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Current Research in Agricultural Sciences

December 2020, Volume 7, 2, pp 58-63

Reference Evapotranspiration by Hargreaves and Modified Hargreaves Equations under Semi-Arid Environment

Muhammad Hafeez


Zia Ahmad Chatha


Allah Bakhsh


Abdul Basit


Alamgir Akhtar Khan


Fatima Tahira

Muhammad Hafeez 1

Zia Ahmad Chatha 2

Allah Bakhsh 3 Abdul Basit 3 Alamgir Akhtar Khan 5
Fatima Tahira 6

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

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

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

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

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

Pages: 58-63

DOI: 10.18488/journal.68.2020.72.58.63

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Article History:

Received: 20 April, 2020
Revised: 03 June, 2020
Accepted: 28 September, 2020
Published: 17 November, 2020


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.


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


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This study received no specific financial support.

Competing Interests:

The authors declare that they have no competing interests.


The authors would like to thank Pakistan Meteorological Department, Quetta for providing the climatic data records used in this research.

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