Estimated reference evapotranspiration of the Paulista Plateau through multiple regressions with missing data estimated via main component analysis
DOI:
https://doi.org/10.33448/rsd-v11i8.31120Keywords:
Principal components analysis; Multiple regression; Missing data.Abstract
Evapotranspiration is a physical phenomenon that promotes the complex transfer of water to the atmosphere through the relationship between climatological water balance, surface water evaporation and transpiration from agricultural crops. Obtaining reliable measurements of evapotranspiration is a complex task. The objective of this work was to apply the multivariate technique Principal Component Analysis to fill in missing data and model the reference evapotranspiration by multiple regression, with subsequent comparison with the Penman-Monteith model. Principal Component Analysis, the EM algorithm, was applied to reconstruct the climatic database of 30 automatic weather stations in the Western Plateau of São Paulo, located in the northwest of the State of São Paulo, Brazil. Measures for the period 2013-2017. Subsequently, an exploratory analysis of the climatic variables was carried out to verify the grouping of the most relevant climatic variables in the physical processes of evapotranspiration. These clusters were the basis for the construction of different reference evapotranspiration estimation models through Multiple Regressions. The results showed the best performances for EToRLM4 (rRMSE = 5.23%), EToRNLM4 (rRMSE = 6.39%). The values of the statistical indicatives of the validation base of RLM4 and RNLM4 indicate that both multiple regression models can be used to estimate the reference evapotranspiration.
References
Adeloye, A. J.; Rustum, R.; Kariyama, I. D (2012). Neural Computing Modeling of the reference crop evapotranspiration. Environmental Modelling e Software, v. 29, pp. 61-73.
Allen, R. G., Pereira, L. S., Raes, D. & Smith, M. (1998). Crop evapotranspiration: guidelines for computing crop water requirements. Rome: FAO. 300p. (Irrigation and Drainage Paper, 56).
Allen, R. G.; Pruitt, W. O. (1991). FAO-24 reference evapotranspiration factors. Journal of Irrigation and Drainage Engineering, v. 177, 758 - 773. doi: https://doi.org/10.1061/(ASCE)0733-9437(1991)117:5(758)
Almedeij, J. (2012). Modeling Pan Evaporation for Kuwait by Multiple Linear Regression. The Scientific World Journal, Article ID 574742, 9 pages, doi: 10.1100/2012/574742.
Althoff, D.; Bazame, H. C.; Filgueiras, R. et al. (2018). Heuristic methods applied in reference evapotranspiration modeling. Ciência e Agrotecnologia, v. 42, n. 3, pp. 314-324.
Benavides, J. G., & Lopez Diaz, Y. J. (1970). Formula para el calculo de la evapotranspiracion potencial adaptada al tropico (15º N - 15º S). Agronomia Tropical, Maracay, 20(5), 335-345.
Bilgili, M. (2010). Prediction of soil temperature using regression and artificial neural network models. Meteorology and Atmospheric Physic, v. 110, pp. 59-70. DOI: 10.1007/s00703-010-0104-x
Blaney, H. F.; Criddle, W. D. (1950). Determining Water Requirements in Irrigated Areas from Climatological and Irrigation Data. US Dep. of Agr. Tech. Pap. No. 96, p. 48.
Bogawski, P.; Bednorz, E. (2014). Comparison and Validation of Selected Evapotranspiration Models for Conditions in Poland (Central Europe). Water Resources Management, v. 28, pp. 5021-5038. doi: https://doi.org/10.1007/s11269-014-0787-8
Cristea, N. C.; Kampf, S. K.; Burges, S. J. (2013). Linear models for estimating annual and growing season reference evapotranspiration using averages of weather variables. International Journal of Climatology, v. 33, pp. 376–387. doi: https://doi.org/10.1002/joc.3430
García-Diego, F.; F. J.; Zarzo, M. (2010). Microclimate monitoring by multivariate statistical control: The renaissance frescoes of the Cathedral of Valencia (Spain). Journal of Cultural Heritage, v. 11, pp. 339-344. doi: https://doi.org/10.1016/j.culher.2009.06.002.
