Document Type : Research Paper


1 M.Sc. Alumni, Department. of Water Sciences and Engineering, Faculty of Agriculture and Natural Resources, Imam Khomeini International University, Qazvin, Iran

2 Assoc. Professor, Department of Water Sciences and Engineering, Faculty of Agriculture and Natural Resources, Imam Khomeini International University, Qazvin, Iran


In order to determine the amount of irrigation water, it is required to calculate the amount of the plant water requirement or evapotranspiration. The equations used to calculate evapotranspiration do not use the same climatic parameters and are not suitable for all climatic conditions due to their experimental nature. Potential evapotranspiration (ETp) and reference evapotranspiration (ETo) are different in concepts, equations, and contexts; however, many researchers have considered the use of the two terms to be the same. This study provided a comprehensive review of the ETp and ETo equations. In this regard, using meteorological data of synoptic station and lysimetric information of the region, reference and potential evapotranspiration were compared and studied based on four experimental groups during 4 years. The equations were calibrated using statistical indicators to select the most ideal model. The results showed that the evapotranspiration potential and the reference are completely different from each other, so that in the same method of the temperature equations of ETo and ETp, the RMSE calculated was 1.17 and 1.1, mm/day, respectively. According to the studies from the ETo and ETo, the temperature group equations had the best performance, showing the superiority of this group of equations in areas with arid and semi-arid climate.


