Theoretical and Applied Climatology

, Volume 130, Issue 3–4, pp 1099–1109 | Cite as

Predicting the reference evapotranspiration based on tensor decomposition

  • Negin Misaghian
  • Shahaboddin Shamshirband
  • Dalibor PetkovićEmail author
  • Milan Gocic
  • Kasra Mohammadi
Original Paper


Most of the available models for reference evapotranspiration (ET0) estimation are based upon only an empirical equation for ET0. Thus, one of the main issues in ET0 estimation is the appropriate integration of time information and different empirical ET0 equations to determine ET0 and boost the precision. The FAO-56 Penman–Monteith, adjusted Hargreaves, Blaney–Criddle, Priestley–Taylor, and Jensen–Haise equations were utilized in this study for estimating ET0 for two stations of Belgrade and Nis in Serbia using collected data for the period of 1980 to 2010. Three-order tensor is used to capture three-way correlations among months, years, and ET0 information. Afterward, the latent correlations among ET0 parameters were found by the multiway analysis to enhance the quality of the prediction. The suggested method is valuable as it takes into account simultaneous relations between elements, boosts the prediction precision, and determines latent associations. Models are compared with respect to coefficient of determination (R 2), mean absolute error (MAE), and root-mean-square error (RMSE). The proposed tensor approach has a R 2 value of greater than 0.9 for all selected ET0 methods at both selected stations, which is acceptable for the ET0 prediction. RMSE is ranged between 0.247 and 0.485 mm day−1 at Nis station and between 0.277 and 0.451 mm day−1 at Belgrade station, while MAE is between 0.140 and 0.337 mm day−1 at Nis and between 0.208 and 0.360 mm day−1 at Belgrade station. The best performances are achieved by Priestley–Taylor model at Nis station (R 2 = 0.985, MAE = 0.140 mm day−1, RMSE = 0.247 mm day−1) and FAO-56 Penman–Monteith model at Belgrade station (MAE = 0.208 mm day−1, RMSE = 0.277 mm day−1, R 2 = 0.975).


Mean Absolute Error Reference Evapotranspiration Tensor Model Tensor Decomposition Left Singular Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The study was supported by ICT COST Action IC1408 Computationally-intensive methods for the robust analysis of non-standard data (CRoNoS) and the Ministry of Education, Science and Technological Development, Republic of Serbia (Grant No. TR37003).


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Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  • Negin Misaghian
    • 1
  • Shahaboddin Shamshirband
    • 2
  • Dalibor Petković
    • 3
    Email author
  • Milan Gocic
    • 4
  • Kasra Mohammadi
    • 5
  1. 1.Young Researchers and Elite Club, Mashhad BranchIslamic Azad UniversityMashhadIran
  2. 2.Department of Computer System and Information technology, Faculty of Computer Science and Information TechnologyUniversity of MalayaKuala LumpurMalaysia
  3. 3.Teacher-Training FacultyUniversity of NišVranjeSerbia
  4. 4.Faculty of Civil Engineering and ArchitectureUniversity of NišNisSerbia
  5. 5.Department of Mechanical and Industrial EngineeringUniversity of MassachusettsAmherstUSA

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