{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T07:25:31Z","timestamp":1777101931770,"version":"3.51.4"},"reference-count":46,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,5,29]],"date-time":"2021-05-29T00:00:00Z","timestamp":1622246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00151\/2020 (C-MAST)"],"award-info":[{"award-number":["UIDB\/00151\/2020 (C-MAST)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["Centro-01-0145-FEDER000017 - EMaDeS - Energy"],"award-info":[{"award-number":["Centro-01-0145-FEDER000017 - EMaDeS - Energy"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>In recent years, deep learning algorithms have been successfully applied in the development of decision support systems in various aspects of agriculture, such as yield estimation, crop diseases, weed detection, etc. Agriculture is the largest consumer of freshwater. Due to challenges such as lack of natural resources and climate change, an efficient decision support system for irrigation is crucial. Evapotranspiration and soil water content are the most critical factors in irrigation scheduling. In this paper, the ability of Long Short-Term Memory (LSTM) and Bidirectional LSTM (BLSTM) to model daily reference evapotranspiration and soil water content is investigated. The application of these techniques to predict these parameters was tested for three sites in Portugal. A single-layer BLSTM with 512 nodes was selected. Bayesian optimization was used to determine the hyperparameters, such as learning rate, decay, batch size, and dropout size.The model achieved the values of mean square error values within the range of 0.014 to 0.056 and R2 ranging from 0.96 to 0.98. A Convolutional Neural Network (CNN) model was added to the LSTM to investigate potential performance improvement. Performance dropped in all datasets due to the complexity of the model. The performance of the models was also compared with CNN, traditional machine learning algorithms Support Vector Regression, and Random Forest. LSTM achieved the best performance. Finally, the impact of the loss function on the performance of the proposed models was investigated. The model with the mean square error as loss function performed better than the model with other loss functions.<\/jats:p>","DOI":"10.3390\/app11115029","type":"journal-article","created":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:22:15Z","timestamp":1622420535000},"page":"5029","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["Modeling Soil Water Content and Reference Evapotranspiration from Climate Data Using Deep Learning Method"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2319-8211","authenticated-orcid":false,"given":"Khadijeh","family":"Alibabaei","sequence":"first","affiliation":[{"name":"C-MAST Center for Mechanical and Aerospace Science and Technologies, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"},{"name":"Department of Electromechanical Engineering, University of Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1691-1709","authenticated-orcid":false,"given":"Pedro D.","family":"Gaspar","sequence":"additional","affiliation":[{"name":"C-MAST Center for Mechanical and Aerospace Science and Technologies, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"},{"name":"Department of Electromechanical Engineering, University of Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7540-3854","authenticated-orcid":false,"given":"T\u00e2nia M.","family":"Lima","sequence":"additional","affiliation":[{"name":"C-MAST Center for Mechanical and Aerospace Science and Technologies, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"},{"name":"Department of Electromechanical Engineering, University of Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,29]]},"reference":[{"key":"ref_1","unstructured":"(2019). World Urbanization Prospects: The 2018 Revision (ST\/ESA\/SER.A\/420), United Nations, Department of Economic and Social Affairs, Population Division. Technical Report."},{"key":"ref_2","unstructured":"Vermesan, O., and Friess, P. (2016). Internet of Food and Farm 2020. Digitising the Industry, River Publishers."},{"key":"ref_3","unstructured":"FAO (2020, May 01). World Agriculture 2030: Main Findings. Available online: http:\/\/www.fao.org\/english\/newsroom\/news\/2002\/7833-en.html."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1007\/s00484-011-0485-7","article-title":"Neural network approach to reference evapotranspiration modeling from limited climatic data in arid regions","volume":"56","author":"Laaboudi","year":"2012","journal-title":"Int. J. Biometeorol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"104320","DOI":"10.1016\/j.cageo.2019.104320","article-title":"Modelling of soil moisture retention curve using machine learning techniques: Artificial and deep neural networks vs support vector regression models","volume":"133","author":"Achieng","year":"2019","journal-title":"Comput. Geosci."