Main Subjects

Abtew, W. (1996). Evapotranspiration measurements and modeling for three wetland systems in south florid. Jawra J. Am. Water Resour. Assoc. 32, 465–473.
Ahooghalandari, M., Khiadani, M. and Jahromi, M. E. (2016). Developing Equations forEstimating Reference Evapotranspiration in Australia. Water Resour. Manag. 30, 3815–3828.
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, No. 56, Rome, Italy.
Albrecht, F. (1950). Die Methoden zur Bestimmung der Verdunstung der natürlichen Erdoberfläche.Archiv. Für Meteorologie Geophysik Und Bioklimatologie Serie B 2,1–38.
BahmanAbadi, B. and Kaviani, A. (2020). Estimation of Potential Evaporationspiration in Different Climates of Iran. Iran. Soil Water Res., 51(6), 1479-1499. [In Persian]
Bakhtiari, B., Ghahreman, N., Liaghat, A. and Hoogenboom, G. (2011). Evaluation of reference evapotranspiration models for a semiarid environment using lysimeter measurements. J. Agr. Sci. Tech. 13, 223–237.
Brockamp, B. and Wenner, H., (1963). Verdunstungsmessungen auf den Steiner See bei Münster. Dt Gewässerkundl Mitt., 7, 149–154.
Baier, W., Robertson, G.W. (1965). Estimation of latent evaporation from simple weather observations. Can. J. Plant. Sci. 45, 276–284.
Blaney, H. F., Criddle, W. D. (1950). Determining water requirements in irrigated areas from climatological and irrigation data. Soil conservation service technical paper96, Soil conservation service. US Department of Agriculture, Washington.
Caprio, J. M. (1974). Phenology and seasonality modeling. In: Springer, V. (Ed.), The solar thermal unit concept in problems related to plant development and potential evapotranspiration, pp. 353–364 New York.
Chang, X., Wang, S., Gao, Z., Luo, Y., Chen, H., (2018). Forecast of Daily Reference Evapotranspiration Using a Modified Daily Thornthwaite Equation and Temperature Forecasts. Irrig. Drain. 68, 297–317.
Castaneda, L., Rao, P. (2005). Comparison of methods for estimating reference evapotranspiration in Southern California. J. Environ. Hydrol. 13, 1–10.
Christiansen, J.E. (1968). Pan evaporation and evapotranspiration from climatic data. J. Irrig. Drain. Eng. Division. 94, 243–266.
Djaman, K.; Balde, A.B.; Sow, A.; Muller, B.; Irmak, S.; N’Diaye, M.K.; Manneh, B.; Moukoumbi, Y.D.; Futakuchi, K.; Saito, K. (2015). Evaluation of sixteen reference evapotranspiration methods under sahelian conditions in the senegal river valley. J. Hydrol. Reg. Stud., 3, 139–159.
Djaman, K., Tabari, H., Balde, A. B., Diop, L., Futakuchi, K., Irmak, S., (2016). Analyses, calibration and validation of evapotranspiration models to predict grass-reference evapotranspiration in the Senegal river delta. J. Hydrol., 8, 82–94.
Doorenbos, J., Pruitt, W. (1977). Guidelines for predicting crop water requirements, Irrig. Drain. Paper No. 24. FAO, Rome, Italy.
 De Bruin, H. (1981). The determination of (reference crop) evapotranspiration from routine weather data. Evaporation in relation to hydrology. Proceedings of Technical Meeting 38, Committee for Hydrological Research TNO, Evaporation in relation to hydrology. Proc. Inform., 25, 25–37.
Dalton, J. (1802). Experimental essays on the constitutions of mixed gases; on the force of steam of vapor from waters and other liquids in different temperatures, both in a Torricellian vacuum and in air; on evaporation; and on the expansion of gases by heat. Mem. Manch. Lit. Philos. Soc. 5, 535-602.
Farzanpour, H. Shiri, J. Sadraddini, A. A. Trajekovic, S. (2018). Global comparison of 20 reference evapotranspiration equations in a semi-arid region of Iran. Hydrol. Res., doi: 10.2166/nh. 2018.174.
Feng, Y., Jia, Y., Cui, N. Zhao, L. Li, C. and Gong, D. (2017). Calibration of Hargreaves model for reference evapotranspiration estimation in Sichuan basin of southwest China. J. Agri. Water Manage., 181, 1–9.
Gocic, M. and Trajkovic, S. (2014). Analysis of trends in reference evapotranspiration data in a humid climate. Hydrol. Sci. J. 59, 165–180.
Helm, P., Stirling, R. and Glendinning, S. )2016(. The Implications of Using Estimated Solar Radiation on the Derivation of Potential Evapotranspiration and Soil Moisture Deficit within an Embankment. Procedia Eng. 143, 697–707.
Hargreaves, G. H. and Samani, Z. A. )1982(. Estimating potential evapotranspiration. J. Irrig. Drain. Eng. Division 108, 225–230.
 Hargreaves, G. H. and Samani, Z.A. )1985(. Reference crop evapotranspiration from temperature. Appl. Eng. Agric. 1, 96–99.
Harbeck, G., Kohler, M. and Koberg, G. (1954). Water loss investigations: Lake Hefner studies. Technical Report. United States Geological Survey Professional Paper269.
Hamon, W. R. (1960). Estimating potential evapotranspiration. J. Hydraul. Division 87,107–120.
Hargreaves, G. H. (1975). Moisture availability and crop production. Trans. Asae 18, 980–984.
Irmak, S., Haman, D. Z., Irmak, A., Jones, J. W., Campbell, K. L. and Yeager, T. H. (2017). New irrigation-plant production system for water conservation in ornamental nurseries: Quantification and evaluation of irrigation, runoff, plant bio mass, and irrigation efficiencies. Appl. Eng. Agr. ASAE 19(6), 651–665.
Jensen, M. E., Burman, R. D. and Allen, R. G. (1990). Evapotranspiration and irrigation water requirements. Agr. Soc. Civil Eng., New York.
