Interpretable Reference Evapotranspiration Estimation Model Combining Multi-Strategy Crested Porcupine Optimizer and CNN-LSTM

Interpretable Reference Evapotranspiration Estimation Model Combining Multi-Strategy Crested Porcupine Optimizer and CNN-LSTM | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Interpretable Reference Evapotranspiration Estimation Model Combining Multi-Strategy Crested Porcupine Optimizer and CNN-LSTM Xu Yao, Yingnan Wang, Jingji Liu, Jiaxuan Shi, Kelun Ma, Xuerui Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9547130/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract High-precision estimation of reference evapotranspiration (ET₀) is an important foundation for agricultural irrigation regulation and regional water resource optimization management. This paper proposes a hybrid model that integrates Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM), combined with the Adaptive Cauchy-Simulated Annealing hybrid Crested Porcupine Optimizer (ACSA-CPO) to globally optimize key hyperparameters of the model for ET₀ estimation. ET₀ is calculated by the Penman–Monteith (PM) formula and used as the reference baseline for model training and evaluation. The model extracts local temporal features of meteorological time series through CNN and captures long-term temporal dependencies using LSTM, thereby improving the model's ability to model complex nonlinear processes. The ACSA-CPO enhances the hyperparameter search capability effectively by introducing a multi-strategy collaborative optimization mechanism, further improving the model's estimation accuracy for ET₀. Experiments are conducted based on daily meteorological data of Changchun, Jilin Province from 2020 to 2025 in the ERA5 reanalysis dataset. The results show that the proposed model achieves superior performance in the rapid ET₀ estimation task, with Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), coefficient of determination (R²) and Nash-Sutcliffe Efficiency (NSE) of 1.753 mm/day, 2.174 mm/day, 18.3%, 0.8713 and 0.859, respectively. Comparative experiments with Particle Swarm Optimization (PSO) and Sparrow Search Algorithm (SSA) and ablation analysis further verify the effectiveness and stability of the proposed model. In addition, the Shapley Additive Explanations (SHAP) method is used for model interpretability analysis. The results indicate that the impacts of meteorological variables on ET₀ present obvious nonlinear characteristics, among which solar radiation, wind speed and air temperature make differentiated contributions to ET₀ in different value ranges, thus providing a more physically meaningful interpretation for the model estimation results. This study provides an effective data-driven scheme for rapid reference evapotranspiration estimation and agricultural water resource management, especially offering technical support for efficient ET₀ acquisition under the condition of missing meteorological data. Earth and environmental sciences/Climate sciences Physical sciences/Engineering Earth and environmental sciences/Environmental sciences Earth and environmental sciences/Hydrology Physical sciences/Mathematics and computing CNN-LSTM reference evapotranspiration estimation hyperparameter optimization SHAP interpretability time series modeling Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 17 May, 2026 Reviewers agreed at journal 16 May, 2026 Reviewers agreed at journal 15 May, 2026 Reviewers agreed at journal 15 May, 2026 Reviewers invited by journal 04 May, 2026 Editor invited by journal 04 May, 2026 Editor assigned by journal 29 Apr, 2026 Submission checks completed at journal 29 Apr, 2026 First submitted to journal 27 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9547130","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":635441012,"identity":"3feb75d6-bbaa-434b-a104-d662223cfc1e","order_by":0,"name":"Xu Yao","email":"","orcid":"","institution":"Jilin Agricultural University","correspondingAuthor":false,"prefix":"","firstName":"Xu","middleName":"","lastName":"Yao","suffix":""},{"id":635441013,"identity":"d5eb6ce2-5f76-463c-86b2-55178c4e84a3","order_by":1,"name":"Yingnan 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evapotranspiration estimation, hyperparameter optimization, SHAP interpretability, time series modeling","lastPublishedDoi":"10.21203/rs.3.rs-9547130/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9547130/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHigh-precision estimation of reference evapotranspiration (ET₀) is an important foundation for agricultural irrigation regulation and regional water resource optimization management. This paper proposes a hybrid model that integrates Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM), combined