},{"key":"ref_6","unstructured":"Allen, R.G., Pereira, L.S., Raes, D., and Smith, M. (1998). Crop Evapotranspiration\u2014Guidelines for Computing Crop Water Requirements FAO Irrigation and Drainage Paper 56, FAO\u2014Food and Agriculture Organization of the United Nations."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"105474","DOI":"10.1016\/j.compag.2020.105474","article-title":"A survey on intelligent agents and multi-agents for irrigation scheduling","volume":"176","author":"Jimenez","year":"2020","journal-title":"Comput. Electron. Agric."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2513","DOI":"10.5194\/hess-19-2513-2015","article-title":"Extending periodic eddy covariance latent heat fluxes through tree sap-flow measurements to estimate long-term total evaporation in a peat swamp forest","volume":"19","author":"Clulow","year":"2015","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s00271-010-0230-8","article-title":"Artificial neural networks approach in evapotranspiration modeling: A review","volume":"29","author":"Kumar","year":"2011","journal-title":"Irrig. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1016\/j.jhydrol.2016.11.007","article-title":"A comparison of numerical and machine-learning modeling of soil water content with limited input data","volume":"543","author":"Karandish","year":"2016","journal-title":"J. Hydrol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Adeyemi, O., Grove, I., Peets, S., Domun, Y., and Norton, T. (2018). Dynamic Neural Network Modelling of Soil Moisture Content for Predictive Irrigation Scheduling. Sensors, 18.","DOI":"10.3390\/s18103408"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yamac, S.S., Seker, C., and Negis, H. (2020). Evaluation of machine learning methods to predict soil moisture constants with different combinations of soil input data for calcareous soils in a semi arid area. Agric. Water Manag., 234.","DOI":"10.1016\/j.agwat.2020.106121"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Fernandez-Lopez, A., Marin-Sanchez, D., Garcia-Mateos, G., Ruiz-Canales, A., Ferrandez-Villena-Garcia, M., and Molina-Martinez, J.M. (2020). A Machine Learning Method to Estimate Reference Evapotranspiration Using Soil Moisture Sensors. Appl. Sci., 10.","DOI":"10.3390\/app10061912"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Tseng, D., Wang, D., Chen, C., Miller, L., Song, W., Viers, J., Vougioukas, S., Carpin, S., Ojea, J.A., and Goldberg, K. (2018, January 20\u201324). Towards Automating Precision Irrigation: Deep Learning to Infer Local Soil Moisture Conditions from Synthetic Aerial Agricultural Images. Proceedings of the 2018 IEEE 14th International Conference on Automation Science and Engineering (CASE), Munich, Germany.","DOI":"10.1109\/COASE.2018.8560431"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1007\/s40333-016-0049-0","article-title":"Modeling spatio-temporal distribution of soil moisture by deep learning-based cellular automata model","volume":"8","author":"Song","year":"2016","journal-title":"J. Arid. Land"},{"key":"ref_16","first-page":"149","article-title":"Temperature based generalized wavelet-neural network models to estimate evapotranspiration in India","volume":"5","author":"Adamala","year":"2018","journal-title":"Inf. Process. Agric."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.compag.2018.11.031","article-title":"Reference evapotranspiration estimation and modeling of the Punjab Northern India using deep learning","volume":"156","author":"Saggi","year":"2019","journal-title":"Comput. Electron. Agric."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105700","DOI":"10.1016\/j.compag.2020.105700","article-title":"Reference evapotranspiration time series forecasting with ensemble of convolutional neural networks","volume":"177","author":"Alves","year":"2020","journal-title":"Comput. Electron. Agric."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1016\/j.jhydrol.2018.04.065","article-title":"Developing a Long Short-Term Memory (LSTM) based model for predicting water table depth in agricultural areas","volume":"561","author":"Zhang","year":"2018","journal-title":"J. Hydrol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.neunet.2014.09.003","article-title":"Deep learning in neural networks: An overview","volume":"61","author":"Schmidhuber","year":"2015","journal-title":"Neural Netw."},{"key":"ref_21","unstructured":"Drucker, H., Burges, C.J.C., Kaufman, L., Smola, A., and Vapnik, V. (1996, January 2\u20135). Support Vector Regression Machines. Proceedings of the 9th International Conference on Neural Information Processing Systems, NIPS\u201996, Denver, CO, USA."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1214\/aoms\/1177703732","article-title":"Robust estimation of a location parameter","volume":"35","author":"Huber","year":"1964","journal-title":"Ann. Math. Stat."},{"key":"ref_24","unstructured":"Mu\u00f1oz Sabater, J. (2021, April 15). ERA5-Land hourly data from 1981 to present. Copernicus Climate Change Service (C3S) Climate Data Store (CDS). Available online: https:\/\/cds.climate.copernicus.eu\/cdsapp#!