Analysis of the Accuracy Comparison of Five Different Models of Valiantzas Equation in the Estimation of Reference Evapotranspiration

Document Type : Research Paper


1 Ph.D at Irrigation and Drainage, Urmia niversity.

2 Ph.D Student of Irrigation and Drainage, Urmia University

3 Professor, Department of Water Engineering, Urmia University

4 Assosiate Professor, Department of Water Engineering, University of Tabriz.


Evapotranspiration is one of the most important factors in hydrological cycle. Potential evapotranspiration is used to design in irrigation and drainage networks and hydrological studies (Davis & Dukes, 2010). The conducted studies in different regions of the world have shown that the FAO-Penman-Monteith model can be presented as the most accurate method under various climatic conditions (Irmak et al, 2003, ASCE-EWRI, 2005, Jabloun & Sahli, 2008, Martinez & Thepadia, 2010 and Azhar & Perera, 2011). The calibration of the mentioned equation using lysimetric data in a wide range of climatic conditions and its applicability without the requirement for local calibration in different climatic conditions are the benefits of the FAO-Penman-Monteith equation (Landeras et al, 2008). On the other hand, the Valiantzas model is one of the newest methods for estimating ETo. Advantages of using the Valiantzas equations in the estimation of reference evapotranspiration include simple application for spatial calibration, easy application for temporal distribution of reference evapotranspiration values, easy use for routine hydrological applications and simplicity of equations for other hydrological applications (a, b, c, Valiantzas, 2013). The purpose of this study was to evaluate and compare the accuracy of five different Valiantzas models for estimating reference evapotranspiration at the studied stations located in the northwest of Iran (Urmia Lake basin) including Urmia, Salmas, Mahabad, Takab, Tabriz, Sarab and Maragheh and providing the best version of the Valiantzas as the results of which are the highest concurrence with the FAO-Penman-Monteith method.


