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Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India

Arvind Singh Tomar
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In order to estimate reference evapotranspiration (ET0) with the widely accepted FAO-56 PM model especially, in developing countries like India, quality of data and difficulties in gathering all necessary, weather parameters can present serious limitations. Keeping in view, the relevance of precise ET0 estimation, an attempt has been made to evaluate, decide and select alternative radiation-based methods to get almost at par ET0 values (from observed climatic data) on the basis of their performance with widely acclaimed FAO-56 PM method as an index for sub-humid Tarai region of Uttarakhand, India. The higher value of Agreement index of ET0 values obtained with FAO24-Radiation method confirms its appropriateness, whereas, value of ET0 method/ET0 FAO-56 PM ratio as 1.00 by Castaneda-Rao method validates its suitability in place of FAO-56 PM at the study area located in the Indian sub-humid region.

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Arvind Singh Tomar , 2015. Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India. International Journal of Agricultural Research, 10: 65-73.

DOI: 10.3923/ijar.2015.65.73

Received: May 29, 2015; Accepted: August 17, 2015; Published: October 14, 2015


World Bank and the UN through a study indicated that the irrigated agriculture will need to provide 70% of the world’s increased food requirements in 2025 (Anonymous, 2003). Postel (1999) indicated that food production levels needed in 2025 could require up to 2,000 cubic kilometers of additional irrigation water for cultivating crops. Water management and crop yields can be improved with the help of increased use of reliable methods for estimating crop evapotranspiration. Many methods have been proposed and used over the last 50 years and various international agencies are attempting to develop an accord with respect to the best and most appropriate methods to use for ET0 calculations (Smith et al., 1991; Allen et al., 1994a, b; IWMI., 1997).

In India, about 70% population is dependent on agriculture and allied activities (Tripathi and Prasad, 2009). Due to inadequate and uneven distribution of rainfall during crop growth period, it becomes necessary to apply additional water to the soil in the form of irrigation for plant use (Hansen et al., 1980). In order to improve crop water use efficiency, accurate estimation of evapotranspiration (ET), the sum of amount of water returned to atmosphere through combined process of evaporation and transpiration, is essentially required for efficient water management (Watson and Burnett, 1995; Tomar and Ranade, 2001).

Lysimeter are normally used for measuring ET directly by considering change in soil moisture from known volume of soil covered with vegetation (Watson and Burnett, 1995), but its use is very expensive, takes more time to install and requires more maintenance due to which ET is estimated with the help of a large number of empirical or semi-empirical formulae. A modification of ET concept is reference evapotranspiration (ET0) that provides a standard crop (a short, clipped grass) with an unlimited water supply so that a user can calculate maximum evaporative demand from that surface for a given day. This value, adjusted for a particular crop, is the consumptive use (or demand) and its deficit represents that component of consumptive use that goes unfilled during the given time period. This deficit value is the amount of water that must be supplied through irrigation to meet the water demand of crops (Dingman, 1994; Allen et al., 1998).

The FAO Penman-Monteith (FAO-56 PM) method is recommended as the standard method for determining ET0, as it is physically based and explicitly incorporates both physiological and aerodynamic parameters. The superior performance of this method in various climates has been evaluated and confirmed by various researchers (Allen et al., 1998; Jensen et al., 1990; Smith et al., 1991; Allen et al., 1994a; Chiew et al., 1995; Allen et al., 2000; Walter et al., 2000). The method requires solar radiation, wind speed, air temperature and humidity data but all these input variables may not be available for a given location due to non-availability of well-established weather stations and thus, some parameters are not recorded. Especially, in developing countries like India, quality of data and difficulties in gathering all necessary weather parameters can present serious limitations. The FAO Expert Consultation on Methodologies for Crop Water Requirements recommended that empirical methods be validated for new regions using standard FAO-56 PM method (Smith et al., 1991; Allen et al., 1994b). Keeping in view the relevance of precise ET0 estimation and unavailability of all the required meteorological dataset, an attempt has been made in the present study to evaluate, decide and select alternative radiation-based methods to get almost at par ET0 values from observed climatic data on the basis of their performance with widely acclaimed FAO-56 PM method as an index for Tarai region, situated in the foothills of the great Himalayas in Uttarakhand, India.