with the Adaptive Cauchy-Simulated Annealing hybrid Crested Porcupine Optimizer (ACSA-CPO) to globally optimize key hyperparameters of the model for ET₀ estimation. ET₀ is calculated by the Penman\u0026ndash;Monteith (PM) formula and used as the reference baseline for model training and evaluation. The model extracts local temporal features of meteorological time series through CNN and captures long-term temporal dependencies using LSTM, thereby improving the model's ability to model complex nonlinear processes. The ACSA-CPO enhances the hyperparameter search capability effectively by introducing a multi-strategy collaborative optimization mechanism, further improving the model's estimation accuracy for ET₀. Experiments are conducted based on daily meteorological data of Changchun, Jilin Province from 2020 to 2025 in the ERA5 reanalysis dataset. The results show that the proposed model achieves superior performance in the rapid ET₀ estimation task, with Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), coefficient of determination (R\u0026sup2;) and Nash-Sutcliffe Efficiency (NSE) of 1.753 mm/day, 2.174 mm/day, 18.3%, 0.8713 and 0.859, respectively. Comparative experiments with Particle Swarm Optimization (PSO) and Sparrow Search Algorithm (SSA) and ablation analysis further verify the effectiveness and stability of the proposed model. In addition, the Shapley Additive Explanations (SHAP) method is used for model interpretability analysis. The results indicate that the impacts of meteorological variables on ET₀ present obvious nonlinear characteristics, among which solar radiation, wind speed and air temperature make differentiated contributions to ET₀ in different value ranges, thus providing a more physically meaningful interpretation for the model estimation results. This study provides an effective data-driven scheme for rapid reference evapotranspiration estimation and agricultural water resource management, especially offering technical support for efficient ET₀ acquisition under the condition of missing meteorological data.\u003c/p\u003e","manuscriptTitle":"Interpretable Reference Evapotranspiration Estimation Model Combining Multi-Strategy Crested Porcupine Optimizer and CNN-LSTM","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-13 10:52:40","doi":"10.21203/rs.3.rs-9547130/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"271533828147643293459121302361665237729","date":"2026-05-18T03:45:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"295034954159576391944729813885781253613","date":"2026-05-16T11:04:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"94056756816968735448098420407460609987","date":"2026-05-15T19:02:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"76794799570661472915692223611992630317","date":"2026-05-15T07:16:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-05T01:49:18+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-05-04T19:31:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-30T02:31:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-30T02:31:13+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-04-28T02:03:19+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f8f9aff6-26cc-4a4b-b2c6-a809139233ab","owner":[],"postedDate":"May 13th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"271533828147643293459121302361665237729","date":"2026-05-18T03:45:33+00:00","index":27,"fulltext":""},{"type":"reviewerAgreed","content":"295034954159576391944729813885781253613","date":"2026-05-16T11:04:34+00:00","index":26,"fulltext":""},{"type":"reviewerAgreed","content":"94056756816968735448098420407460609987","date":"2026-05-15T19:02:06+00:00","index":25,"fulltext":""},{"type":"reviewerAgreed","content":"76794799570661472915692223611992630317","date":"2026-05-15T07:16:22+00:00","index":24,"fulltext":""},{"type":"reviewersInvited","content":"8","date":"2026-05-05T01:49:18+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-05-04T19:31:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-30T02:31:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-30T02:31:13+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":67628065,"name":"Earth and environmental sciences/Climate sciences"},{"id":67628066,"name":"Physical sciences/Engineering"},{"id":67628067,"name":"Earth and environmental sciences/Environmental sciences"},{"id":67628068,"name":"Earth and environmental sciences/Hydrology"},{"id":67628069,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-13T10:52:40+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-13 10:52:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9547130","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9547130","identity":"rs-9547130","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}