Hargreaves, G. H, Samani, Z. A. (1985). Reference crop evapotranspiration from temperature. Applied Engineering in Agriculture, v. 1, n. 2, pp. 96-99. doi: http://dx.doi.org/10.13031/2013.26773
Ikudayisi, Akinola & Adeyemo, Josiah. (2016). Effects of Different Meteorological Variables on Reference Evapotranspiration Modeling: Application of Principal Component Analysis. International Journal of Environmental, Chemical, Ecological, Geological and Geophysical Engineering. 10. 623-627.
Iqbal, M. (1983). An introduction to solar radiation. New York: Academic Press, 390 p.
Jensen, M. E.; Haise, H. R. (1963). Estimating evapotranspiration from solar radiation. Proceeding of the American Society of Civil Engineers, Journal of Irrigation and Drainage Division, v. 89, p. 15-41.
Josse, J.; Husson, F. (2016). missMDA: A Package for Handling Missing Values in Multivariate Data Analysis. Journal of Statistical Software, v. 70, pp. 1-31. doi: https://doi.org/10.18637/jss.v070.i01
Josse, J.; Husson, F. (2012). Handling missing values in exploratory multivariate data analysis methods. Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2012, 153 (2), pp.79-99. ⟨hal-00811888⟩
Josse, J.; Husson, F.; Pagès, J. (2009). Gestion des donn´ees manquantes en Analyse en Composantes Principales. Journal de la Société Française de Statistique, v. 150, n. 2, pp. 28-51. http://www.numdam.org/item/JSFS_2009__150_2_28_0/
Khanmohammadi, N.; Rezaie, H.; Montaseri, M. et al. (2018). The application of multiple linear regression method in reference evapotranspiration trend calculation. Stochastic Environmental Research and Risk Assessment, v. 32, pp. 661-673. DOI:10.1007/s00477-017-1378-z
Kisi, O; Demir, V. (2016). Evapotranspiration Estimation using Six Different Multi-layer Perceptron Algorithms. Irrigation e Drainage Systems Engineering, v. 5, n. 2, pp. 1-6. https://doi.org/10.1080/02626667.2019.1678750
Kisi, O; Cimen, M. (2011). Evapotranspiration modeling using a wavelet regression model. Irrigation Science, v. 29, pp. 241-252. doi:10.1007/s00271-010-0232-6
Köppen, W.; Geiger, R. (1928). Klimate der Erde. Gotha: Verlag Justus Perthes. Wall-map 150cmx200cm.
Ladlani, I.; Houichi, L.; Djemili, L. et al. (2014). Estimation of Daily Reference Evapotranspiration (ETo) in the North of Algeria Using Adaptive Neuro-Fuzzy Inference System (ANFIS) and Multiple Linear Regression (MLR) Models: A Comparative Study. Arabian. Journal for Science and Engineering, DOI 10.1007/s13369-014-1151-2.
Laaboudi, A.; Brahim, M.; Draoui, B. (2012). Conceptual Reference Evapotranspiration Models for Different Time Steps. Petroleum & Environmental Biotechnology. Volume 3. 10.4172/2157-7463.1000123.
Landeras, G.; Ortiz-Barredo, A.; López, J. J. (2008). Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain). Agricultural Water Management, v. 95, pp. 553-565. doi: 10.1016/j.agwat.2007.12.011
Mahida, H. R.; Patel, V. N. (2015). Impact of Climatological Parameters on Reference Crop Evapotranspiration using Multiple Linear Regression Analysis. SSRG International Journal of Civil Engineering (SSRG-IJCE), v. 2, pp. 21-24. doi:10.14445/23488352/IJCE-V2I1P103
Makkink, G. F. (1957). Testing the Penman formula by means of lysimeters. Journal of the Institution of Water Engineers, v. 11, n. 3, pp. 277-288.
