{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T02:57:47Z","timestamp":1763348267686,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,13]],"date-time":"2020-05-13T00:00:00Z","timestamp":1589328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Fund of the Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station in China Three Gorges University","award":["No. 2019KJX02"],"award-info":[{"award-number":["No. 2019KJX02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The study investigates the potential of two new machine learning methods, least-square support vector regression with a gravitational search algorithm (LSSVR-GSA) and the dynamic evolving neural-fuzzy inference system (DENFIS), for modeling reference evapotranspiration (ETo) using limited data. The results of the new methods are compared with the M5 model tree (M5RT) approach. Previous values of temperature data and extraterrestrial radiation information obtained from three stations, in China, are used as inputs to the models. The estimation exactness of the models is measured by three statistics: root mean square error, mean absolute error, and determination coefficient. According to the results, the temperature or extraterrestrial radiation-based LSSVR-GSA models perform superiorly to the DENFIS and M5RT models in terms of estimating monthly ETo. However, in some cases, a slight difference was found between the LSSVR-GSA and DENFIS methods. The results indicate that better prediction accuracy may be obtained using only extraterrestrial radiation information for all three methods. The prediction accuracy of the models is not generally improved by including periodicity information in the inputs. Using optimum air temperature and extraterrestrial radiation inputs together generally does not increase the accuracy of the applied methods in the estimation of monthly ETo.<\/jats:p>","DOI":"10.3390\/e22050547","type":"journal-article","created":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T10:27:19Z","timestamp":1589452039000},"page":"547","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Reference Evapotranspiration Modeling Using New Heuristic Methods"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2650-8123","authenticated-orcid":false,"given":"Rana","family":"Muhammad Adnan","sequence":"first","affiliation":[{"name":"College of Hydrology and Water Resources, State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China"}]},{"given":"Zhihuan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"}]},{"given":"Xiaohui","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Hydropower and Information Engineering, Huazhong University of Science &amp; Technology, Wuhan 430074, China"},{"name":"Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station, China Three Gorges University, Yichang 443002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7847-5872","authenticated-orcid":false,"given":"Ozgur","family":"Kisi","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, School of Technology, Ilia State University, 0162 Tbilisi, Georgia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5018-8505","authenticated-orcid":false,"given":"Ahmed","family":"El-Shafie","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Faculty of Engineering, University Malaya, Kuala Lumpur 50603, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7464-8377","authenticated-orcid":false,"given":"Alban","family":"Kuriqi","sequence":"additional","affiliation":[{"name":"CERIS\u2014Civil Engineering Research and Innovation for Sustainability, Instituto Superior T\u00e9cnico\u2014Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"given":"Misbah","family":"Ikram","sequence":"additional","affiliation":[{"name":"College of Hydrology and Water Resources, State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China"},{"name":"Department of Irrigation and Drainage, University of Agriculture, Faisalabad 38000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,13]]},"reference":[{"key":"ref_1","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":"2018","journal-title":"Meteorol. 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