-6.

    Das S, Forer L, Schönherr S, Sidore C, Locke AE, Kwong A, Vrieze SI, Chew EY, Levy S, and McGue M, 2016. Next-generation genotype imputation service and methods, Nature Genetics, 48(10), 1284–1287, Rehamnia:10.1038/ng.3656.

    Hakimi Khansar H, 2021. Simulation of behavior of the Kabudval Dam during construction with 3D numerical modeling, Amirkabir Journal of Civil Engineering, 53(9), 20–20, doi:10.22060/ceej.2020.18172 .6790.

    Hakimi Khansar H, Salimi H, and Shiri J, 2024. Extended estimation of daily inflow of Sefidroud dam using meta-heuristic algorithms combined with fuzzy neural inference system, Amirkabir Journal of Civil Engineering, 56(1), 3–22, doi:10.22060/ceej. 2024.22456.8102 (In Persian).

    Hecht-Nielsen R, 1988. Neurocomputing: Picking the human brain, IEEE Spectrum, 25(3), 36–41, doi:10.1109/6.4520.

    Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, and Chen H, 2019. Harris hawks optimization: Algorithm and applications, Future Generation Computer Systems, 97, 849–872, doi:10.1016/j.future.2019.02.028.

    Hipni A, El-shafie A, Najah A, Karim OA, Hussain A, and Mukhlisin M, 2013. Daily forecasting of dam water levels: Comparing a support vector machine (SVM) model with adaptive neuro fuzzy inference system (ANFIS), Water Resources Management, 27(10), 3803–3823, doi.org/10.1007/s11269 -013-0382-4.

    Kişi Ö, 2008. River flow forecasting and estimation using different artificial neural network techniques, Hydrology Research, 39(1), 27–40, doi:10.2166/nh.2008.026.

    Kisi O, Shiri J, and Nikoofar B, 2012. Forecasting daily lake levels using artificial intelligence approaches, Computers & Geosciences, 41, 169–180, doi:10.1016/j. cageo.2011.08.027.

    Kohavi R, 1995. A study of cross-validation and bootstrap for accuracy estimation and model selection, In Proceedings of the 14th International Joint Conference on Artificial Intelligence, Morgan Kaufmann, 2, 1137–1145.

    Lai V, Huang YF, Koo CH, and Ahmed AN, 2022. A review of reservoir operation optimisations: from traditional models to metaheuristic algorithms, Archives of Computational Methods in Engineering, 29, 3435–3457, doi:10.1007/s11831-021-09701 -8.

    Lewis-Beck MS, 2005. Election forecasting: Principles and practice, The British Journal of Politics and International Relations, 7(2), 145–164, doi:10.1111/j.1467-856X.2005. 00178.x.

    Li MF, Tang XP, Wu W, and Liu HB, 2013. General models for estimating daily global solar radiation for different solar radiation zones in mainland China, Energy Conversion and Management, 70, 139–148, doi:10.1016/ j.enconman.2013.03.004.

    Ma C, and Iqbal M, 1984. Statistical comparison of solar radiation correlations monthly average global and diffuse radiation on horizontal surfaces, Solar Energy, 33, 143–148.

    Maroufpoor S, Maroufpoor E, Bozorg-Haddad O, Shiri J, and Yaseen ZM, 2019. Soil moisture simulation using hybrid artificial intelligent model: Hybridization of adaptive neuro fuzzy inference system with grey wolf optimizer algorithm, Journal of Hydrology, 575, 544–556.

    Mirjalili S, and Lewis A, 2016. The whale optimization algorithm, Advances in Engineering Software, 95, 51–67, doi:10. 1016/j.advengsoft.2016.01.008.

    Modabberi H, Hashemi MMR, Ashournia M, and Rahimipour MA, 2017. Sensitivity analysis and vulnerability mapping of the Guilan aquifer using Drastic method, Reviews on Environmental Health and Environmental Science, 4(1), 27–41, doi:10.18488/journal.80.2017.41.27.41.

    Modaberi H, and Shokoohi A, 2020. Determining water requirement of Anzali Wetland based on eco-tourism indices within the framework of IWRM, Iranian Journal of Soil and Water Research, 51(10), 2501–2517, doi:10.22059/ijswr.2020.303554.6686 33 (In Persian with English Abstract).

    Parsa J, Hakimi Khansar H, Hoseinzadeh Dalir A, and Shiri J, 2021. Simulation of soil stress in earth dams using artificial intelligence models and determination of effective features, Amirkabir Journal of Civil Engineering, doi:10. 22060/ceej.2021.18682 .6925.

    Patino CM, and Ferreira JC, 2015. Confidence intervals: A useful statistical tool to estimate effect sizes in the real world, Jornal Brasileiro de Pneumologia, 41, 565–566, doi:10.1590/S1806-375620150000003 14.

    Rehamnia I, and Mahdavi-Meymand A, 2025. Advancing reservoir water level predictions: evaluating conventional, ensemble and integrated swarm machine learning approaches, Water Resources Management, 39(2), 779–794, doi:10.1007/s11269-024-03999-0.

    Refaeilzadeh P, Tang L, and Liu H, 2009. Cross-validation, In Liu L and Özsu MT (Eds.), Encyclopedia of Database Systems, Springer, 532–538.

    Sammen SS, Mohamed T, Ghazali A, Sidek L, and El-Shafie A, 2017. An evaluation of existent methods for estimation of embankment dambreach parameters, Natural Hazards, 87(1), 545566, doi:10.1007/s11069 -017-2764-z.

    Shamim MA, Hassan M, Ahmad S, and Zeeshan M, 2016. A comparison of artificial neural networks (ANN) and local linear regression (LLR) techniques for predicting monthly reservoir levels, KSCE Journal of Civil Engineering, 20(2), 971–977, doi:10. 1007/s12205-015-0298-z.

    • Socha K, and Dorigo M, 2008. Ant colony optimization for continuous domains, European Journal of Operational Research, 185(3), 1155–1173, doi:10.1016/j.ejor.2006 .06.046.

    Soleymani Z, Mahmoodabadi N, and Nouri MM, 2016. Language skills and phonological awareness in children with cochlear implants and noral hearing, International Journal of Pediatric Otorhinolaryngology, 83, 16–21.

    Stone RJ, 1993. Improved statistical procedure for the evaluation of solar radiation estimation models, Solar Energy, 51(4), 289–291.

    Valizadeh N, and El-Shafie A, 2013. Forecasting the level of reservoirs using multiple input fuzzification in ANFIS, Water Resources Management, 27(9), 3319–3331, doi:10.1007/ s11269-013-0349-5.

    Willmott CJ, and Matsuura K, 2006. On the use of dimensioned measures of error to evaluate the performance of spatial interpolators, International Journal of Geographical Information Science, 20(1), 89–102, doi:10.1080 /13658810500286976.

     

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Hydraulics and Water Science
Volume 36, Issue 1
April 2026
Pages 25-43

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