Study area and weather dataset: The present study was conducted to perform comparative analysis of various radiation-based ET0 methods for Pantnagar (79.49°E, 29.03°N, 243.80 m msl), located in Udham Singh Nagar district on the basis of 24 years of daily meteorological dataset consisting of temperature (maximum and minimum); relative humidity (maximum and minimum) and duration of actual sunshine hours collected from Govind Ballabh Pant University of Agriculture and Technology, Pantnagar in Uttarakhand (Fig. 1).

FAO-56 penman monteith model and radiation-based ET0 methods: The original Penman-Monteith combination equation, combined with equations of aerodynamic and surface resistance called as "FAO-56 Penman Monteith model" (Allen et al., 1998; Smith et al., 1991) is given below:

Image for - Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India

where, ET0 is reference evapotranspiration (mm day–1), Rn is net radiation at crop surface (MJ m–2 day–1), G is soil heat flux density (MJ m–2 day–1), T is mean daily air temperature (°C), u2 is wind speed at 2 m height (m sec–1), es is saturation vapour pressure (kPa), ea is actual vapour pressure (kPa), es-ea is saturation vapour pressure deficit (kPa), Δ is slope of vapour pressure curve (kPa °C–1) and γ is psychometric constant (kPa °C–1).

Image for - Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India
Fig. 1: Index map of the study area

Being the FAO-56 PM method gives proximate close values with actual values measured in a wide range of location and climatic conditions and, therefore, in the present study, it was chosen as index method for ET0 computation. The commonly used 20 radiation-based ET0 equations considered in this study are summarized in Table 1.

Assumptions and statistical analysis: The analysis of results to draw fruitful inferences from them in terms of statistical indices was being done as it has been pointed out by Fox (1981) and Willmott (1982) that commonly used correlation measures e.g., correlation coefficient, coefficient of determination and tests of statistical significance in general are often inappropriate or misleading.

Table 1: Details of radiation-based ET0 methods considered in the study
Image for - Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India
ET0: Reference crop evapotranspiration (mm day–1), G: Soil heat flux density (MJ m–2 day–1), Rn: Net radiation (MJ m–2 day–1), Rs: Solar radiation (MJ m–2 day–1), Tav: Average daily air temperature (°C), Tmax: Maximum air temperature (°C), Tmin: Minimum air temperature (°C), u2: Mean daily wind speed at 2 m height (m sec–1), Δ: Slope of saturation vapor pressure-temperature curve (kPa °C–1), γ: Psychometric constant (kPa °C–1), λ: Latent heat of vaporization (MJ kg–1) and a, CT, T1, Tx, α: Experimental coefficients

Different statistical indices considered to evaluate performance of different methods includes; Agreement index (D), Root Mean Square Error (RMSE), Mean Bias Error (MBE), Maximum Absolute Error (MaxE), Percentage Error (%), Coefficient of determination (R2) and Standard Error of Estimate (SEE). The "Agreement Index" (D) is being proposed, as a descriptive measure (Willmott, 1981, 1982; Willmott and Wicks, 1980). The computational forms of considered statistical indices are presented in Table 2. On the basis of literature, reviewed on different statistical indices, higher values of D and R2 (near to "1.00"), values near to "0.00" for RMSE, MBE, MAXE, PE and SEE were considered "good" for deciding the performance of considered methods. The quantification of under and over-estimation of ET0 method as compared to that obtained with FAO-56 PM model was being done in terms of their ratio and its value near to "1.00" was considered "good".

