{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T01:13:54Z","timestamp":1774314834135,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T00:00:00Z","timestamp":1674604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Water"],"abstract":"<jats:p>Modeling potential evapotranspiration (ET0) is an important issue for water resources planning and management projects involving droughts and flood hazards. Evapotranspiration, one of the main components of the hydrological cycle, is highly effective in drought monitoring. This study investigates the efficiency of two machine-learning methods, random vector functional link (RVFL) and relevance vector machine (RVM), improved with new metaheuristic algorithms, quantum-based avian navigation optimizer algorithm (QANA), and artificial hummingbird algorithm (AHA) in modeling ET0 using limited climatic data, minimum temperature, maximum temperature, and extraterrestrial radiation. The outcomes of the hybrid RVFL-AHA, RVFL-QANA, RVM-AHA, and RVM-QANA models compared with single RVFL and RVM models. Various input combinations and three data split scenarios were employed. The results revealed that the AHA and QANA considerably improved the efficiency of RVFL and RVM methods in modeling ET0. Considering the periodicity component and extraterrestrial radiation as inputs improved the prediction accuracy of the applied methods.<\/jats:p>","DOI":"10.3390\/w15030486","type":"journal-article","created":{"date-parts":[[2023,1,26]],"date-time":"2023-01-26T01:57:07Z","timestamp":1674698227000},"page":"486","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":84,"title":["Modeling Potential Evapotranspiration by Improved Machine Learning Methods Using Limited Climatic Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6917-7873","authenticated-orcid":false,"given":"Reham R.","family":"Mostafa","sequence":"first","affiliation":[{"name":"Information Systems Department, Faculty of Computers and Information Sciences, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7847-5872","authenticated-orcid":false,"given":"Ozgur","family":"Kisi","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Technical University of L\u00fcbeck, 23562 L\u00fcbeck, Germany"},{"name":"School of Technology, Ilia State University, 0162 Tbilisi, Georgia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2650-8123","authenticated-orcid":false,"given":"Rana Muhammad","family":"Adnan","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3897-7565","authenticated-orcid":false,"given":"Tayeb","family":"Sadeghifar","sequence":"additional","affiliation":[{"name":"Department of Marine Physics, Faculty of Marine Sciences, Tarbiat Modares University, Tehran 14115-111, Iran"},{"name":"Department of Physics, Technical and Vocational University (TU), Tehran 16846-13114, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7464-8377","authenticated-orcid":false,"given":"Alban","family":"Kuriqi","sequence":"additional","affiliation":[{"name":"CERIS, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal"},{"name":"Civil Engineering Department, University for Business and Technology, 10000 Pristina, Kosovo"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110833","DOI":"10.1016\/j.rser.2021.110833","article-title":"Ecological impacts of run-of-river hydropower plants\u2014Current status and future prospects on the brink of energy transition","volume":"142","author":"Kuriqi","year":"2021","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"W09405","DOI":"10.1029\/2007WR006331","article-title":"Agricultural green and blue water consumption and its influence on the global water system","volume":"44","author":"Rost","year":"2008","journal-title":"Water Resour. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"124371","DOI":"10.1016\/j.jhydrol.2019.124371","article-title":"Least square support vector machine and multivariate adaptive regression splines for streamflow prediction in mountainous basin using hydro-meteorological data as inputs","volume":"586","author":"Adnan","year":"2020","journal-title":"J. Hydrol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3801","DOI":"10.3390\/s90503801","article-title":"A Review of Current Methodologies for Regional Evapotranspiration Estimation from Remotely Sensed Data","volume":"9","author":"Li","year":"2009","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"128444","DOI":"10.1016\/j.jhydrol.2022.128444","article-title":"Global land surface evapotranspiration monitoring by ETMonitor model driven by multi-source satellite earth observations","volume":"613","author":"Zheng","year":"2022","journal-title":"J. Hydrol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0378-3774(03)00200-2","article-title":"Assessment of evapotranspiration estimation models for use in semi-arid environments","volume":"64","author":"DehghaniSanij","year":"2004","journal-title":"Agric. Water Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1007\/s11600-020-00446-9","article-title":"Modelling reference evapotranspiration by combining neuro-fuzzy and evolutionary strategies","volume":"68","author":"Alizamir","year":"2020","journal-title":"Acta Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"81279","DOI":"10.1007\/s11356-022-21410-8","article-title":"Improved weighted ensemble learning for predicting the daily reference evapotranspiration under the semi-arid climate conditions","volume":"29","author":"Zerouali","year":"2022","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s11442-013-1015-9","article-title":"Evapotranspiration estimation methods in hydrological models","volume":"23","author":"Zhao","year":"2013","journal-title":"J. Geogr. Sci."