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Current Research in Agricultural Sciences

June 2020, Volume 7, 1, pp 6-14

Penman and Thornwait Equations for Estimating Reference Evapotranspiration Under Semi-Arid Environment

Muhammad Hafeez


Allah Bakhsh


Abdul Basit


Zia Ahmad Chattha


Alamgir Akhtar Khan


Muhammad Adnan Majeed


Fatima Tahira

Muhammad Hafeez 1

Allah Bakhsh 2 Abdul Basit 2 Zia Ahmad Chattha 4
Alamgir Akhtar Khan 5
Muhammad Adnan Majeed 6
Fatima Tahira 7

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

  2. Department of Botany, Ghazi University, Dera Ghazi Khan, Pakistan. 2

  3. Faculty of Agricultural Engineering, University of Agriculture, Faisalabad, Pakistan. 4

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

  5. University of Waikato, New Zealand. 6

  6. Department of Mathematics, Institute of Southern Punjab, Multan, Pakistan. 7

Pages: 6-14

DOI: 10.18488/journal.68.2020.71.6.14

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Article History:

Received: 17 January, 2020
Revised: 19 February, 2020
Accepted: 24 March, 2020
Published: 22 April, 2020


The estimation of reference evapotranspiration (ETo) is required for effective development and management of agriculture water systems. In order to define the most accurate method to estimate ETo in semi-arid climatic environment of Faisalabad, Lahore and Peshawar. Penman and Thornwait ETo methods are compared with standard Penman-Monteith (PM) ETo method. The statistical results show that Penman ETo method overestimates PM ETo method in all the semi-arid climatic regions of Faisalabad, Lahore and Peshawar by 34.91%, 39.51% and 30.75%, respectively. The R2 were 0.98, 0.98 and 0.99 at Faisalabad, Lahore and Peshawar weather stations, respectively. The RMSE were 2.47 mm/day, 2.64 mm/day and 2.19 mm/day at Faisalabad, Lahore and Peshawar weather station, respectively. The MBE of -2.41 mm/day, -2.58 mm/day and -2.13 mm/day were noted at Faisalabad, Lahore and Peshawar weather stations, respectively. The statistical result of Thornwait (Th) ETo method as compared with PM ETo method indicates underestimation of ETo in winter season and overestimation of ETo in summer season by 13.81%, 22.43% and 14.54% at Faisalabad, Lahore and Peshawar stations, respectively. The R2 of 0.92, 0.89 and 0.95 were noted at Faisalabad, Lahore and Peshawar weather stations, respectively. The RMSE were 2.14 mm/day, 2.36 mm/day and 1.16 mm/day at Faisalabad, Lahore and Peshawar weather stations, respectively. The MBE were -0.68 mm/day, -1.12 mm/day and 0.61 mm/day at Faisalabad, Lahore and Peshawar weather stations, respectively. Overall, Thornwait method gave better estimation of ETo than Penman ETo method at all the weather stations.
Contribution/ Originality
The main objective of this research is to compare the performance of Penman and Thornwait ETo methods against standard PM ETo method under semi-arid climatic conditions of Lahore, Faisalabad and Peshawar, Pakistan.


Penman, Thornwait, Penman-Monteith, 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 Metrological Department, Lahore and Peshawar for providing the climatic data records used in this research.

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