Table 2: Computational forms of considered statistical indices
Image for - Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India
Image for - Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India: Mean of FAO-56 PM ET0 (mm day–1), Oi: FAO-56 PM ET0 (mm day–1), Image for - Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India: Mean of FAO-56 PM ET0 (mm day–1), Pi: Predicted value of ET0 (mm day–1) estimated by using other equations, n: Total number of observations


Cross comparison of radiation-based ET0 equations: The performance of considered radiation-based ET0 equations was evaluated by comparing their monthly ET0 estimates with those obtained with FAO-56 PM model by plotting daily ET0 values averaged over month period plotted against corresponding values obtained by FAO-56 PM model. The long-term average ratio of ET0 method/ET0 FAO-56 PM were also computed to quantify over-and under-estimation of considered equations relative to the FAO-56 PM ET0 values.

The statistical analysis of radiation-based ET0 equations for study area (Table 3) indicated that the FAO24-Radiation method performed best as it gave optimal value of D as 0.96 among 10 best methods obtained for study area. The lowest value of MBE was obtained with Irmak Rs method (0.27) and the lowest value of SEE was obtained with Turc method as 0.11. Considering calculated values of RMSE among 10 best methods, Stephens method was observed best, as it gave lowest RMSE value (2.80 mm day–1) among all other considered methods, whereas, the best value for ratio of ET0 method/ET0 FAO-56 PM was obtained with Castaneda-Rao method as 1.00.

Among 16 evaluated ET0 models, Sahoo et al. (2012) found the performance of FAO24-Radiation method best in the sub-humid valley rangeland in the eastern Himalayas. Similarly, Razzaghi and Sepaskhah (2010) found this model the most-appropriate among considered nine ET0 methods. Kashyap and Panda (2001) mentioned that FAO24-Radiation method shouldn’t be recommended for estimating ET0 in sub-humid climatic regions, however, Irmak et al. (2008) favoured its use in concurrence with the findings of Giridhar and Viswanadh (2007) and the present study. In Tabari (2010) found that the Makkink model performed well in cold humid climates in contradiction to the findings of this study. Similarly, the conclusion made by Zhai et al. (2010) that the Abtew method should be used only at the high plateau regions is in good agreement with the results obtained in this study.

Table 3: Statistical performance of radiation-based methods versus FAO-56 PM model for estimating ET0 values
Image for - Comparative Performance of Reference Evapotranspiration Equations at Sub-Humid Tarai Region of Uttarakhand, India
Abt: Abtew, BG: Berengena-gavilan, Cap: Caprio, CR: Castaneda-rao, Chr: Christiansen, dBr: de Bruin, FRad: FAO24-Radiation, Han: Hansen, IRs: Irmak Rs, IRn: Irmak Rn, JH: Jensen-Haise, JR: Jones-Ritchie, Mak: Makkink, MB: McGuinness-bordne, MPT: Modified priestley-taylor, PT: Priestley-taylor, Ste: Stephens, SS: Stephens-stewart, Tur: Turc, XS: Xu-singh, D: Agreement index, RMSE: Root mean square error (mm day–1), MBE: Mean bias error (mm day–1), MAXE: Maximum absolute error (mm day–1), PE: Percentage error of estimate (%), R2: Coefficient of determination, SEE: Standard error of estimate (mm day–1), Ratio: Ratio of ET0 method/ET0 FAO-56 PM

Xystrakis and Matzarakis (2011) found equation proposed by Turc (1961) useful on the basis of evaluation of 13 empirical ET0 equations for Southern Greece, as it gave less monthly absolute error and in a recent research work, Djaman et al. (2015) concluded that Turc equation underestimated ET0 values in accordance with results obtained in the present study.