},{"key":"ref_10","first-page":"570","article-title":"Deep learning versus gradient boosting machine for pan evaporation prediction","volume":"16","author":"Malik","year":"2022","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/s00704-021-03747-1","article-title":"Intercomparison and uncertainty assessment of methods for estimating evapotranspiration using a high-resolution gridded weather dataset over Brazil","volume":"146","author":"Monteiro","year":"2021","journal-title":"Theor. Appl. Clim."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107343","DOI":"10.1016\/j.agwat.2021.107343","article-title":"Resolving data-hungry nature of machine learning reference evapotranspiration estimating models using inter-model ensembles with various data management schemes","volume":"261","author":"Chia","year":"2021","journal-title":"Agric. Water Manag."},{"key":"ref_13","first-page":"1119","article-title":"Analysis of various surface energy balance models for evapotranspiration estimation using satellite data","volume":"24","author":"Aryalekshmi","year":"2021","journal-title":"Egypt. J. Remote Sens. Space Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.compag.2015.02.010","article-title":"Soft computing approaches for forecasting reference evapotranspiration","volume":"113","author":"Motamedi","year":"2015","journal-title":"Comput. Electron. Agric."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s00704-021-03525-z","article-title":"Estimation of daily evapotranspiration in Ko\u0161ice City (Slovakia) using several soft computing techniques","volume":"144","author":"Kaya","year":"2021","journal-title":"Theor. Appl. Clim."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1002\/met.1676","article-title":"Evaluation of several soft computing methods in monthly evapotranspiration modelling","volume":"25","author":"Gavili","year":"2017","journal-title":"Meteorol. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"105758","DOI":"10.1016\/j.agwat.2019.105758","article-title":"Light Gradient Boosting Machine: An efficient soft computing model for estimating daily reference evapotranspiration with local and external meteorological data","volume":"225","author":"Fan","year":"2019","journal-title":"Agric. Water Manag."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Shamshirband, S., Amirmojahedi, M., Goci\u0107, M., Akib, S., Petkovi\u0107, D., Piri, J., and Trajkovic, S. (2016). Estimation of Reference Evapotranspiration Using Neural Networks and Cuckoo Search Algorithm. J. Irrig. Drain. Eng., 142.","DOI":"10.1061\/(ASCE)IR.1943-4774.0000949"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4534822","DOI":"10.1155\/2022\/4534822","article-title":"Estimating Daily Rice Crop Evapotranspiration in Limited Climatic Data and Utilizing the Soft Computing Algorithms MLP, RBF, GRNN, and GMDH","volume":"2022","author":"Aghelpour","year":"2022","journal-title":"Complexity"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s00704-021-03855-y","article-title":"Estimation of daily reference evapotranspiration with limited climatic data using machine learning approaches across different climate zones in New Mexico","volume":"147","author":"Mokari","year":"2021","journal-title":"Theor. Appl. Clim."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107281","DOI":"10.1016\/j.agwat.2021.107281","article-title":"Exploring machine learning and multi-task learning to estimate meteorological data and reference evapotranspiration across Brazil","volume":"259","author":"Ferreira","year":"2021","journal-title":"Agric. Water Manag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4013","DOI":"10.1007\/s00521-021-06661-9","article-title":"A hybrid deep neural network approach to estimate reference evapotranspiration using limited climate data","volume":"34","author":"Sharma","year":"2021","journal-title":"Neural Comput. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109113","DOI":"10.1016\/j.asoc.2022.109113","article-title":"DeepEvap: Deep reinforcement learning based ensemble approach for estimating reference evapotranspiration","volume":"125","author":"Sharma","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"109221","DOI":"10.1016\/j.asoc.2022.109221","article-title":"Long-term forecasting of monthly mean reference evapotranspiration using deep neural network: A comparison of training strategies and approaches","volume":"126","author":"Chia","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Thongkao, S., Ditthakit, P., Pinthong, S., Salaeh, N., Elkhrachy, I., Linh, N.T.T., and Pham, Q.B. (2022). Estimating FAO Blaney-Criddle b-Factor Using Soft Computing Models. Atmosphere, 13.","DOI":"10.3390\/atmos13101536"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhao, L., Zhao, X., Li, Y., Shi, Y., Zhou, H., Li, X., Wang, X., and Xing, X. (2022). Applicability