[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125798-en":3,"doc-seo-125798-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125798,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling","Machine learning models—including artificial neural networks (ANN), generalized neural regression networks (GRNN), and adaptive neuro-fuzzy interface systems (ANFIS)—are widely used for accurate predictions, yet they can yield inconsistent results for linear problem settings. To address this, the study proposes hybridizations of machine learning with autoregressive integrated moving average (ARIMA) to improve evapotranspiration (ET0) forecasting accuracy and generality. Models are trained and tested on daily ET0 data collected over 2010–2020 in Samsun, Türkiye. Results indicate ARIMA–GRNN cuts RMSE by 48.38%, ARIMA–ANFIS by 8.56%, and ARIMA–ANN by 6.74% versus traditional ARIMA, supporting reliable daily ET0 estimation for agriculture and water management.","Purdue University  \nPurdue e-Pubs  \n\n| Purdue University Libraries Open Access Publishing Fund | Purdue Libraries and School of Information Studies |\n| --- | --- |\n| 3-24-2023\u003Cbr>Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling\u003Cbr>Erdem Kucuktopcu\u003Cbr>Follow this and additional works at: [https://docs.lib.purdue.edu/fund](https://docs.lib.purdue.edu/fund) |  |\n\nThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. [Please contact epubs@purdue.edu](Please contact epubs@purdue.edu) for additional information.  \n sustainability   \nArticle  \nHybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling  \nErdem Küçüktopcu 1, *, Emirhan Cemek 2, Bilal Cemek 1 and Halis Simsek 3  \nCitation: Küçüktopcu, E.; Cemek, E.; Cemek, B.; Simsek, H. Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling. Sustainability 2023, 15, 5689. [https://doi.org/10.3390/](https://doi.org/10.3390/)[ ](https://doi.org/10.3390/)su15075689  \nAcademic Editor: Sushant Mehan  \nReceived: 1 March 2023  \nRevised: 20 March 2023  \nAccepted: 23 March 2023  \nPublished: 24 March 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Department of Agricultural Structures and Irrigation, Ondokuz Mayıs University, 55139 Samsun, Türkiye  \n2 Hydraulics and Water Resources Engineering Program, Department of Civil Engineering, Istanbul Technical University, 34469 Istanbul, Türkiye  \n3 Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, IN 47907, USA  \n* Correspondence: [erdem.kucuktopcu@omu.edu.tr](erdem.kucuktopcu@omu.edu.tr)  \nAbstract: Machine learning (ML) models, including artificial neural networks (ANN), generalized neural regression networks (GRNN), and adaptive neuro-fuzzy interface systems (ANFIS), have received considerable attention for their ability to provide accurate predictions in various problem domains. However, these models may produce inconsistent results when solving linear problems. To overcome this limitation, this paper proposes hybridizations of ML and autoregressive integrated moving average (ARIMA) models to provide a more accurate and general forecasting model for evapotranspiration (ET 0) . The proposed models are developed and tested using daily ET 0 data collected over 11 years (2010–2020) in the Samsun province of Türkiye. The results show that the ARIMA–GRNN model reduces the root mean square error by 48.38%, the ARIMA–ANFIS model by 8.56%, and the ARIMA–ANN model by 6.74% compared to the traditional ARIMA model. Consequently, the integration of ML with ARIMA models can offer more accurate and dependable prediction of daily ET 0, which can be beneficial for many branches such as agriculture and water management that require dependable ET 0 estimations.  \nKeywords: Box–Jenkins; time series modeling; evapotranspiration; artificial intelligence  \n1. Introduction  \nEfficient irrigation management is a critical aspect of modern agricultural techniques, and accurately estimating evapotranspiration (ET) is essential for effective water resource management, irrigation scheduling, watershed management, and drainage system planning [1] . ET is a method used to measure the water requirements of a crop, which comprises the movement of water vapor from the soil into the air through evaporation from the soil and transpiration from the plants [2] . The first step in determining the ET of an agricultural system is to calculate the reference evapotranspiration (ET 0), which is a widely accepted method for quantifying the water requirements of a crop. However, estimating ET 0 is a","cbCaifeNBDKUbzdx","https://ap.wps.com/l/cbCaifeNBDKUbzdx","pdf",3154004,1,16,"English","en",105,"# Abstract\n# Introduction\n## Importance of evapotranspiration and ET0 estimation\n## Indirect estimation methods and limitations\n## Motivation for machine learning approaches\n# Proposed hybrid modeling approach\n# Experimental setup and data\n# Results and performance comparison\n# Conclusions","[{\"question\":\"Why are ARIMA and machine learning hybrid models used for ET0 forecasting?\",\"answer\":\"Machine learning models can produce inconsistent results in linear problem settings. Hybridizing ML with ARIMA aims to improve both accuracy and general forecasting capability for daily ET0.\"},{\"question\":\"What data and location were used to develop and test the proposed models?\",\"answer\":\"Daily ET0 data covering 11 years (2010–2020) from the Samsun province of Türkiye were used for model development and testing.\"},{\"question\":\"How much did the hybrid models improve accuracy compared with traditional ARIMA?\",\"answer\":\"Relative to traditional ARIMA, ARIMA–GRNN reduced RMSE by 48.38%, ARIMA–ANFIS by 8.56%, and ARIMA–ANN by 6.74%.\"}]","Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling | PDF",1785901266,40,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"hybrid-statistical-and-machine-learning-methods-for-daily-evapotranspiration-modeling","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/hybrid-statistical-and-machine-learning-methods-for-daily-evapotranspiration-modeling/125798/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are ARIMA and machine learning hybrid models used for ET0 forecasting?","Question",{"text":75,"@type":76},"Machine learning models can produce inconsistent results in linear problem settings. Hybridizing ML with ARIMA aims to improve both accuracy and general forecasting capability for daily ET0.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What data and location were used to develop and test the proposed models?",{"text":80,"@type":76},"Daily ET0 data covering 11 years (2010–2020) from the Samsun province of Türkiye were used for model development and testing.",{"name":82,"@type":73,"acceptedAnswer":83},"How much did the hybrid models improve accuracy compared with traditional ARIMA?",{"text":84,"@type":76},"Relative to traditional ARIMA, ARIMA–GRNN reduced RMSE by 48.38%, ARIMA–ANFIS by 8.56%, and ARIMA–ANN by 6.74%.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":29,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]