Main Subjects

1-    Ahooghalandari, M., Khiadani, M. and Jahromi, M.E., 2017. Calibration of Valiantzas’ reference evapotranspiration equations for the Pilbara region, Western Australia. Theoretical and applied climatology, 128(3-4), pp.845-856.
2-    Allen, R.G., Pereira, L.S., Raes, D. and Smith, M., 1998. Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. Fao, Rome, 300(9), p.D05109.
3-    Anderson, R.G., Lo, M.H. and Famiglietti, J.S., 2012. Assessing surface water consumption using remotely‐sensed groundwater, evapotranspiration, and precipitation. Geophysical Research Letters, 39(16).
4-    ASCE-EWRI., 2005. The ASCE standardized reference evapotranspiration equation. In: Allen, R. G., Walter, I. A., Elliot, R. L., et al.(Eds.), Environmental and Water Resources Institute (EWRI) of the American Society of Civil. Engineers, ASCE, Standardiza-tion of Reference Evapotranspiration Task Committee Final Report. American Society of Civil Engineers (ASCE), Reston, VA,pp.213.
5-    Azhar, A.H. and Perera, B.J.C., 2010. Evaluation of reference evapotranspiration estimation methods under Southeast Australian conditions. Journal of Irrigation and Drainage Engineering, 137(5), pp.268-279.
6-    Bastiaanssen, W.G.M., Noordman, E.J.M., Pelgrum, H., Davids, G., Thoreson, B.P. and Allen, R.G., 2005. SEBAL model with remotely sensed data to improve water-resources management under actual field conditions. Journal of Irrigation and Drainage Engineering, 131(1), pp.85-93.
7-    Davis, S.L. and Dukes, M.D., 2010. Irrigation scheduling performance by evapotranspiration-based controllers. Agricultural water management, 98(1), pp.19-28.
8-     DehghaniSanij, H., Yamamoto, T. and Rasiah, V., 2004. Assessment of evapotranspiration estimation models for use in semi-arid environments. Agricultural water management, 64(2), pp.91-106.
9-    Djaman, K., Balde, A.B., Sow, A., Muller, B., Irmak, S., N’Diaye, M.K., Manneh, B., Moukoumbi, Y.D., Futakuchi, K. and Saito, K., 2015. Evaluation of sixteen reference evapotranspiration methods under sahelian conditions in the Senegal River Valley. Journal of Hydrology: regional studies, 3, pp.139-159.
10- Djaman, K., Irmak, S., Kabenge, I. and Futakuchi, K., 2016. Evaluation of FAO-56 penman-monteith model with limited data and the valiantzas models for estimating grass-reference evapotranspiration in Sahelian conditions. Journal of Irrigation and Drainage Engineering, 142(11), p.04016044.
11-  Ferguson, I.M. and Maxwell, R.M., 2011. Hydrologic and land–energy feedbacks of agricultural water management practices. Environmental Research Letters, 6(1), p.014006.
12-  Fisher, J.B., DeBiase, T.A., Qi, Y., Xu, M. and Goldstein, A.H., 2005. Evapotranspiration models compared on a Sierra Nevada forest ecosystem. Environmental Modelling & Software, 20(6), pp.783-796.
13- Fisher, D.K. and Pringle III, H.C., 2013. Evaluation of alternative methods for estimating reference evapotranspiration. Agricultural Sciences, 4(08), p.51. -60.
14- Holwerda, F., Bruijnzeel, L.A., Barradas, V.L. and Cervantes, J., 2013. The water and energy exchange of a shaded coffee plantation in the lower montane cloud forest zone of central Veracruz, Mexico. Agricultural and forest meteorology, 173, pp.1-13
15-  Irmak, S., Irmak, A., Allen, R.G. and Jones, J.W., 2003. Solar and net radiation-based equations to estimate reference evapotranspiration in humid climates. Journal of irrigation and drainage engineering, 129(5), pp.336-347.
16- Jabloun, M.D. and Sahli, A., 2008. Evaluation of FAO-56 methodology for estimating reference evapotranspiration using limited climatic data: Application to Tunisia. Agricultural water management, 95(6), pp.707-715.
17-  Jakimavičius, D., Kriaučiūnienė, J., Gailiušis, B. and Šarauskienė, D., 2013. Assessment of uncertainty in estimating the evaporation from the Curonian Lagoon. Baltica, 26(2), pp.177-186.
18-  Jun, W., Xinhua, W., Meihua, G. and Xuyan, X.U., 2012. Impact of climate change on reference crop evapotranspiration in Chuxiong City, Yunnan Province. Procedia Earth and Planetary Science, 5, pp.113-119.
19-  Kisi, O., 2013. Comparison of different empirical methods for estimating daily reference evapotranspiration in Mediterranean climate. Journal of Irrigation and Drainage Engineering, 140(1), p.04013002.
20- Kueppers, L.M., Snyder, M.A. and Sloan, L.C., 2007. Irrigation cooling effect: Regional climate forcing by land‐use change. Geophysical Research Letters, 34(3).
21-  Landeras, G., Ortiz-Barredo, A. and 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, 95(5), pp.553-565.
22-  Lo, M.H. and Famiglietti, J.S., 2013. Irrigation in California's Central Valley strengthens the southwestern US water cycle. Geophysical Research Letters, 40(2), pp.301-306.
23-  Martinez, C.J. and Thepadia, M., 2009. Estimating reference evapotranspiration with minimum data in Florida. Journal of irrigation and drainage engineering, 136(7), pp.494-501.
24-  Meissner, R., Rupp, H., Seeger, J., Ollesch, G. and Gee, G.W., 2010. A comparison of water flux measurements: passive wick‐samplers versus drainage lysimeters. European journal of soil science, 61(4), pp.609-621.
25- Puma, M.J. and Cook, B.I., 2010. Effects of irrigation on global climate during the 20th century. Journal of Geophysical Research: Atmospheres, 115(D16).
26-  Sabziparvar, A.A., Tabari, H., Aeini, A. and Ghafouri, M., 2010. Evaluation of class A pan coefficient models for estimation of reference crop evapotranspiration in cold semi-arid and warm arid climates. Water resources management, 24(5), pp.909-920.
27- Steinman, B.A., Rosenmeier, M.F., Abbott, M.B. and Bain, D.J., 2010. The isotopic and hydrologic response of small, closed‐basin lakes to climate forcing from predictive models: Application to paleoclimate studies in the upper Columbia River basin. Limnology and Oceanography, 55(6), pp.2231-2245.
28-  Tabari, H., 2010. Evaluation of reference crop evapotranspiration equations in various climates. Water resources management, 24(10), pp.2311-2337.
29-  Tabari, H., Grismer, M.E. and Trajkovic, S., 2013. Comparative analysis of 31 reference evapotranspiration methods under humid conditions. Irrigation Science, 31(2), pp.107-117.
30-  Tang, Q., Peterson, S., Cuenca, R.H., Hagimoto, Y. and Lettenmaier, D.P., 2009. Satellite‐based near‐real‐time estimation of irrigated crop water consumption. Journal of Geophysical Research: Atmospheres, 114(D5).
31- Trajkovic, S. and Kolakovic, S., 2009. Evaluation of reference evapotranspiration equations under humid conditions. Water Resources Management, 23(14), p.3057 –3067.
32- Valiantzas, J.D., 2013a. Simple ETo forms of Penman's equation without wind and/or humidity data. I: theoretical development. Irrigation and Drainage Engineering, 139(1),pp.1–8.
33- Valiantzas, J.D., 2013b. Simple ETo forms of Penman's equation without wind and/or humidity data. II: comparisons with reduced set-FAO and other methodologies. Irrigation and Drainage Engineering, 139(1),pp.9–19.
34- Valiantzas, J.D., 2013c. Simplified reference evapotranspiration formula using an empirical impact factor for Penman's aerodynamic term. Hydrologic Engineering, 18(1),pp.108–114.
35-  Valipour, M., 2015. Investigation of Valiantzas’ evapotranspiration equation in Iran. Theoretical and applied climatology, 121(1-2), pp.267-278.
36- Zhao, L., Xia, J., Xu, C.Y., Wang, Z., Sobkowiak, L. and C. Long., 2013. Evapotranspiration estimation methods in hydrological models. Geographical Sciences, 23(2),pp.359–369.
37- Zhao, J., Xu, Z.X., Zuo, D. P. and X.M. Wang., 2015. Temporal variations of reference evapotranspiration and its sensitivity to meteorological factors in Heihe river basin, China. Water Science and Engineering, 8(1),pp.1-8.
Volume 41, Issue 3
November 2018
Pages 119-132
  • Receive Date: 08 January 2016
  • Revise Date: 08 February 2017
  • Accept Date: 19 February 2017
  • First Publish Date: 23 October 2018