Comparison of Bio-Inspired Optimization-Based MLP Models for Monthly Reference Evapotranspiration Estimation in Southeastern Türkiye

Authors

DOI:

https://doi.org/10.36253/ijam-3853

Keywords:

Machine learning, Evapotranspiration, Global Performance Index, Bio-Inspired Algorithms

Abstract

This study evaluates the performance of hybrid multilayer perceptron (MLP) models with six different biologically inspired meta-heuristic optimization algorithms for the estimation of monthly reference evapotranspiration (ET₀) in Southeast Anatolia, Türkiye. Using NASA POWER data (1984-2024) as main source of climatic data, model input variables for six provinces were determined by Recursive Feature Elimination (RFE) method. Moth-Flame Optimization (MFO), Dolphin Echolocation Optimization (DEO), Firefly Optimization (FOA), Grey Wolf Optimization (GWO), Golden Jackal Optimization (GJO) and Cuckoo Search Optimization (CSO) algorithms were used in the optimization of MLP models. Model performance was evaluated using the coefficient of determination (R²), Nash–Sutcliffe efficiency (NSE), root mean square error (RMSE), mean absolute error (MAE), RMSE-to-observation standard deviation ratio (RSR), and global performance index (GPI). The results show that DEO-MLP achieved the best overall performance among the investigated hybrid models, with mean values across the six stations of NSE = 0.970, R² = 0.972, MAE = 0.39, RSR = 0.17, and GPI = 0.33. The superior performance of DEO-MLP model was demonstrated by low error rates and high accuracy levels compared to the other models. In contrast, the MFO-MLP, CSO-MLP and GJO-MLP models exhibited lower accuracy levels. In general, the results demonstrate that the predictive performance of MLP models varies according to the meta-heuristic optimization algorithm employed, with DEO-MLP showing the best overall performance among the investigated hybrid models. This study is expected to contribute to the development of agricultural water management strategies in Southeast Anatolia and other regions characterized by similar climatic conditions and provides a practical modelling framework for estimating ET₀ when the availability of long-term ground-based meteorological observations is limited.

References

Adnan R.M., Mostafa R.R., Islam A.R.M.T., Kisi O., Kuriqi A., Heddam S., 2021. Estimating reference evapotranspiration using hybrid adaptive fuzzy inferencing coupled with heuristic algorithms. Comput Electron Agric 191: 106541. https://doi.org/10.1016/j.compag.2021.106541.

Ahmadi F., Mehdizadeh S., Mohammadi B., Pham Q.B., Doan T.N.C., Vo N.D., 2021. Application of an artificial intelligence technique enhanced with intelligent water drops for monthly reference evapotranspiration estimation. Agric Water Manag 244: 106622. https://doi.org/10.1016/j.agwat.2020.106622.

Allen R.G., Pereira L.S., Raes D., Smith M., 1998. Crop evapotranspiration—Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56. Rome: Food and Agriculture Organization of the United Nations.

Antonopoulos V.Z., Antonopoulos A.V., 2017. Daily reference evapotranspiration estimates by artificial neural networks technique and empirical equations using limited input climate variables. Comput Electron Agric 132:86–96.https://doi.org/10.1016/j.compag.2016.11.011.

Bakhtiari B., Mohebbi-Dehaghani A., Qaderi K., 2022. Comparative analysis of data-driven methods for daily reference evapotranspiration estimation of Southern Caspian Sea. Meteorol Appl 29:e2091. https://doi.org/10.1002/met.2091.

Bashir R.N., Mzoughi O., Shahid M.A., Alturki N., Saidani O., 2024. Principal Component Analysis (PCA) and feature importance-based dimension reduction for reference evapotranspiration (ET₀) predictions of Taif, Saudi Arabia. Computers and Electronics in Agriculture 222:109036. https://doi.org/10.1016/j.compag.2024.109036.

Bayram S., Çıtakoğlu H., 2023. Modeling monthly reference evapotranspiration process in Turkey: application of machine learning methods. Environ Monit Assess 195(67). https://doi.org/10.1007/s10661-022-10662-z.

