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© 2020 Conscientia Beam. All Rights Reserved. 

REFERENCE EVAPOTRANSPIRATION BY HARGREAVES AND MODIFIED 
HARGREAVES EQUATIONS UNDER SEMI-ARID ENVIRONMENT   

 

 

 Muhammad 
Hafeez1+ 
Zia Ahmad Chatha2 
Allah Bakhsh3  
Abdul Basit4  
Alamgir Akhtar Khan5 
Fatima Tahira6 

 

1Department of Agricultural Engineering, Faculty of Agricultural sciences 
and Technology, Bahauddin Zakariya University, Multan, Pakistan. 

 
2Department of Food Engineering, Faculty of Agricultural Engineering, 
University of Agriculture, Faisalabad, Pakistan. 

 
3,4Department of Botany, Ghazi University, Dera Ghazi Khan, Pakistan. 

 
5Department of Agricultural Engineering, MNSUA, Multan, Pakistan. 

 
6Department of Mathematics, Institute of Southern Punjab, Multan, 
Pakistan. 

 

 
(+ Corresponding author) 

 ABSTRACT 
 
Article History 
Received: 20 April 2020 
Revised: 3 June 2020 
Accepted: 28 September 2020 
Published: 17 November 2020  
 

Keywords 
Hargreaves equation 
Calibrated Hargreaves equation 
FAO-56 equation 
Reference evapotranspiration 
Semi-arid 
Environment. 
 

 
The Penman-Monteith (FAO-56 PM) ETo equation is considered as the standard ETo 
equation to estimate reference evapotranspiration (ETo) under all the weather 
conditions of the world. But there are many regions of the globe where all the climatic 
data is not available to evaluate FAO-56 PM ETo equation. So, Hargreaves (HG) ETo 
equation can be used which required very small number of weather data. The HG ETo 
equation requires only air temperature as input data which is available at most of the 
weather stations of the world. But the major drawback of HG ETo equation is that it 
overestimates or underestimates FAO-56 PM ETo equation. So it becomes necessary to 
modify HG ETo Equation according to the local climatic conditions before it is being 
applied. The HGorg and modified HG ETo equations are assessed for ETo estimation 
under cold and hot semi-arid climatic conditions of Quetta and Zhob weather stations 
by using 9 years meteorological data of each weather station against FAO-56PM ETo 
equation. The original HG ETo equation overestimates FAO-56 PM ETo equation at 
Zhob weather station by giving percentage error of 15.82% and underestimate at 
Quetta weather station by giving percentage error of 35.02%. The coefficient of original 
HG ETo equation was modified by using a simple mathematical logic. The 
overestimation at Zhob weather station reduced to 1.89% and underestimation at 
Quetta station reduced to 0.87% by using modified HG ETo equation. The variations of 
original HG ETo equation with FAO-56 PM ETo equation has RMSE of 0.89 mm/day 
at Zhob weather station and 1.74 mm/day at Quetta weather station. The variations of 
modified HG ETo equation with FAO-56 PM ETo equation has RMSE of 0.27 
mm/day at Zhob weather station and 0.29 mm/day at Quetta weather station.  
 

Contribution/Originality: The objective of this research is to modify the Hargreaves (HG) ETo equation 

according to the regional semi-arid conditions of Quetta and Zhob weather stations of Baluchistan Province. 

 

1. INTRODUCTION 

Land and water are two important factors, which are required for agricultural development and 

strong economy of a country [1]. Pakistan lies in arid to semi-arid region where average annual rainfall is 254 

Current Research in Agricultural Sciences 
2020 Vol. 7, No. 2, pp. 58-63. 
ISSN(e): 2312-6418 
ISSN(p): 2313-3716 
DOI: 10.18488/journal.68.2020.72.58.63 
© 2020 Conscientia Beam. All Rights Reserved. 

 
 
 

 
 
 

 

 
 
 
 

https://orcid.org/0000-0002-3262-7014
https://www.doi.org/10.18488/journal.68.2020.72.58.63


Current Research in Agricultural Sciences, 2020, 7(2): 58-63 

 

 
59 

© 2020 Conscientia Beam. All Rights Reserved. 

to 356 mm against a potential demand (of water for maximum crop production) of 1778 mm. This gap between the 

demands and supplies is met through applying irrigation. Moreover, the country is facing threat of rapidly 

increasing population with the annual growth rate of 2.05 percent. It has been observed that water availability for 

agriculture is expected to decline globally to 62 percent by 2020 as was available (72%) in 1995 and from 87% to 

73% in developing countries [2]. The use of fresh water as drinking has enlarged at more than the two times as the 

rate of public increasing in the 20th century [3]. It is expected that in 2025 the rate in increase of new water 

extractions is rising and established countries will be 50% and 18%, respectively [4]. Reference 

evapotranspiration (ETo) is one of the most significant factor to design and manage water reservoirs [5]. 

