International Journal of
Water Resources and Environmental Engineering

  • Abbreviation: Int. J. Water Res. Environ. Eng.
  • Language: English
  • ISSN: 2141-6613
  • DOI: 10.5897/IJWREE
  • Start Year: 2009
  • Published Articles: 314

Full Length Research Paper

Reference evapotranspiration in São Paulo State: Empirical methods and machine learning techniques

Bartolomeu Felix Tangune
  • Bartolomeu Felix Tangune
  • Rural Engineering Departament, Eduardo Mondlane University, Vilankulo, Mozambique.
  • Google Scholar
Joao Francisco Escobedo
  • Joao Francisco Escobedo
  • Rural Engineering Department, FCA/UNESP, Botucatu, São Paulo, Brazil.
  • Google Scholar

  •  Received: 03 March 2018
  •  Accepted: 10 April 2018
  •  Published: 31 May 2018


Reference evapotranspiration (ETo) is a key factor for water management and irrigation scheduling. In this paper, eight empirical methods, including four temperature-based (Benevides-Lopez, Hamon, Blaney-Criddle Original and Hargreaves-Samani: HS), four radiation-based (Abtew: AB, Jensen and Haise, Makkink and Irmak) and machine learning techniques (MLT) were tested against Penman Monteith FAO 56 method. The MLT comprised six architectures for artificial neural networks (ANN) as well as  support vector machine (SVM). The results of the empirical methods showed that AB method performed best with Mean Bias Error (MBE) = -0.17 mm day-1; Root Mean Square Error (RMSE) = 0.45 mm day -1 and R2 = 0.89. However, in case of missing data of solar radiation (Rs), HS method can be a perfect alternative (MBE = 0.51 mm day-1; RMSE = 0.82 mm day-1 and R2 = 0.87). Afterwards, performance of AB and HS methods was compared to performance resulting from MLT. In MLT, 70% of data was used for training and the remaining 30%  was used  for validation. The used ANNs were of multilayer perceptron type, with backpropagation algorithm; in support vector machine, Kernel’s radial basic function was used with regression sequential minimal optimization algorithm. The results obtained with MLT is as follows: MBE = 0.07 mm day-1; RMSE = 0.20 mm day-1; R2 = 0.96 for A6 (ANN) and MBE = 0.00 mm day-1; RMSE = 0.18 mm day-1; R2 = 0.95 for S6 (SVM). A6 and S6 architectures were composed of maximum temperature (T max.), minimum (Tmin.), average temperature (T), extraterrestrial radiation (Ra) and Rs. The HS method was the worst method in terms of performance, while AB method had the best results than A1 and S1, which only used T. 
Key words: Evapotranspiration, support vector machine, empirical methods, artificial neural networks.