Bellido-Jiménez J.A., Estévez J., García-Marín A.P., 2022. A regional machine learning method to outperform temperature-based reference evapotranspiration estimations in Southern Spain. Agric Water Manag 274:107955.https://doi.org/10.1016/j.agwat.2022.107955.

Chopra N., Ansari M.M., 2022. Golden jackal optimization: A novel nature-inspired optimizer for engineering applications. Expert Syst Appl 198:116924.https://doi.org/10.1016/j.eswa.2022.116924.

Citakoglu H., Cobaner M., Haktanir T., Kisi O., 2014. Estimation of monthly mean reference evapotranspiration in Turkey. Water Resour Manag 28(1):99–111.https://doi.org/10.1007/s11269-013-0474-1.

Darst B.F., Malecki K.C., Engelman C.D., 2018. Using recursive feature elimination in random forest to account for correlated variables in high dimensional data. BMC Genet 19:1–6. https://doi.org/10.1186/s12863-018-0633-8.

Delgado-Ramírez G., Bolaños-González M.A., Quevedo-Nolasco A., López-Pérez A., Estrada-Ávalos J., 2023. Estimation of reference evapotranspiration in a semi-arid region of Mexico. Sensors 23(15):7007. https://doi.org/10.3390/s23157007.

Despotovic M., Nedic V., Despotovic D., Cvetanovic S., 2015. Review and statistical analysis of different global solar radiation sunshine models. Renew Sustain Energy Rev 52:1869–1880. https://doi.org/10.1016/j.rser.2015.08.035.

Elbeltagi A., Katipoğlu O.M., Kartal V., Danandeh Mehr A., Berhail S., Elsadek E.A., 2024. Advanced reference crop evapotranspiration prediction: A novel framework combining neural nets, bee optimization algorithm, and mode decomposition. Appl Water Sci 14:256. https://doi.org/10.1007/s13201-024-02308-x.

Fan J., Yue W., Wu L., Zhang F., Cai H., Wang X., Lu X., Xiang Y., 2018. Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China. Agricultural and Forest Meteorology 263:225–241. https://doi.org/10.1016/j.agrformet.2018.08.019.

Ferreira L.B., Cunha F.F.D., Oliveira R.A.D., Filho E.I.F., 2019. Estimation of reference evapotranspiration in Brazil with limited meteorological data using ANN and SVM—A new approach. J Hydrol 572:556–570. https://doi.org/10.1016/j.jhydrol.2019.03.028.

Gao F., Feng G., Ouyang Y., Wang H., Fisher D., Adeli A., Jenkins J., 2017. Evaluation of reference evapotranspiration methods in arid, semiarid, and humid regions. J Am Water Resour Assoc 53(4):791–808. https://doi.org/10.1111/1752-1688.12530.

Gao L., Gong D., Cui N., Lv M., Feng Y., 2021. Evaluation of bio-inspired optimization algorithms hybrid with artificial neural network for reference crop evapotranspiration estimation. Comput Electron Agric 190:106466.https://doi.org/10.1016/j.compag.2021.106466.

GAP Regional Development Administration, 2024. 2024 GAP son durum. Şanlıurfa, Türkiye: Southeastern Anatolia Project Regional Development Administration.

Hargreaves, G.H. and Samani, Z.A., 1985: Reference Crop Evapotranspiration from Temperature. Applied Engineering in Agriculture, 1, 96-99. https://doi.org/10.13031/2013.26773

Hasan I.A., Yuce M.I., 2024. Prediction of potential evapotranspiration via machine learning and deep learning for sustainable water management in the Murat River Basin. Sustainability 16(24):11077. https://doi.org/10.3390/su162411077.

He Z., Xia K., Niu W., Aslam N., Hou J., 2018. Semisupervised SVM based on cuckoo search algorithm and its application. Math Probl Eng 243764: 1–13. https://doi.org/10.1155/2018/8243764.