\/dataset\/reanalysis-era5-land?tab=overview."},{"key":"ref_25","unstructured":"(2018). IFS Documentation CY45R1\u2014Part IV: Physical processes. IFS Documentation CY45R1, ECMWF. Number 4 in IFS Documentation."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"389","DOI":"10.5194\/hess-19-389-2015","article-title":"ERA-Interim\/Land: A global land surface reanalysis data set","volume":"19","author":"Balsamo","year":"2015","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1063\/1.1745010","article-title":"Capillary conduction of liquids through porous mediums","volume":"1","author":"Richards","year":"1931","journal-title":"Physics"},{"key":"ref_28","unstructured":"Montgomery, D.C., Jennings, C.L., and Kulahci, M. (2011). Introduction to Time Series Analysis and Forecasting, Wiley."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Benesty, J., Chen, J., Huang, Y., and Cohen, I. (2009). Pearson Correlation Coefficient. Noise Reduction in Speech Processing, Springer.","DOI":"10.1007\/978-3-642-00296-0_5"},{"key":"ref_30","unstructured":"Kreyszig, E., Kreyszig, H., and Norminton, E.J. (2011). Advanced Engineering Mathematics, Wiley. [10th ed.]."},{"key":"ref_31","unstructured":"Patterson, J., and Gibson, A. (2017). Deep Learning: A Practitioner\u2019s Approach, O\u2019Reilly."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-Term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2673","DOI":"10.1109\/78.650093","article-title":"Bidirectional recurrent neural networks","volume":"45","author":"Schuster","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","unstructured":"Sermanet, P., Eigen, D., Zhang, X., Mathieu, M., Fergus, R., and LeCun, Y. (2013). OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks. arXiv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/TPAMI.2016.2599174","article-title":"Long-Term Recurrent Convolutional Networks for Visual Recognition and Description","volume":"39","author":"Donahue","year":"2017","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_36","unstructured":"Gal, Y., and Ghahramani, Z. (2016, January 5\u201310). A Theoretically Grounded Application of Dropout in Recurrent Neural Networks. Proceedings of the 30th International Conference on Neural Information Processing Systems, NIPS\u201916, Barcelona, Spain."},{"key":"ref_37","first-page":"xiv+254","article-title":"Bayesian approach to global optimization","volume":"Volume 37","author":"Mockus","year":"1989","journal-title":"Mathematics and its Applications (Soviet Series)"},{"key":"ref_38","unstructured":"Bergstra, J., Bardenet, R., Bengio, Y., and K\u00e9gl, B. (2011, January 12\u201314). Algorithms for Hyper-Parameter Optimization. Proceedings of the 24th International Conference on Neural Information Processing Systems, NIPS\u201911, Granada, Spain."},{"key":"ref_39","unstructured":"Brochu, E., Cora, V.M., and de Freitas, N. (2009). A Tutorial on Bayesian Optimization of Expensive Cost Functions with Application to Active User Modeling and Hierarchical Reinforcement Learning, University of British Columbia\u201a Department of Computer Science. Technical Report."},{"key":"ref_40","unstructured":"Nogueira, F. (2020, August 01). Bayesian Optimization: Open Source Constrained Global Optimization Tool for Python. Available online: https:\/\/github.com\/fmfn\/BayesianOptimization."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"8995","DOI":"10.1029\/JC090iC05p08995","article-title":"Statistics for the evaluation and comparison of models","volume":"90","author":"Willmott","year":"1985","journal-title":"J. Geophys. Res. Ocean."},{"key":"ref_42","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., and Devin, M. (2020, April 01). TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. Available online: tensorflow.org."},{"key":"ref_43","unstructured":"Chollet, F. (2020, April 01). Keras. Available online: https:\/\/keras.io."},{"key":"ref_44","unstructured":"Kingma, D.P., and Ba, J. (2015, January 7\u20139). Adam: A Method for Stochastic Optimization, 2014. Proceedings of the 3rd International Conference for Learning Representations, San Diego, CA, USA. arxiv:1412.6980."},{"key":"ref_45","first-page":"1471","article-title":"Training and Testing Low-degree Polynomial Data Mappings via Linear SVM","volume":"11","author":"Chang","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_46","unstructured":"Sutton, R.S., and Barto, A.G. (2018). Reinforcement Learning: An Introduction, The MIT Press. [2nd ed.]."}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/11\/11\/5029\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:10:18Z","timestamp":1760163018000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/11\/11\/5029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,29]]},"references-count":46,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["app11115029"],"URL":"https:\/\/doi.org\/10.3390\/app11115029","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,29]]}}}