of hybrid bionic optimization models with kernel-based extreme learning machine algorithm for predicting daily reference evapotranspiration: A case study in arid and semi-arid regions, China. Environ. Sci. Pollut. Res., 1\u201317.","DOI":"10.1007\/s11356-022-23786-z"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ikram, R.M.A., Mostafa, R.R., Chen, Z., Islam, A.R.M.T., Kisi, O., Kuriqi, A., and Zounemat-Kermani, M. (2023). Advanced Hybrid Metaheuristic Machine Learning Models Application for Reference Crop Evapotranspiration Prediction. Agronomy, 13.","DOI":"10.3390\/agronomy13010098"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s13201-022-01667-7","article-title":"Data intelligence and hybrid metaheuristic algorithms-based estimation of reference evapotranspiration","volume":"12","author":"Elbeltagi","year":"2022","journal-title":"Appl. Water Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Adnan, R.M., Mostafa, R.R., Islam, A.R.M.T., Gorgij, A.D., Kuriqi, A., and Kisi, O. (2021). Improving Drought Modeling Using Hybrid Random Vector Functional Link Methods. Water, 13.","DOI":"10.3390\/w13233379"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1016\/j.ymssp.2009.10.011","article-title":"Application of relevance vector machine and logistic regression for machine degradation assessment","volume":"24","author":"Caesarendra","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0925-2312(94)90053-1","article-title":"Learning and generalization characteristics of the random vector functional-link net","volume":"6","author":"Pao","year":"1994","journal-title":"Neurocomputing"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sch\u00f6lkopf, B., and Smola, A.J. (2002). Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT-Press.","DOI":"10.7551\/mitpress\/4175.001.0001"},{"key":"ref_33","first-page":"211","article-title":"Sparse Bayesian learning and the relevance vector machine","volume":"1","author":"Tipping","year":"2001","journal-title":"J. Mach. Learn. Res."},{"key":"ref_34","first-page":"095965181876297","article-title":"tate prediction for the actuators of civil aircraft based on a fusion framework of relevance vector machine and autoregressive integrated moving average. Proceedings of the Institution of Mechanical Engineers Part I","volume":"232","author":"Guo","year":"2018","journal-title":"J. Syst. Control Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1007\/s11071-019-05043-0","article-title":"Hummingbirds optimization algorithm-based particle filter for maneuvering target tracking","volume":"97","author":"Zhang","year":"2019","journal-title":"Nonlinear Dyn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"114194","DOI":"10.1016\/j.cma.2021.114194","article-title":"Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications","volume":"388","author":"Zhao","year":"2021","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.anbehav.2009.07.007","article-title":"Organized flight in birds","volume":"78","author":"Bajec","year":"2009","journal-title":"Anim. Behav."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"104314","DOI":"10.1016\/j.engappai.2021.104314","article-title":"QANA: Quantum-based avian navigation optimizer algorithm","volume":"104","author":"Zamani","year":"2021","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Dimitriadou, S., and Nikolakopoulos, K.G. (2022). Multiple Linear Regression Models with Limited Data for the Prediction of Reference Evapotranspiration of the Peloponnese, Greece. Hydrology, 9.","DOI":"10.3390\/hydrology9070124"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Dimitriadou, S., and Nikolakopoulos, K.G. (2022). Artificial Neural Networks for the Prediction of the Reference Evapotranspiration of the Peloponnese Peninsula, Greece. Water, 14.","DOI":"10.3390\/w14132027"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"e1841","DOI":"10.1002\/met.1841","article-title":"Comprehensive assessment of 12 soft computing approaches for modelling reference evapotranspiration in humid locations","volume":"27","author":"Shiri","year":"2019","journal-title":"Meteorol. Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"106541","DOI":"10.1016\/j.compag.2021.106541","article-title":"Estimating reference evapotranspiration using hybrid adaptive fuzzy inferencing coupled with heuristic algorithms","volume":"191","author":"Adnan","year":"2021","journal-title":"Comput. Electron. Agric."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Niaghi, A.R., Hassanijalilian, O., and Shiri, J. (2021). Estimation of Reference Evapotranspiration Using Spatial and Temporal Machine Learning Approaches. Hydrology, 8.","DOI":"10.3390\/hydrology8010025"}],"container-title":["Water"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4441\/15\/3\/486\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:15:40Z","timestamp":1760120140000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4441\/15\/3\/486"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,25]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["w15030486"],"URL":"https:\/\/doi.org\/10.3390\/w15030486","relation":{},"ISSN":["2073-4441"],"issn-type":[{"value":"2073-4441","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,25]]}}}