Jensen, M. E. and Haise, H. R. (1963). Estimating evapotranspiration from solar radiation. Proceedings of the American society of civil engineers. J. Irrig. Drain. Eng. Division 89, 15–41.
Katerji, N. and Rana, G. (2011). Crop reference evapotranspiration: a discussion of the concept, analysis of the process and validation. Water Resour. Manag. 25(6), 1581–1600.
Kuzmin, P. (1957). Hydrophysical investigations of land waters. Int. Assoc. Sci. Hydrol. Publ., 3, 468–478.
López-Urrea, R., de Santa, O. F. M., Fabeiro, C. and Moratalla, A. (2006). Testing evapotranspiration equations using lysimeter observations in a semiarid climate. Agri. Water Manage., 85, 15–26.
McMahon, T., Finlayson, B. and Peel, M.) 2016(. Historical developments of models for estimating evaporation using standard meteorological data. Wiley Interdiscipl. Rev. Water 3, 788–818.
Muhammad, M. K. I., Nashwan, M. S., Shahid, S., Ismail, T., Song, Y. H. and Chung, E.-S. (2019). Evaluation of empirical reference evapotranspiration models using compromise programming: a case study of Peninsular Malaysia. Sustain., 11, 4267. doi:10.3390/su11164267.
Mahringer, W., (1970). Verdunstungsstudien am neusiedler See. Archiv für Meteorologie, Geophysik und Bioklimatologie, Serie B 18, 1–20.
McCloud, D. (1955). Water requirements of field crops in Florida as influenced by climate. Proc. Soil Sci. Soc. Fla. 15, 165–172.
Makkink, G., (1957). Testing the Penman formula by means of lysimeters. J. I. Water Eng. 11, 277–288.
Monteith, J. L. (1965). Evaporation and environment. Symp. Soc. Exp. Biol. 19, 205–234.
Nazari, R. and Kaviani, A. (2015). Evaluation of potential evapotranspiration and evapotranspiration methods with a lysimeter values in a climate Semi dry (Case Study: Qazvin Plain). J. Ecohydrol., 3(1), 19-30 [In Persian].
 Oudin, L., Michel, C. and Anctil, F. (2005). Which potential evapotranspiration input for a lumped rainfall-runoff model: Part 1— Can rainfall-runoff models effectively handle detailed potential evapotranspiration inputs? J. Hydrol. 303, 275–289.
Parajuli, K., Jones, S. B., Tarboton, D. G., Flerchinger, G. N., Hipps, L. E., Allen, L. N. and Seyfried, M. S.) 2019(. Estimating actual evapotranspiration from stony-soils in montane ecosystems. Agr. Forest Meteorol. 265, 183–194.
Paredes, P. and Pereira, L. (2019). Computing FAO56 reference grass evapotranspiration PMETo from temperature with focus on solar radiation. Agri. Water Manage., 215, 86–102.
Priestley, C. and Taylor, R. (1972). On the assessment of surface heat flux and evaporation using large-scale parameters. Mon. Weather Rev., 100, 81–92.
Penman, H. L. (1948). Natural evaporation from open water, hare soil and grass. P. Roy. Soc. Lond. 193, 120–145.
 Penman, H. L. (1963). Vegetation and Hydrology, Tech. Commun. 53, Commonwealth Bureau of Soils. Soil Sci 96, 357.
Raziei, T. and Pereira L. S. (2013). Estimation of ET0 with Hargreaves-Samani and FAO-PM temperature methods for a wide range of climates in Iran. Agri. Water Manage., 121, 1-18. doi:10.1016/j.agwat.2012.12.019.
Romanenko, V. (1961). Computation of the autumn soil moisture using a universal relationship for a large area. Proc. Ukrainian Hydrometeorol. Res., 3, 12–25.
Song, X., Lu, F., Xiao, W., Zhu, K., Zhou, Y. and Xie, Z. (2019). Performance of 12 reference evapotranspiration estimation methods compared with the Penman–Monteith method and the potential influences in northeast China. Meteorol. Appl. 26, 83–96.
Stephens, J. C. and Stewart, E. H. (1963). A comparison of procedures for computing evaporation and evapotranspiration. Publication, 62, 123–133.
 Stephens, J. C. (1965). Discussion of estimating evaporation from insolation. J. Hydraul., 504, 171–182.
 Schendel, U. (1967). Vegetationswasserverbrauch und-wasserbedarf. Habilitation, Kiel. 137, 1–11 [In German].
 Szász, G. (1973). A potenciális párolgás meghatározásának új módszere. [New method for calculating potential evapotranspiration]. Hidrológiai Közlöny. 10, 435–442 [In German].
Trajkovic, S. (2007). Hargreaves versus Penman-Monteith under Humid Conditions. J. Irrig. Drain. Eng. 133 (1), 38–42.
Trabert, W. (1896). Neue Beobachtungen uber verdampfungsge schwindigkeiten. Meteorol. Z.13, 261-263 [In German].
Tasumi, M. (2019). Estimating evapotranspiration using METRIC model and Landsat data for better understandings of regional hydrology in the western Urmia Lake Basin. Agri. Water Manage. 226, 105805.
Thornthwaite, C. W. (1948). An approach toward a rational classification of climate. Geog. Rev., 33(1), 55–94.
Vanzyl, W. H., De Jager, J. M. and Maree, C. J. (1989). The relationship between daylight evaporation from short vegetation and the USWB Class A pan. Agri. Forest Meteorol., 46, 107-118.
Valiantzas, J. D. (2013a). Simple ET0 forms of Penman’s equation without wind and/or humidity data. I: theoretical development. J. Irrig. Drain. Eng. 139, 1–8.
Valiantzas, J. D. (2006). Simplified versions for the Penman evaporation equation using routine weather data. J. Hydrol., 331, 690–702.
Valiantzas, J. D. (2012). Simplified reference evapotranspiration formula using an empirical impact factor for Penman’s aerodynamic term. J. Hydrol. Eng., 18, 108–114.
Yates, D. and Strzepek, K. (1994). Potential evapotranspiration methods and their impact on the assessment of river basin runoff under climate change, first ed. IIASA, Austria.