Mallikarjuna, P.; Jyothy, S. A.; Reddy, K. C. S. (2013). Daily Reference Evapotranspiration Estimation using Linear Regression and ANN Models. Journal of The Institution of Engineers (India), v. 97, n. 4, pp. 215-221. doi: 10.1007/s40030-013-0030-2
Manikumari, N.; Vinodhini, G. (2016). Regression Models for Predicting Reference Evapotranspiration. In ternational Journal of Engineering Trends and Technology (IJETT), v. 38, n. 3, pp. 134-139. doi:0.14445/22315381/IJETT-V38P224
Marofi, S; Mohammad M, S.; Kourosh, M.; et al. (2011). Investigation of meteorological extreme events over coastal regions of Iran. Theoretical and Applied Climatology. 103. 401-412. DOI: 10.1007/s00704-010-0298-3.
Martí, P.; Gasque, M. (2010). Ancillary data supply strategies for improvement of temperature-based ETo ANN models. Agricultural Water Management, v. 97, pp. 939-955. doi: https://doi.org/10.1016/j.agwat.2010.02.002
Martí, P.; González-altozano, M. (2011). Reference evapotranspiration estimation without local climatic data. Irrigation Science, v. 29, pp. 479-495. doi: 10.1007/s00271-010-0243-3
Martí, P.; Zarzo, M. (2012). Multivariate statistical monitoring of ETo: A new approach for estimation in nearby locations using geographical inputs. Agricultural and Forest Meteorology, v. 152, pp. 125 - 134. doi: 10.1016/j.agrformet.2011.08.008
Melo Prado, B. Q.; Fernandes, H. R.; Araújo, T. G. et al. (2016). Avaliação de variáveis climatológicas da cidade de Uberlândia (MG) por meio da análise de componentes principais. Engenharia Sanitária e Ambiental, v. 21, n. 21, pp. 407 - 413. doi:https://doi.org/10.1590/s1413-41522016147040.
Mohan, S.; Arumugam, N. (1996). Relative Importance of Meteorological Variables in Evapotranspiration: Factor Analysis Approach. Water Resources Management, v. 10, pp. 1 - 20. doi: https://doi.org/10.1007/BF00698808
Oracle Corporation. (2019). Chapter 1 General Information. MySQL 5.7 Reference Manual, 2019. Disponível em: https://dev.mysql.com/doc/refman/5.7/en/introduction.html. Acesso em: 08 abr. 2019.
Ozbayoglu, G.; Ozbayoglu, M. E. (2006). A new approach for the prediction of ash fusion temperatures: a case study using Turkish lignites. Fuel, v. 85, pp. 545–552. doi: 10.1016/j.fuel.2004.12.020
Penman, H. L. (1948). Natural evaporation from open water, bare soil, and grass. Proceedings of the Royal Society, London, v. 193, n. 1, p. 120-146. doi: https://doi.org/10.1098/rspa.1948.0037.
Priestley, C. H. B., Taylor, R. J. (1972). On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review, v. 100, n. 2, pp. 81-92. doi: http://dx.doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2
R Core Team. (2020). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Rolim, G. S.; Camargo, M. B. P.; Lania, D. G.; et al. (2007). Classificação climática de Köppen e de Thornthwaite e sua aplicabilidade na determinação de zonas agroclimáticas para o estado de São Paulo. Bragantia, Campinas, v. 66, n. 4, p. 711-720. doi: https://doi.org/10.1590/S0006-87052007000400022.
Santos, C. M.; Souza, J. L.; Ferreira Júnior, R. A. et al. (2014). On modeling global solar irradiation using air temperature for Alagoas State, Northeastern Brazil. Energy, v. 71, 338-398. doi: 10.1016/j.energy.2014.04.116
Shiri, J.; Nazemi, A. H.; Sadraddini, A. A.; et al. (2014). Comparison of heuristic and empirical approaches for estimating reference evapotranspiration from limited inputs in Iran. Computers and Eletronics in Agriculture, v. 108, pp. 230-241.