Huang J., Liu J., Ye Y., Jiang Y., Lai Y., Qin X., Zhang L., Jiang Y., 2024. Mapping soil properties in the Haihun River sub-watershed, Yangtze River Basin, China, by integrating machine learning and variable selection. Sensors 24(12):3784. https://doi.org/10.3390/s24123784.

Huo Z., Feng S., Kang S., Dai X., 2012. Artificial neural network models for reference evapotranspiration in an arid area of northwest China. J Arid Environ 82:81–90. doi:10.1016/j.jaridenv.2012.01.016.

Jia H., Ma J., Song W., 2019. Multilevel thresholding segmentation for color image using modified moth-flame optimization. IEEE Access 7:44097–44134. https://doi.org/10.1109/access.2019.2908718.

Jiang S., Liang C., Cui N., Zhao L., Liu C., Feng Y., Hu X., Gong D., Zou Q., 2020. Water use efficiency and its drivers in four typical agroecosystems based on flux tower measurements. Agric For Meteorol 295:108200. https://doi.org/10.1016/j.agrformet.2020.108200.

Kartal V., 2024. Prediction of monthly evapotranspiration by artificial neural network model development with Levenberg–Marquardt method in Elazig, Turkey. Environ Sci Pollut Res 31:20953–20969. https://doi.org/10.1007/s11356-024-32464-1.

Kaveh A,. Farhoudi N., 2013. A new optimization method: Dolphin echolocation. Adv Eng Softw 59:53–70. https://doi.org/10.1016/j.advengsoft.2013.03.004.

Khairan H.E., Zubaidi S.L., Raza S.F., Hameed M., Al-Ansari N., Ridha H.M., 2023. Examination of single- and hybrid-based metaheuristic algorithms in ANN reference evapotranspiration estimating. Sustainability 15(19):14222. https://doi.org/10.3390/su151914222.

Kiani F., Seyyedabbasi A., Nematzadeh S., Candan F., Çevik T., Anka F.A., Randazzo G., Lanza S., Muzirafuti A., 2022. Adaptive metaheuristic-based methods for autonomous robot path planning: Sustainable agricultural applications. Appl Sci 12(3):943. https://doi.org/10.3390/app12030943.

Kisi O., Alizamir M., 2018. Modelling reference evapotranspiration using a new wavelet conjunction heuristic method: Wavelet extreme learning machine vs wavelet neural networks. Agric For Meteorol 263:41–48. https://doi.org/10.1016/j.agrformet.2018.08.007.

Kisi O., Keshtegar B., Zounemat-Kermani M., Heddam S., Trung N.T., 2021. Modeling reference evapotranspiration using a novel regression-based method: Radial basis M5 model tree. Theor Appl Climatol 145:639–659. https://doi.org/10.1007/s00704-021-03645-6.

Kumar M., Raghuwanshi N.S., Singh R., 2011. Artificial neural networks approach in evapotranspiration modeling: A review. Irrig Sci 29(1):11–25. https://doi.org/10.1007/s00271-010-0230-8.

Landeras G., Ortiz-Barredo A., López J.J., 2008. Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain). Agric Water Manag 95(5):553–565. https://doi.org/10.1016/j.agwat.2007.12.011.

Li M.F., Tang X.P., Wu W., Liu H.B. 2013. General models for estimating daily global solar radiation for different solar radiation zones in mainland China. Energy Convers Manag 70:139–148.https://doi.org/10.1016/j.enconman.2013.03.004.

Li Y., Li T., Liu H., 2017. Recent advances in feature selection and its applications. Knowl Inf Syst 53(3):551–577.https://doi.org/10.1007/s10115-017-1059-8.

Li Z., Zhou Y., Zhang S., Song J., 2016. Lévy-flight moth-flame algorithm for function optimization and engineering design problems. Math Probl Eng 423930, 1–22. https://doi.org/10.1155/2016/1423930.

Liu C., Cui N., Gong D., Hu X., Feng Y., 2020. Evaluation of seasonal evapotranspiration of winter wheat in humid region of East China using large-weighted lysimeter and three models. J Hydrol 590:125388. https://doi.org/10.1016/j.jhydrol.2020.125388.

