Evapotranspiration (ET) plays a vital role in hydrological processes and water resources management, including irrigation scheduling (Shahid 2011), vapour flux modelling (Fisher et al. 2009), surface water runoff modelling (Wigmosta et al. 1994), water balance estimation (Jaber et al. 2016), groundwater recharge estimate (Salem et al. 2017; Salehie et al. 2022c), reservoir management (Ismail et al. 2017), water stress assessment (Mohsenipour et al. 2018) and climate change impact assessment (Shiru et al. 2018; Salehie et al. 2022a, b). ET is responsible for nearly two-thirds of water losses from the earth's surface. The most significant consequence of climate change on many service sectors would from the modification of ET (Hamed et al. 2022a, b). However, the highest impacts of the ET changes would be on agriculture and irrigation. Accurate ET calculation is, therefore, crucial for agricultural water resources development, planning, and management (Ahmed et al. 2018; Hamed et al. 2022c).
Eddy covariance, remote sensing and weighted lysimeter are some of the direct experimental methods used to determine actual ET in addition to more indirect approaches such as catchment water balances, hydrometeorological equations and energy balances (Rana and Katerji 2000). However, the lysimeter estimation of ET is considered the most accurate technique (Gavilán et al., 2006; Tao et al., 2018). Lysimeter records total precipitation received and total soil water lost from a vegetative surface to estimate the actual ET and thus, provides a direct and accurate estimation of actual ET. A defined coefficient based on surrounding landuse is then used to estimate potential ET from actual ET. The major drawback of lysimetric estimation is its cost and complexity. Reliable ET estimation using a lysimeter needs skilled technical persons and a long time (Liou and Kar 2014; Zhang et al. 2016). The major drawback of the eddy covariance method is its uncertainty. Many remote sensing methods based on eddy covariance have been developed and used for ET estimation in recent years (Ha et al. 2015; Noumonvi et al. 2019). It can provide high spatial and temporal resolution of ET estimates globally. However, the estimated ET is prone to complex nonlinear bias in space and time, which is often very difficult to correct (Muhammad et al. 2021).
The limitations of experimental and remote sensing methods and the increasing availability of weather observation data have led to many empirical ET models. ET relies on the balance of energy in the atmosphere and the amount of water released by plants (Pereira et al. 1997). Therefore, the empirical ET models are classified based on their required inputs. ET has been classified into different groups (Muhammad et al. 2019). However, most literature grouped it into four: (i) temperature, (ii) radiation, (iii) mass transfer, and (iv) combined. Most of these empirical formulations are area-specific as they were developed considering the regional climate and were suitable for implementation in a specific region (Muhammad et al. 2019). Some of them have been developed by modifying the established methods. However, the use of the models depends on their skill in estimating the ET of a region of interest. Only a few empirical formulations have been globally recognized, such as the Penman-Monteith (PM) method (Penman 1948). The main limitations of this method are that it requires several meteorological variables and an extensive data span to comprehend the ET pattern accurately. Furthermore, getting long-term data of multiple climatic factors in most developing countries is difficult (Ahmed et al. 2017a; Nashwan et al. 2019b). The limitations have made the PM method unsuitable for ET estimates in many regions.
A huge number of global research have been undertaken to find the most appropriate ET model (Ali and Shui 2009; Tabari et al. 2013; Bogawski and Bednorz 2014; Hosseinzadeh Talaee et al. 2014; Muniandy et al. 2016; Song et al. 2019; Sobh et al. 2022). Nandagiri and Kovoor, (2006) evaluated the performance of several ET models over different climatic zones of India. They showed that the temperature-based 'Hargreaves method' provides ET estimates close to the PM med in all regions, except the radiation-based 'Truc method' in the humid region. Wei et al., (2019) compared the skills of several eddy covariance ET methods in arid regions and showed that 'Shuttleworth-Wallace' was the best method. Ndulue et al., (2019) assessed the relative skills of 15 solar radiation models in ET estimation at three humid tropical stations. They showed large variability in the performance of different methods in different stations. Singh et al., (2021) compared the performance of five ET models in the northern region of India and found 'Hargreaves' as the best one after PM in the region. Islam and Alam, (2021) revealed that 'Abtew' is the best out of 15 ET models in Bangladesh. Sobh et al., (2022) evaluated the performance of 31 empirical equations compared to PM in arid Egypt and found that 'Ritchie' was the best one.
The performance of these models in a certain place frequently depends on the local climate (Muhammad et al. 2019). Therefore, finding a suitable model based on the availability of data and the performance of the ET estimate model is a challenging endeavour. Such assessment is vital for predominantly arid Pakistan, where the influence of evapotranspiration on the hydrological process and water resources is more significant than in other climatic zones. However, studies related to identifying and ranking ET models according to required climate variables are absent for Pakistan. Only a single study was conducted by Azhar et al., (2014) to assess the skill of a few models in estimating ET in the Semiarid region of Pakistan. They employed in-situ data of eight locations for this purpose. The results revealed that the 'reduced set PM method' best estimates ET where all variables required for PM are unavailable. The study evaluated only five ET models using observed data of eight locations for only five years (2005–2009). In some cases, ET data based on assumptions or using models were employed as observation, which has limited the acceptability of the results. Habeeb et al., (2021) evaluated the performance of only Hargreaves method and its modified version in estimating ET in Pakistan. They showed the modified version of Hargreaves performs better than its original version in estimating ET in Pakistan.
The performance of 30 empirical ET models has been evaluated in this study to rank them for Pakistan according to required climate variables. The PM ET was considered as the reference in the study. Existing literature suggests that the PM method provides very near to observed ET all over the globe. Therefore, it has been widely used as the reference for performance evaluation of other empirical models where in-situ data for a longer period is not available (Nandagiri and Kovoor 2006a; Islam and Alam 2021; Habeeb et al. 2021). Previous studies used different statistics to assess the performance of ET for their ranking in a region (Muniandy et al. 2016; Muhammad et al. 2019). Statistical metrics often give contradictory results, making the ranking of ET estimation methods challenging (Nashwan and Shahid 2019a; Nashwan et al. 2019b). Therefore, Kling-Gupta Efficiency, an integrated statistical metric, was used to rank ET models in this study.