Considering the limitations associated with reliability and availability of good quality weather data especially in developing countries, the widely acclaimed and well-proven FAO-56 PM model cannot be used to estimate ET0 due to which identification of simpler ET0 equations is required. In this study, the performance of 20 radiation-based ET0 equations as compared to standard, widely accepted and well-proven FAO-56 PM model was evaluated. The following conclusions were drawn from the findings of the present study:

In terms of highest D and lowest RMSE values, FAO24-Radiation ET0 method was adjudged best, whereas, Abtew method performed worst
Castaneda-Rao method gave best estimate of FAO-56 PM model
ET0 equations given by McGuinness-Bordne, Berengena-Gavilan, Caprio, FAO24-Radiation, Irmak Rs, Irmak Rn and Hansen over-estimated FAO-56 PM model values
The de Bruin, modified Priestley-Taylor, Stephens, Makkink, Stephens-Stewart, Jensen-Haise, Xu-Singh, Jones-Ritchie, Turc, Christiansen and Abtew methods under-estimated values calculated with FAO-56 PM model
Similar kind of site-specific evaluation of available global ET0 equations (which requires less number of meteorological parameters) in different climatic regions is required to be undertaken to identify, decide and use them in place of standard FAO-56 PM method which requires more number of meteorological parameters for estimating ET0 values


1:  Abtew, W., 1996. Evapotranspiration measurements and modeling for three wetland systems in south florida. J. Am. Water Resour. Assoc., 32: 465-473.
CrossRef  |  Direct Link  |  

2:  Allen, R.G., I.A. Walter, R. Elliot, B. Mecham and M.E. Jensen et al., 2000. Issues, requirements and challenges in selecting and specifying a standardized ET equation. Proceedings of the 4th Decennial National Irrigation Symposium, November 14-16, 2000, American Society of Agricultural Engineers, Phoenix, AZ., USA -

3:  Allen, R.G., L.S. Pereira, D. Raes and M. Smith, 1998. Crop evapotranspiration-guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56, FAO, Rome, Italy. http//

4:  Allen, R.G., M. Smith, A. Perrier and L.S. Pereira, 1994. An update for the definition of reference evapotranspiration. Bull. Int. Commission Irrig. Drain., 43: 1-35.
Direct Link  |  

5:  Allen, R.G., M. Smith, L.S. Pereira and A. Perrier, 1994. An update for the calculation of reference evapotranspiration. ICID Bull., 43: 35-92.
Direct Link  |  

6:  Anonymous, 2003. Prospects for irrigated agriculture-whether irrigated area and irrigation water must increase to meet food needs in the future. Report No. 26029, The World Bank Agriculture and Rural Development Department, pp: 111.

7:  Berengena, J. and P. Gavilan, 2005. Reference evapotranspiration estimation in a highly advective semiarid environment. J. Irrig. Drain. Eng., 131: 147-163.
CrossRef  |  Direct Link  |  

8:  Caprio, J.M., 1974. The Solar Thermal Unit Concept in Problems Related to Plant Development and Potential Evapotranspiration. In: Phenology and Seasonality Methoding: Ecological Studies, Lieth, H. (Ed.). Springer-Verlag, New York, pp: 353-364

9:  Castaneda, L. and P. Rao, 2005. Comparison of methods for estimating reference evapotranspiration in Southern California. J. Environ. Hydrol., 13: 1-10.
Direct Link  |  

10:  Chiew, F.H.S., N.N. Kamaladasa, H.M. Malano and T.A. McMahon, 1995. Penman-monteith, FAO-24 reference crop evapotranspiration and class-A pan data in Australia. Agric. Water Manage., 28: 9-21.
CrossRef  |  Direct Link  |  

11:  Christiansen, J.E., 1968. Pan evaporation and evapotranspiration from climatic data. J. Irrig. Drain. Div., 94: 243-265.