The Penman-Monteith (FAO-56 PM) ETo equation currently recognized as a reference equation for the estimation 

of ETo [6]. The FAO-56 PM ETo equation needs large amount of meteorological data i-e; atmospheric 

temperature, relative humidity, sunshine duration and wind speed, which is not accessible for all meteorological 

stations. Therefore, it appears reasonably to substitute it by other ETo equations like Hargreaves (HG) 

ETo equation which requires small number of weather parameters [7].  When input meteorological 

parameters for FAO-56 PM equation is deficient particularly in developing countries like Pakistan, then equation 

established by Hargreaves and Samani can be applied with assurance after regional adjustment in parameters. The 

HG ETo equation needs very small meteorological input data i-e only temperature data. Many scholars tried to 

evaluate the accuracy of HG ETo equation by adjusting it according to regional environment conditions including 

Bachour, et al. [8] and Berti, et al. [6]. Hargreaves and Allen [9] recommended that Hargreaves ETo equation can 

be executed with assurance after modification according to regional environmental conditions and provides most 

accurate result for monthly estimation of ETo because at routinely time period there are more variation in 

atmospheric temperature, wind speed etc. The Hargreaves ETo equation is executed after regional modification 

when all compulsory metrological data for the evaluation of  Penman-Monteith ( FAO-56 PM) ETo equation is not 

accessible [10]. The objective of this research is to modify the Hargreaves (HG) ETo equation according to the 

regional semi-arid conditions of Quetta and Zhob weather stations of Baluchistan province, Pakistan. 

 

2. MATERIALS AND METHODS 

2.1. Geographical Location of the Study Area 

The weather data of two weather stations i-e Quetta and Zhob weather stations is used to assess original 

Hargreaves (HGorg) ETo and modified Hargreaves (HGmod) ETo equations for the estimation of monthly ETo. 

Both stations are located in Baluchistan Province, Pakistan.  

The environment of these metrological stations, GPS (Global positioning system) and period of average 

monthly weather data used for the modification of Hargreaves (HG) method are given below in Table 1. 

 
Table-1. Geographical and climatic characteristics of selected weather stations. 

Station Latitude Longitude Elevation Date Period Climate 
Quetta 300 -05’ 

N 
660-57’ E 1719 2001-2009 Cold semi-arid 

Zhob 310–21’ N 660-58’ E 1405 2001-2009 Hot semi-arid 
 

 

2.2. Reference Evapotranspiration (ETo) Equations 

2.2.1. Penman-Monteith (FAO-56 PM) ETo Equation 

For the estimation of Penman-Monteith (FAO-56 PM) ETo computer model CROPWAT 8.0 is applied which 

was suggested by FAO (Food and Agriculture organization). The input meteorological data needed are minimum 

and maximum air temperature, relative humidity, wind speed and sunshine hours. The monthly ETo is estimated by 

applying computer model (FAO CROPWAT 8.0, 2009) the following FAO-56 PM equation is applied as 

recommended by Gough and Scott [11]:   



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© 2020 Conscientia Beam. All Rights Reserved. 

                                                                 (1) 

Where, 

ETo = reference evapotranspiration (mm day-1); Rn = net radiation at the crop surface (MJm-2 /day); G =soil 

heat flux density (MJ m2/day); T = mean daily air temperature at 2 m height (°C); U2 = wind speed at 2 m height 

(m/s); es =saturation vapour pressure (kPa); ea = actual vapour pressure (kPa); es-ea = saturation vapour pressure 

deficit (kPa); ∆ = slope vapour pressure curve (kPa/ °C); γ is the psychometric constant (kPa (°C)−1) The 

computation of all data required for the calculation of the ETo followed the method of Hargreaves and Allen [9]. 

 

2.2.2. Original Hargreaves (HG) ETo Equation 

The ETo calculated by applying Hargreaves ETo equation is given by Hargreaves and Samani [12]:  

          (2) 

Where,  

ETo HG (org) = reference evapotranspiration (mm/day) by original ETo equation before modification ; T, 

Tmax and Tmin= average, maximum and minimum air temperature (o C) respectively. 

