Table 1 The 30 potential evapotranspiration (PET) models selected for this study

Temperature-based

1

Baier–Robertson

\(PET = 0.157T_{{\max }} + 0.158\left( {T_{{{\text{max}}}} - T_{{{\text{min}}}} } \right) + 0.109R_{a} - 5.39\)

Baier and Robertson (1965)

2

Blaney–Criddle

\(PET = kp\left( {0.46T_{a} + 8.13} \right)\)

Blaney and Criddle (1950)

3

Kharrufa

\(PET = 0.34pT_{a}^{{1.3}}\)

Kharrufa (1985)

4

McCloud

\(PET = 0.254 \times 1.07^{{1.8T_{a} }}\)

Xiang et al. (2020)

5

Oudin

\(\left\{ {_{{PET = 0,T_{a} \le - 5^\circ C}}^{{PET = \left( {\lambda \rho } \right)^{ - 1} R_{a} \left( {\left( {T_{a} + 5} \right)/100} \right),T_{a} > - 5^\circ C}} } \right.\)

Oudin et al. (2005)

6

Romanenko

\(PET = 4.5\left( {1 + T_{a} /25} \right)^{2} \left( {1 - e_{a} /e_{s} } \right)\)

(Seiller and Anctil 2016)

7

Schendel

\(PET = \left( {16T_{a} } \right)/RH\)

(Bormann 2011)

8

Thornthwaite

\(\left\{ \begin{gathered} PET\, = \,0,T_{a} \le \,0^\circ C \hfill \\ PET\, = \,16\left( {{{10T_{a} } \mathord{\left/ {\vphantom {{10T_{a} } {\sum\limits_{i\, = \,1}^{12} {\left( {{{T_{a} } \mathord{\left/ {\vphantom {{T_{a} } 5}} \right. \kern-0pt} 5}} \right)}^{1.514} }}} \right. \kern-0pt} {\sum\limits_{i\, = \,1}^{12} {\left( {{{T_{a} } \mathord{\left/ {\vphantom {{T_{a} } 5}} \right. \kern-0pt} 5}} \right)}^{1.514} }}} \right)^{A} ,T_{a} > 0^\circ C \hfill \\ \end{gathered} \right.\,\)

Thornthwaite (1948)

Aerodynamic-based

9

Albrecht

\(PET = \left( {0.1005 + 0.297\mu _{2} } \right)\left( {e_{s} - e_{a} } \right)\)

Xiang et al. (2020)

10

Brockamp–Wenner

\(PET = 0.543\mu _{2}^{{0.456}} \left( {e_{s} - e_{a} } \right)\)

Bormann (2011)

11

Harbeck

\(PET = 0.0578\mu _{8} \left( {e_{s} - e_{a} } \right) \times 25.4\)

Singh and Xu (1997)

12

Kuzmin

\(PET = \left( {1 + 0.21\mu _{2} } \right)\left( {e_{s} - e_{a} } \right) \times 6\)

Xiang et al. (2020)

13

Mahringer

\(PET = 2.86\mu _{8}^{{^{{0.5}} }} \left( {e_{s} - e_{a} } \right)\)

Mahringer (1970)

14

Rohwer

\(PET = 0.44\left( {1 + 0.27\mu _{2} } \right)\left( {e_{s} - e_{a} } \right)\)

Zhao et al. (2013)

15

Trabert

\(PET = 0.3075\mu _{8}^{{0.5}} \left( {e_{s} - e_{a} } \right)\)

Bormann (2011)

Radiation-based

16

Abtew

\(PET = \alpha R_{s} /\lambda\)

Zhao et al. (2013)

17

Christiansen

\({\text{PET = 0}}{\text{.385R}}_{{\text{s}}}\)

18

Doorenbos–Pruitt

\(PET = \alpha \left( {\frac{\Delta }{{\Delta + \gamma }}\frac{{R_{s} }}{\lambda }} \right) + b\)

Doorenbos and Pruitt (1975)

19

Hargreaves

\(PET = 0.0135\left( {T_{a} + 17.8} \right)\frac{{R_{s} }}{\lambda }\)

Hargreaves (1975)

20

Jensen–Haise

\(PET = \left( {0.014T_{a} - 0.37} \right)\left( {0.000673R_{s} } \right) \times 25.4\)

Zhao et al. (2013)

21

Makkink

\(PET = 0.61\frac{\Delta }{{\Delta + \gamma }}\frac{{R_{s} }}{\lambda } - 0.12\)

Xu and Singh (2002)

22

Milly–Dunne

\(PET = 0.8\frac{{\left( {R_{n} - G} \right)}}{\lambda }\)

Milly and Dunne (2016)

23

Priestley–Taylor

\(PET = 1.26\frac{\Delta }{{\Delta + \gamma }}\frac{{\left( {R_{n} - G} \right)}}{\lambda }\)

Priestley and Taylor (1972)

24

Stephens

\(PET = \left( {0.0158T_{a} + 0.09} \right)R_{s}\)

Stephens (1965)

25

Stephens–Stewart

\(PET = \left( {0.0082T_{a} - 0.19} \right)\left( {R_{s} /1500} \right) \times 25.4\)

Zheng et al. (2017)

26

Turc

\(\left\{ {_{{PET = 0.013\left( {T_{a} /\left( {T_{a} + 15} \right)} \right) \times \left( {R_{s} + 50} \right),RH \ge 50{\text{\% }}}}^{{PET = 0.013\left( {T_{a} /\left( {T_{a} + 15} \right)} \right) \times \left( {R_{s} + 50} \right)\left( {1 + \left( {50 - RH} \right)/70} \right),RH < 50{\text{\% }}}} } \right.\)

Zhao et al. (2013)

Combination

27

Penman

\(PET = \frac{{\Delta \left( {R_{n} - G} \right)}}{{\lambda \left( {\Delta + \gamma } \right)}} + \frac{\gamma }{{\Delta + \gamma }}\frac{{6.43\left( {1 + 0.536\mu _{2} } \right)\left( {e_{s} - e_{a} } \right)}}{\lambda }\)

Yang et al. (2021)

28

Penman–Monteith

\(PET = \frac{{0.408\Delta \left( {R_{n} - G} \right) + \gamma \frac{{900}}{{T_{a} + 273}}\mu _{2} \left( {e_{s} - e_{a} } \right)}}{{\Delta + \gamma \left( {1 + 0.34\mu _{2} } \right)}}\)

(Zhao et al. 2013)

29

Rijtema

\(PET = \frac{{\Delta \left( {R_{n} - G} \right)/\lambda + \gamma r\mu _{2}^{{0.75}} \left( {e_{s} - e_{a} } \right)}}{{\left( {\Delta + \gamma } \right)}}\)

Bormann (2011)

30

Wright–Jensen

\(PET = \frac{{\Delta \left( {R_{n} - G} \right)}}{{\lambda \left( {\Delta + \gamma } \right)}} + \frac{\gamma }{{\Delta + \gamma }}2.63\left( {0.75 + 0.993\mu _{2} } \right)\left( {e_{s} - e_{a} } \right)\)

Allen (1986)