. 2021 Jul 7;7(7):e07487. doi: 10.1016/j.heliyon.2021.e07487

Table 2.

The original form of the 15 empirical models (abbreviated as ET_emp models).

No	Models	Models Input	Equations	References
Temperature-based
1	Hargreaves–Samani	R_{a, Tave}, T_max, T_min	ET_hs = [0.0023 Ra (T_ave +17.8) (T_max − T_min)^0.517]/λ	(Hargreaves and Samani, 1985)
2	Berti et al.	R_{a, Tave}, T_max, T_min	ET_ber = [0.00193 Ra (T_ave +17.8) (T_max − T_min)^0.5]/λ	(Berti et al., 2014)
Radiation-based
3	Makkink	R_s, T	ET_mak = 0.61 $\frac{Δ}{Δ + γ}$ $\frac{Rs}{λ} - 0.12$	Makkink, 1957
4	Jensen–Haise	R_s, T	ET_jh =(0.025T + 0.08) $\frac{Rs}{λ}$	Jensen and Haise, 1963
5	Irmak	R_s, T	ET_irm = 0.149Rs + 0.079T - 0.611	Irmak et al., 2003
6	Tabari	R_s, T_max, T_min	ET_tab = 0.156R_s - 0.0112T_max +0.0733T_min - 0.478	Tabari et al., 2013
7	Priestley–Taylor	Rn, T	ET_pt = 1.26 $\frac{Δ}{Δ + γ}$ $\frac{Rn - G}{λ}$	Priestley and Taylor, 1972
8	Abtew	Rs, T_max	ET_abt = $\frac{1}{56}$ $\frac{Rs Tmax}{λ}$	Abtew, 1996
Mass transfer-based
9	Penman	u₂, e_s-e_a	ET_pen = 0.35 (1 + 0.98/100u₂) (e_s-e_a)	Penman, 1948
10	WMO	u₂, e_s-e_a	ET_wmo = (0.1298 + 0.0934u₂) (e_s-e_a)	WMO, 1996
11	Trabert	u₂, e_s-e_a	ET_tra = 3.075u₂^0.5 (e_s-e_a)	Trabert, 1896
Combined
12	Doorenbos-Pruitt	R_n, u₂, e_s-e_a	ET_dp $= [\frac{Δ}{Δ + γ} (Rn - G) + 2.7 \frac{Δ}{Δ + γ} (1 + 0.864 U_{2}) (e_{s} - e_{a})] / λ$	Doorenbos and Pruitt, 1977
13	Valianlzas1	R_n, T, RH	ET_va1 = 0.0393 R_s– $\sqrt{T + 9.5}$ 0.19 R_s^0.6 Φ^0.15 + 0.078 (T+20) (1 - $\frac{R H}{100}$ )	Valiantzas, 2013; 2013a
14	Valianlzas2	R_n, T, T_min	ET_va2 = 0.0393 R_s– $\sqrt{T + 9.5}$ 0.19 R_s^0.6 Φ^0.15 + 0.0061 (T+20) (1.12T - T_min -2)^0.7	Valiantzas, 2013; 2013a
15	Valianlzas3	R_n, T, RH, u₂	ET_va3 = 0.0393 R_s– $\sqrt{T + 9.5}$ 0.19 R_s^0.6 Φ^0.15 + 0.078 (T+20) (1 - $\frac{R H}{100}$ ) u₂^0.7	Valiantzas, 2013; 2013a

Note: R_a is the extraterrestrial radiation (MJ·m⁻²·d⁻¹), R_s is the solar radiation (MJ·m⁻²·d⁻¹), R_n is the net solar radiation (MJ·m⁻²·d⁻¹), T_ave, T_max, and T_min are mean, maximum, and minimum temperature (◦C), respectively, u₂ is the wind speed at 2 m height (The unit of u₂ is in m·s⁻¹ in all equations except the Penman model, where u₂ is in miles·d⁻¹), e_s and e_a are saturation and actual vapor pressure, respectively (The units of e_s and e_a are in hP_a in all equations except the Penman model, where e_s and e_a are in mmHg.), RH is the relative humidity (%), Δ is the slope of the vapor pressure curve (kP_a·◦C⁻¹), γ is the psychrometric constant (kP_a·◦C⁻¹), λ is the latent heat of vaporization (≈2.45 MJ·kg⁻¹), G is the soil heat flux density (MJ·m⁻²·d⁻¹), and ϕ is the latitude (rad). The abbreviations of the 15 empirical models are arranged in order that the models appear in Table 2: hs, berti, pen, wmo, tra, mak, pt, jh, abt, irm, tab, dp, va1, va2, and va3.