 

2.2.3. Modified Hargreaves ETo Equation 

The performance of original Hargreaves (HGorg) ETo equation is improved by adjusting the parameter of the 

original HG ETo equation method according to regional weather conditions. The original HG ETo equation is 

modified by resulting new value of constant by applying simple mathematical logic. In the original HG ETo 

equation, ETo HG (org) was set equal to ETo PM and the constant ‘0.0023’ was set as ‘M’ to be determined. Hence, 

the modified Hargreaves (HGmod) ETo equation can written as: 

  ETo HG mod= ETo PM = M Ra (Tmax – T min) 1/2 [T + 17.8] 

The modified HG equation is in the form 

Y = MX 

Where, Y= ETo PM; X= Ra (Tmax – T min) 1/2 [T + 17.8]. By the determined set of values of Y and X, the 

constant M was calculated. The Hargreaves ETo equation attained by means of above logic i-e by varying the value 

of constant has been written as HGmod equation. The value of Ra (extraterrestrial radiation) used in original 

Hargreaves ETo equation has been determined in research conducted by Hargreaves and Samani [12]. 

 

2.2.4. Statistical Evaluation 

In this study, the roots mean square error (RMSE), percentage error of estimate (PE), standard error of 

estimation (SEE) and coefficient of determination (R2) are used for the evaluation of ETo methods. 

 

 

 



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© 2020 Conscientia Beam. All Rights Reserved. 

Where, Pi= ETo estimated by the PM ETo equation and Oi= ETo estimated by different forms of HG method.  and 

 are the average of Pi and Oi, and n is the total number of data. 

3. RESULTS AND DISCUSSION 

The original Hargreaves (HGorg) ETo equation has been by standard Penman-Monteith ( FAO-56 PM) ETo 

equation for monthly calculation of ETo in semi-arid weather conditions of Quetta and Zhob. The HGorg ETo 

equation indicated underestimation of ETo by 35.02% for cold semi-arid climatic conditions of Quetta weather 

station and overestimation of ETo by 15.82% at hot semi-arid climatic conditions of Zhob weather as shown in 

Figure 1 (a) and 2 (a) and also in Tables 2 and 3. Therefore, the original Hargreaves (HGorg) ETo equation cannot 

be suggested for the estimation of ETo in cold and hot semi-arid climatic conditions of Quetta and Zhob weather 

stations, respectively without being modified. 

 

3.1. Modification of Original Hargreaves (HGorg) Equation 

The modification of original Hargreaves (HGorg) ETo equation is done by determining value of constant term 

that lessen the RMSE and Percentage error between ETo value calculated by standard Penman-Monteith ( FAO-

56 PM) and modified Hargreaves (HGmod) ETo equations. The resultant modified Hargreaves (HGmod) ETo 

equation arrangements are given below. 

 

3.2. Modification at Quetta Station 

ETo HG mod = 0.0031 Ra (Tmax – T min) 1/2 [T + 17.8]                             (3) 

 

3.3. Modification at Zhob Station 

ETo HG mod = 0.0019 Ra (Tmax – T min) 1/2 [T + 17.8]                              (4) 

 

Many researchers including Bachour, et al. [8]; Berti, et al. [6] and Majeed, et al. [13] have done research to 

modify the original Hargreaves ETo  equation by altering the constant value. The ETo estimated by modified 

Hargreaves (HGmod) ETo equation is again examined against the ETo calculated by the Penman-Monteith (FAO-

56 PM) ETo equation. The monthly ETo has been improved by the modified Hargreaves (HGmod) ETo equation. 

The RMSE and percentage error are also reduced as shown in the Table 1 and 2. The calculation of ETo from that 

modified Hargreaves ETo method reduced the percentage error up to 0.87% and 1.89% with RMSE of 0.29 

mm/day and 0.27 mm/day at Quetta and Zhob weather stations, respectively as shown in the Figure 1 (b) and 2 (b) 

and also in the Tables 2 and 3.  

 

 
Figure-1. Comparison of ETo by PM with (a) HG org and (b) HG mod methods at Quetta weather station. 



Current Research in Agricultural Sciences, 2020, 7(2): 58-63 

 

 
62 

© 2020 Conscientia Beam. All Rights Reserved. 

Table-2. Statistical evaluations of HGorg and HGmod compared with FAO-56 PM at Quetta weather station. 

Equation Form Percentage Error RMSE R2 SD SEE Mean 

HG org 35.02 1.74 0.98 2.05 0.31 4.50 
HG mod 0.87 0.29 0.98 2.79 0.31 6.14 

 

 

 
Figure-2. Comparison of ETo by PM with (a) HG org and (b) HG mod methods at Zhob weather station. 

 
Table-3. Statistical evaluations of HGorg and HGcal compared with PM at Zhob weather station. 