12:  De Bruin, H.A.R. and J.N.M. Stricker, 2000. Evaporation of grass under Non-restricted soil moisture conditions. Hydrol. Sci. J., 45: 391-406.
CrossRef  |  Direct Link  |  

13:  Dingman, S.L., 1994. Physical Hydrology. Prentice-Hall, Upper Saddle River, NJ

14:  Djaman, K., A.B. Balde, A. Sow, B. Muller and S. Irmak et al., 2015. Evaluation of sixteen reference evapotranspiration methods under sahelian conditions in the Senegal River Valley. J. Hydro.: Reg. Stud., 3: 139-159.
CrossRef  |  Direct Link  |  

15:  Doorenbos, J. and W.O. Pruitt, 1977. Guidelines for Predicting Crop Water Requirements. 2nd Edn. FAO, Rome, Italy, ISBN: 92-5-200136-0, pp: 179

16:  Fox, D.G., 1981. Judging air quality model performance. Bull. Am. Meteorol. Soc., 62: 599-609.
CrossRef  |  Direct Link  |  

17:  Giridhar, M.V.S. and G.K. Viswanadh, 2007. Comparison of radiation based evapotranspiration equations with FAO-56 Penman Monteith method. Int. J. Comp. Sci. Syst. Anal., 1: 149-158.

18:  Hansen, V.E., O.W. Israelsen and G.E. Stringham, 1980. Irrigation Principles and Practices. 4th Edn., John Wiley and Sons, New York, USA., ISBN-13: 9780471084495, pp: 150

19:  IWMI., 1997. World climate atlas. Version 1, CD-ROM, Colombo, Sri Lanka.

20:  Irmak, S., A. Irmak, R.G. Allen and J.W. Jones, 2003. Solar and net radiation-based equations to estimate reference evapotranspiration in humid climates. J. Irrig. Drain. Eng., 129: 336-347.
CrossRef  |  Direct Link  |  

21:  Irmak, A., S. Irmak and D.L. Martin, 2008. Reference and crop evapotranspiration in south central nebraska. I: Comparison and analysis of grass and alfalfa-reference evapotranspiration. J. Irrigation Drainage Eng., 134: 690-699.
CrossRef  |  Direct Link  |  

22:  Jensen, M.E. and R.H. Haise, 1963. Estimating evapotranspiration from solar radiation. J. Irrigation Drainage Div., 89: 15-41.
Direct Link  |  

23:  Jensen, M.E., 1966. Empirical methods of estimating or predicting evapotranspiration using radiation. Proceedings of the Conference on Evapotranspiration and its Role in Water Resources Management, December 5-6, 1966, Chicago, IL -

24:  Jensen, M.E., R.D. Burman and R.G. Allen, 1990. Evapotranspiration and irrigation water requirements. ASCE Manuals and Reports on Engineering Practice No. 70, American Society of Civil Engineers, New York, pp: 1-360.

25:  Jones, J.W. and J.T. Ritchie, 1990. Crop Growth Models. In: Management of Farm Irrigation Systems, Hoffman, G.J., T.A. Howel and K.H. Solomon (Eds.). ASAE, USA., pp: 63-69

26:  Kashyap, P.S. and R.K. Panda, 2001. Evaluation of evapotranspiration estimation methods and development of crop-coefficients for potato crop in a sub-humid region. Agric. Water Manage., 50: 9-25.
CrossRef  |  Direct Link  |  

27:  Makkink, G.F., 1957. Testing the Penman formula by means of lysimeters. J. Inst. Water Eng., 11: 277-288.

28:  McGuinness, J.L. and E.F. Bordne, 1972. A comparison of lysimeter-derived potential evapotranspiration with computed values. Technical Bulletin No. 1452, Agricultural Research Service, USDA, Washington, DC., pp: 71.