Ma L., Yu J., 2022. Hierarchical clustering cuckoo search optimization implemented in optimal setting of directional overcurrent relays. Math Probl Eng 966149, 1–18. https://doi.org/10.1155/2022/8966149.

Maroufpoor S., Bozorg-Haddad O., Maroufpoor E., 2020. Reference evapotranspiration estimating based on optimal input combination and hybrid artificial intelligent model: Hybridization of artificial neural network with grey wolf optimizer algorithm. J Hydrol 588:125060. https://doi.org/10.1016/j.jhydrol.2020.125060.

Mehdizadeh S., Mohammadi B., Pham Q.B., Duan Z., 2021. Development of boosted machine learning models for estimating daily reference evapotranspiration and comparison with empirical approaches. Water 13(24):3489. https://doi.org/10.3390/w13243489.

Mehdizadeh S., Mohammadi B., Pham Q.B., Khoi D.N., Linh N.T.T., 2020. Implementing novel hybrid models to improve indirect measurement of the daily soil temperature: Elman neural network coupled with gravitational search algorithm and ant colony optimization. Measurement 165:108127. https://doi.org/10.1016/j.measurement.2020.108127.

Mirjalili S., 2015. Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl-Based Syst 89: 228–249. https://doi.org/10.1016/j.knosys.2015.07.006.

Mirjalili S., Mirjalili S.M., Lewis A., 2014. Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007.

Mirzania E., Kashani M.H., Golmohammadi G., Ibrahim O.R., Saroughi M., 2023. Hybrid COOT-ANN: A novel optimization algorithm for prediction of daily crop reference evapotranspiration in Australia. Theor Appl Climatol 154:201–218.https://doi.org/10.1007/s00704-023-04552-8.

Mohapatra S., Mohapatra P., 2023. An improved golden jackal optimization algorithm using opposition-based learning for global optimization and engineering problems. Int J Comput Intell Syst 16:147. https://doi.org/10.1007/s44196-023-00320-8.

Monteiro L.A., Sentelhas P.C., Pedra G.U., 2018. Assessment of NASA/POWER satellite-based weather system for Brazilian conditions and its impact on sugarcane yield simulation. Int J Climatol 38:1571–1581. https://doi.org/10.1002/joc.5282.

Moriasi D.N., Arnold J.G., Van Liew M.W., Bingner R.L., Harmel R.D., Veith T.L., 2007. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900. https://doi.org/10.13031/2013.23153.

Muhammad M.K.I., Shahid S., Ismail T., Harun S., Kisi O., Yaseen Z.M., 2021. The development of evolutionary computing model for simulating reference evapotranspiration over Peninsular Malaysia. Theor Appl Climatol 144:1419–1434. https://doi.org/10.1007/s00704-021-03606-z.

Ndiaye P.M., Bodian A., Diop L., Deme A., Dezetter A., Djaman K., 2020. Evaluation and calibration of alternative methods for estimating reference evapotranspiration in the Senegal River Basin. Hydrology 7(2):24. https://doi.org/10.3390/hydrology7020024.

Ozbuldu M., Irvem A., 2024. Assessment of seven different global climate models for historical temperature and precipitation in Hatay, Türkiye. Int J Environ Sci Technol. https://doi.org/10.1007/s13762-024-06033-5.

Pedregosa F., Varoquaux G., Gramfort A., Michel V., Thirion B., Grisel O., Blondel M., Prettenhofer P., Weiss R., Dubourg V., Vanderplas J., Passos A., Cournapeau D., Brucher M., Perrot M., Duchesnay E., 2011. Scikit-learn: Machine learning in Python. J Mach Learn Res 12:2825–2830.

Priestley, C.H.B. and Taylor, R.J. (1972) On the Assessment of Surface Heat Flux and Evaporation Using Large Scale Parameters. Monthly Weather Review, 100, 81-92. https://doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2

Ravindran S.M., Bhaskaran S.K.M., Ambat S.K.N., 2021. A deep neural network architecture to model reference evapotranspiration using a single input meteorological parameter. Environmental Processes 8:1567–1599. https://doi.org/10.1007/s40710-021-00543-x.