Equation form Percentage Error RMSE R2 SD SEE Mean 

HGorg 15.82 0.81 0.97 2.00 0.27 4.61 

HGmod 1.89 0.27 0.97 1.65 0.27 3.81 
 

 

4. CONCLUSION 

The comparison of reference evapotranspiration (ETo) by original Hargreaves (HGorg) ETo equation and 

standard Penman-Monteith (FAO-56 PM) ETo equation show that the original Hargreaves (HG org) ETo   

equation overestimate FAO-56 PM  ETo equation  in hot semi-arid environment of Zhob weather station and 

underestimate FAO-56 PM ETo equation in cold semi-arid environment of Quetta weather station. The modified 

Hargreaves (HGmod) equation shows better estimation of ETo at both the weather stations. So, it is suggested that 

before using original Hargreaves equation it must be modified according to the local regional environment 

conditions.  

 

Funding: This study received no specific financial support.    
Competing Interests: The authors declare that they have no competing interests.  
Acknowledgement: The authors would like to thank Pakistan Meteorological Department, 
Quetta for providing the climatic data records used in this research. 

 

REFERENCES 

[1] H. Muhammad, A. C. Zia, A. K. Alamgir, B. Allah, B. Abdul, and T. Fatima, "Estimating reference evapotranspiration 

by hargreaves and Blaney-Criddle methods in humid subtropical conditions," Current Research in Agricultural Sciences, 

vol. 7, pp. 15-22, 2020. Available at: 10.18488/journal.68.2020.71.15.22. 

[2] Z. A. Chatha, M. Arshad, A. Bakhah, and A. Shakoor, "Statistical analysis for lining the watercourses," Journal of 

Agricultural Research, vol. 53, pp. 109-118, 2015. 

[3] R. G. Allen, L. S. Pereira, D. Raes, and M. Smith, Crop evapotranspiration-guidelines for computing crop water requirements-

fao irrigation and drainage paper 56. Rome: FAO, 1998. 

[4] L. Feng, T. Li, and W. Yu, "Cause of severe droughts in southwest china during 1951–2010," Climate Dynamics, vol. 43, 

pp. 2033-2042, 2014. Available at: https://doi.org/10.1007/s00382-013-2026-z. 



Current Research in Agricultural Sciences, 2020, 7(2): 58-63 

 

 
63 

© 2020 Conscientia Beam. All Rights Reserved. 

[5] H. Muhammad, B. Allah, B. Abdul, A. C. Zia, A. K. Alamgir, A. M. Muhammad, and T. Fatima, "Penman and 

thornwait equations for estimating reference evapotranspiration under semi-arid environment," Current Research in 

Agricultural Sciences, vol. 7, pp. 6-14, 2020. Available at: 10.18488/journal.68.2020.71.6.14. 

[6] A. Berti, G. Tardivo, A. Chiaudani, F. Rech, and M. Borin, "Assessing reference evapotranspiration by the hargreaves 

method in north-eastern italy," Agricultural Water Management, vol. 140, pp. 20-25, 2014. Available at: 

https://doi.org/10.1016/j.agwat.2014.03.015. 

[7] M. Hafeez and A. A. Khan, "Assessment of Hargreaves and Blaney-Criddle methods to estimate reference 

evapotranspiration under coastal conditions," American Journal of Science, Engineering and Technology, vol. 3, pp. 65-72, 

2018. 

[8] R. Bachour, W. R. Walker, A. F. Torres-Rua, and M. McKee, "Assessment of reference evapotranspiration by the 

hargreaves method in the bekaa valley, lebanon," Journal of Irrigation and Drainage Engineering, vol. 139, pp. 933-938, 

2013. Available at: https://doi.org/10.1061/(asce)ir.1943-4774.0000646. 

[9] G. H. Hargreaves and R. G. Allen, "History and evaluation of Hargreaves evapotranspiration equation," Journal of 

Irrigation and Drainage Engineering, vol. 129, pp. 53-63, 2003. Available at: https://doi.org/10.1061/(asce)0733-

9437(2004)130:5(447.2). 

[10] H. R. Fooladmand, H. Zandilak, and M. H. Ravanan, "Comparison of different types of Hargreaves equation for 

estimating monthly evapotranspiration in the south of Iran," Archives of Agronomy and Soil Science, vol. 54, pp. 321-330, 

2008. Available at: https://doi.org/10.1080/03650340701793603. 

[11] S. Gough and W. Scott, Higher education and sustainable development: Paradox and possibility. London: Routledge, 2007. 

[12] G. H. Hargreaves and Z. A. Samani, "Reference crop evapotranspiration from temperature," Applied Engineering in 

Agriculture, vol. 1, pp. 96-99, 1985. Available at: https://doi.org/10.13031/2013.26773. 

[13] A. Majeed, S. Mehmood, K. Sarwar, G. Nabi, and M. A. Kharal, "Assessment of Reference Evapotranspiration by the 

Hargreaves Method in Southern Punjab Pakistan," European Journal of Advances in Engineering and Technology, vol. 4, 

pp. 64-70, 2017. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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