Shiri, J.; Sadraddini, A. A.; Nazemi, A. H. et al. (2015). Independent testing for assessing the calibration of the Hargreaves-Samani equation: New heuristic alternatives for Iran. Computers and Eletronics in Agriculture, v. 117, pp. 70-80. doi: 10.1016/j.compag.2015.07.010
Silva, I. N.; Spatti, D. H.; Flausino, R. A. (2016a). Redes Neurais Artificiais para engenharia e ciências aplicadas – fundamentos teóricos e aspectos práticos. 2nd ed. Artiliber 431 p.
Silva, H. J. F.; Santos, M. S.; Cabral júnior, J. B. et al. (2016b). Modeling of reference evapotranspiration by multiple linear regression. Journal of Hyperspectral Remote Sensing, v. 6, n. 1, pp. 44-58. doi: https://doi.org/10.5935/2237-2202.20160005%20
Silva, M. B. P.; Escobedo, J. F.; Santos, C. M. et al. (2017). Performance of the Angstrom-Prescott Model (A-P) and SVM and ANN techniques to estimate the daily Global Solar Irradiation in Botucatu/SP/Brazil. Journal of Atmospheric and Solar–Terrestrial Physics, v. 160, pp. 11-23. doi: 10.1016/j.jastp.2017.04.001
Snyder, R. L. (1992). Equation for evaporation pan to evapotranspiration conversions. Journal of Irrigation and Drainage Engineering, v. 118, n. 6, pp. 977-980. doi: http://dx.doi.org/10.1061/(ASCE)0733-9437(1992)118:6(977)
Sriram, A. V.; Rashmi, C. N. (2014). Estimation of Potential Evapotranspiration by Multiple Linear Regression Method. IOSR Journal of Mechanical and Civil Engineering, v. 11, pp. 65-70. doi: 10.9790/1684-11246570
Tabari, H.; Grismer, M. E. (2013). Comparative analysis of 31 reference evapotranspiration methods under humid conditions. Irrigation Science, v. 31, pp. 107-117. doi:10.1007/s00271-011-0295-z
Tabari, H.; Kisi, O.; Ezani, A. et al. (2012). SVM, ANFIS, regression and climate based models for reference evapotranspiration modeling using limited climatic data in a semi-arid highland environment. Journal of Hidrology, v. 444-445, pp. 78-89. doi : 10.1016/j.jhydrol.2012.04.007
Tangune', B. F.; Escobedo, J. F. (2018). Reference evapotranspiration in São Paulo State: Empirical methods and machine learning techniques. International Journal of Water Resources and Environmental Engineering, v. 10, n. 4, pp. 33-44.
Thornthwaite, C. W. (1948). An approach toward a rational classification of climate. Geographical Review, v. 55–94, pp. 38.
Xu, J.; Peng, S.; Wang, W. et al. (2013). Prediction of daily reference evapotranspiration by a multiple regression method based on weather forecast data. Archives of Agronomy and Soil Science, v. 59, n. 11, pp. 1487-1501. doi: 10.1080/03650340.2012.727400
Ye, X. A.; Li, X.; Liu, J. et al. (2014). Variation of reference evapotranspiration and its contributing climatic factors in the Poyang Lake catchment, China. Hydrological Processes, v. 28, pp. 6151-6162. doi: https://doi.org/10.1002/hyp.10117
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Maurício Bruno Prado da Silva; Valter Cesar de Souza; Caroline Pires Cremasco; Marcus Vinícius Contes Calça; Cícero Manoel dos Santos; Camila Pires Cremasco; Luís Roberto Almeida Gabriel Filho ; Sergio Augusto Rodrigues; João Francisco Escobedo
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
1) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2) Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3) Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