Reis M.M., da Silva A.J., Zullo Junior J., Tuffi Santos L.D., Azevedo A.M., Lopes E.M.G., 2019. Empirical and learning machine approaches to estimating reference evapotranspiration based on temperature data. Comput Electron Agric 165:104937. http://dx.doi.org/10.1016/j.compag.2019.104937.

Rodrigues G.C., Braga R.P., 2021. Estimation of daily reference evapotranspiration from NASA POWER reanalysis products in a hot summer Mediterranean climate. Agronomy 11(10):2077. https://doi.org/10.3390/agronomy11102077

Roy D.K., Lal A., Sarker K.K., Saha K.K., Datta B., 2021. Optimization algorithms as training approaches for prediction of reference evapotranspiration using adaptive neuro fuzzy inference system. Agric Water Manag 255:107003. https://doi.org/10.1016/j.agwat.2021.107003.

Safari M.J.S., Mohammadi B., Kargar K., 2020. Invasive weed optimization-based adaptive neuro-fuzzy inference system hybrid model for sediment transport with a bed deposit. J Clean Prod 276:124267. https://doi.org/10.1016/j.jclepro.2020.124267.

Sayyahi F., Farzin S., Karami H., 2021. Forecasting daily and monthly reference evapotranspiration in the Aidoghmoush Basin using multilayer perceptron coupled with water wave optimization. Complexity 2021:6683759. https://doi.org/10.1155/2021/6683759.

Shiri J., Kisi Ö., Anderas G., López J.J., Nazemi A.H., Stuyt L.C.P.M., 2012. Daily reference evapotranspiration modeling by using genetic programming approach in the Basque Country (Northern Spain). J Hydrol 414–415:302–316. https://doi.org/10.1016/j.jhydrol.2011.11.004.

Skhiri A., Ferhi A., Bousselmi A., Khlifi S., Mattar M.A., 2024. Artificial neural network for forecasting reference evapotranspiration in semi-arid bioclimatic regions. Water 16(4):602.https://doi.org/10.3390/w16040602.

Song X., Lu F., Xiao W., Zhu K., Zhou Y., Xie Z., 2019. Performance of 12 reference evapotranspiration estimation methods compared with the Penman–Monteith method and the potential influences in northeast China. Meteorol Appl 26:83–96. https://doi.org/10.1002/met.1739.

Tabari H., Hosseinzadeh Talaee P., 2013. Multilayer perceptron for reference evapotranspiration estimation in a semiarid region. Neural Comput Appl 23:341–348. https://doi.org/10.1007/s00521-012-0904-7.

Taylor K.E., 2001. Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106(D7):7183–7192. https://doi.org/10.1029/2000JD900719.

Tayyeh H.K., Mohammed R., 2023. Analysis of NASA POWER reanalysis products to predict temperature and precipitation in Euphrates River basin. J Hydrol 619:129327. https://doi.org/10.1016/j.jhydrol.2023.129327.

Tikhamarine Y., Malik A., Souag-Gamane D., Kisi O., 2020. Artificial intelligence models versus empirical equations for modeling monthly reference evapotranspiration. Environ Sci Pollut Res Int 27:30001–30019. https://doi.org/10.1007/s11356-020-08792-3.

Türkeş M., Tatlı H., 2009. Use of the standardized precipitation index (SPI) and a modified SPI for shaping the drought probabilities over Turkey. Int J Climatol 29:2270–2282. https://doi.org/10.1002/joc.1862.

Valiantzas J.D., 2015. Simplified limited data Penman’s ET₀ formulas adapted for humid locations. J Hydrol 524:701–707. https://doi.org/10.1016/j.jhydrol.2015.03.021.

Wu L., Zhou H., Ma X., Fan J., Zhang F., 2019. Daily reference evapotranspiration prediction based on hybridized extreme learning machine model with bio-inspired optimization algorithms: Application in contrasting climates of China. J Hydrol 577:123960. https://doi.org/10.1016/j.jhydrol.2019.123960.