29:  Postel, S., 1999. Pillar of Sand: Can the Irrigation Miracle Last? W.W. Norton Co., New York, USA., ISBN-13: 9780393319378, Pages: 313

30:  Priestley, C.H.B. and R.J. Taylor, 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Mon. Weather Rev., 100: 81-92.
CrossRef  |  Direct Link  |  

31:  Razzaghi, F. and A.R. Sepaskhah, 2010. Assessment of nine different equations for ETo estimation using lysimeter data in a semi-arid environment. Arch. Agron. Soil Sci., 56: 1-12.
CrossRef  |  Direct Link  |  

32:  Sahoo, B., I. Walling, B.C. Deka and B.P. Bhatt, 2012. Standardization of reference evapotranspiration models for a subhumid valley rangeland in the eastern Himalayas. J. Irrig. Drain. Eng., 138: 880-895.
CrossRef  |  Direct Link  |  

33:  Smith, M., R.G. Allen, J.L. Monteith, A. Pereira, L. Pereira and A. Segeren, 1991. Report of the expert consultation on procedures for revision of FAO guidelines for prediction of crop water requirements. Land and Water Development Division, United Nations Food and Agriculture Service, Rome, Italy, pp: 75.

34:  Hansen, S., 1984. Estimation of potential and actual evapotranspiration. Nordic Hydrol., 15: 205-212.
Direct Link  |  

35:  Stephens, J.C., 1965. Discussion of estimating evaporation from insolation. J. Hydraul., 91: 171-182.

36:  Tabari, H., 2010. Evaluation of reference crop evapotranspiration equations in various climates. Water Resour. Manage., 24: 2311-2337.
CrossRef  |  Direct Link  |  

37:  Tomar, A.S. and D.H. Ranade, 2001. Pan coefficient determination for evapotranspiration at Indore, Madhya Pradesh. Indian J. Soil Conserv., 29: 173-175.

38:  Tripathi, A. and A.R. Prasad, 2009. Agricultural development in India since independence: A study on progress, performance and determinants. J. Emerg. Knowl. Emerg. Markets, Vol. 1.
Direct Link  |  

39:  Turc, L., 1961. Estimation of irrigation water requirements, potential evapotranspiration: A simple climatic formula evolved up to date. Ann. Agron., 12: 13-49.

40:  Walter, I., R.G. Allen, R. Elliott, M.E. Jensen and D. Itenfisu et al., 2000. ASCE's standardized reference evapotranspiration equation. Proceedings of the 4th Decennial National Irrigation Symposium, November 14-16, 2000, Phoenix, AZ -

41:  Watson, I. and A.D. Burnett, 1995. Hydrology: An Environmental Approach. CRC Press, Boca Raton, FL., ISBN-13: 9781566700870, Pages: 722

42:  Willmott, C.J. and D.E. Wicks, 1980. An empirical method for the spatial interpolation of monthly precipitation within California. Phys. Geog., 1: 59-73.
Direct Link  |  

43:  Willmott, C.J., 1981. On the validation of models. Phys. Geogr., 2: 184-194.
Direct Link  |  

44:  Willmott, C.J., 1982. Some comments on the evaluation of model performance. Bull. Am. Meteorol. Soc., 63: 1309-1313.
CrossRef  |  Direct Link  |  

45:  Xu, C.Y. and V.P. Singh, 2000. Evaluation and generalization of radiation-based methods for calculating evaporation. Hydrol. Process., 14: 339-349.
Direct Link  |  

46:  Xystrakis, F. and A. Matzarakis, 2011. Evaluation of 13 empirical reference potential evapotranspiration equations on the island of Crete in southern Greece. J. Irrig. Drain. Eng., 137: 211-222.
CrossRef  |  Direct Link  |  

47:  Zhai, L., Q. Feng, Q. Li and C. Xu, 2010. Comparison and modification of equations for calculating evapotranspiration (ET) with data from Gansu Province, Northwest China. Irrig. Drain., 59: 477-490.
CrossRef  |  Direct Link  |  

48:  Hansen, S., 1984. Estimation of potential and actual evapotranspiration. Nordic Hydrol., 15: 205-212.
Direct Link  |  

49:  Hansen, S., 1984. Estimation of potential and actual evapotranspiration. Nordic Hydrol., 15: 205-212.
Direct Link  |  

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