Yang X.S., 2010. Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84. https://dx.doi.org/10.1504/IJBIC.2010.032124.

Yang X.S., Deb S., 2009. Cuckoo search via Lévy flights. Proc World Congr Nat Biol Inspired Comput (NaBIC 2009):210–214. IEEE Publ. https://doi.org/10.1109/NABIC.2009.5393690.

Yin L., Wang L., Li T., Lu S., Yin Z., Liu X., Zheng W., 2023. U-Net-STN: A novel end-to-end lake boundary prediction model. Land 12(8):1602. https://doi.org/10.3390/land12081602.

Yu J., Zheng W., Xu L., Zhangzhong L., Zhang G., Shan F., 2020. A PSO-XGBoost model for estimating daily reference evapotranspiration in the solar greenhouse. Intell Autom Soft Comput 26:989–1003. https://doi.org/10.32604/iasc.2020.010130.

Zhang S., Zhou Y., 2017. Template matching using grey wolf optimizer with lateral inhibition. Optik 130:1229–1243. https://doi.org/10.1016/j.ijleo.2016.11.173.

Zhao L., Qing S., Li H., Qiu Z., Niu X., Shi Y., Chen S., Xing X., 2024. Estimating maize evapotranspiration based on hybrid back-propagation neural network models and meteorological, soil, and crop data. Int J Biometeorol 68:511–525. https://doi.org/10.1007/s00484-023-02608-y.

Zhou Q., Chen D., Hu Z., Chen X., 2021. Decompositions of Taylor diagram and DISO performance criteria. Int J Climatol 41:5726–5732. https://doi.org/10.1002/joc.7149.

Zhu B., Feng Y., Gong D., Jiang S., Zhao L., Cui N., 2020. Hybrid particle swarm optimization with extreme learning machine for daily reference evapotranspiration prediction from limited climatic data. Comput Electron Agric 173:105430. https://doi.org/10.1016/j.compag.2020.105430.

Downloads

Published

2026-08-28

How to Cite

Ozbuldu, M. (2026). Comparison of Bio-Inspired Optimization-Based MLP Models for Monthly Reference Evapotranspiration Estimation in Southeastern Türkiye. Italian Journal of Agrometeorology. https://doi.org/10.36253/ijam-3853

Issue

Just Accepted Manuscripts

Section

REVIEW AND RESEARCH ARTICLES

License

Copyright (c) 2026 Mustafa Ozbuldu

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Licence and copyright agreement for IJAM

(revised October 2020)

The following licence and copyright agreement is valid for any article published by IJAM.

Author’s certification

By submitting the manuscript, the authors certify the following:

  • They are authorized by their co-authors to enter into these arrangements.
  • The work described has not been published before (except in the form of an abstract or proceedings-type publication – including discussion papers – or as part of a published lecture or thesis); it is not under consideration for publication elsewhere; and its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work was carried out.
  • They have secured the right to reproduce any material that has already been published or copyrighted elsewhere.
  • They agree to the following licence and copyright agreement:

Copyright

  • The copyright of any article is retained by the author(s). More information on the transfer of copyright can be found below.
  • Authors grant our journals a licence to publish the article and identify itself as the original publisher.
  • Authors grant any third party the right to use the article freely under the stipulation that the original authors are given credit and the appropriate citation details are mentioned.
  • The article is distributed under the Creative Commons Attribution 4.0 License. Unless otherwise stated, associated published material is distributed under the same licence.

Creative Commons Attribution 4.0 License

Anyone is free to share — to copy, distribute, and transmit the work to remix — to adapt the work under the following conditions:

  • Attribution — The original authors must be given credit.
  • For any reuse or distribution, it must be made clear to others what the licence terms of this work are.
  • Any of these conditions can be waived if the copyright holders give permission.
  • Nothing in this licence impairs or restricts the author’s moral rights. The full legal code of this licence.

 

Similar Articles

1 2 3 4 5 6 7 8 > >> 

You may also start an advanced similarity search for this article.