# A Thorough Evaluation of 127 Potential Evapotranspiration Models in Two Mediterranean Urban Green Sites

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## Abstract

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## 1. Introduction

^{−1}. This change in definition and the choice of a specific calculation method is intended to help eliminate problems in measuring a true evapotranspiration rate and provide consistent estimates across regions of the globe. The use of the FAO Penman–Monteith equation overcomes the overestimation problems of the earlier FAO Penman combination method. A hypothetical calculation of reference evapotranspiration can be used to calibrate empirical evapotranspiration equations and be considered as the basis for determining crop coefficients where evapotranspiration cannot be measured simultaneously with specific crop evapotranspiration.

## 2. Materials and Methods

#### 2.1. Study Sites and Instrumentation

#### 2.2. PET Methods

- 12 mass-transfer-based methods following the general form of PET = f (u, T, RH). These methods are based on the assumption that evapotranspiration is affected by the air movements considering also atmospheric dryness, which is expressed by the difference between air vapor pressure at saturation (e
_{s}) and actual vapor pressure (e_{a}). In all cases, the vapor pressure deficit effect is corrected by the addition of the aerodynamic term as a function of wind speed u. For the PET estimation, wind speed (u), air temperature (T) and relative humidity (RH) data are required. The analytical expressions of the 12 mass transfer empirical equations (Equations (1)–(12) used in this work are presented in Table 1. - 48 temperature-based methods following the general forms of PET = f (T), 34 methods (Equations (13)–(46)); PET = f (T, RH), 13 methods (Equations (47)–(59)); and PET = f (T, PR), 1 method (Equation (60)), presented in Table 2.
- 40 radiation-based methods following the general forms of PET = f (Rs), 2 methods (Equations (61) and (62)); PET = f (Rs, T), 21 methods (Equations (63)–(83)); and PET = f (Rs, T, RH), 17 methods (Equations (84)–(100)), presented in Table 3.

Mass Transfer Methods | Equation PET = f (u, T, RH) * | Equation | Ref. |
---|---|---|---|

Dalton 1802 | $\mathrm{PET}=\left(3.648+0.7223\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (1) | [57] |

Fitzgerald 1886 | $\mathrm{PET}=\left(4+1.99\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (2) | [58] |

Trabert 1896 | $\mathrm{PET}=3.075\sqrt{\mathrm{u}}\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (3) | [59] |

Meyer 1926 | $\mathrm{PET}=\left(3.75+0.5026\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (4) | [60] |

Rohwer 1931 | $\mathrm{PET}=\left(3.3+0.891\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (5) | [61] |

Penman 1948 | $\mathrm{PET}=\left(2.625+1.3812\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (6) | [62] |

Albrecht 1950 | $\mathrm{PET}=\left\{\begin{array}{c}\left(1.005+2.97\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right),\mathrm{for}\mathrm{u}\le 1\mathrm{m}/\mathrm{s}\\ 4\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right),\mathrm{for}\mathrm{u}1\mathrm{m}/\mathrm{s}\end{array}\right.$ | (7) | [63,64] |

Brock. and Wenner 1963 | $\mathrm{PET}=5.43{\mathrm{u}}^{0.456}\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (8) | [65] |

WMO 1966 | $\mathrm{PET}=\left(1.298+0.934\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (9) | [66] |

Mahringer 1970 | $\mathrm{PET}=2.86\sqrt{\mathrm{u}}\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)$ | (10) | [67] |

Szász 1973 | $\mathrm{PET}=0.00536{\left(\mathrm{T}+21\right)}^{2}{\left(1+\frac{\mathrm{RH}}{100}\right)}^{2/3}\left(0.0519\mathrm{u}+0.905\right)$ | (11) | [68] |

Linacre 1992 | $\mathrm{PET}=\left(0.015+0.0004\mathrm{T}+0.000001\mathrm{z}\right)\left[\frac{380\left(\mathrm{T}+0.006\mathrm{z}\right)}{84-\mathsf{\phi}}-40+4\mathrm{u}\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{d}}\right)\right]$ | (12) | [69] |

^{−1}, T is the air temperature in °C, T

_{d}is the dew-point in °C, RH is the relative humidity in %, e

_{s}and e

_{a}are the saturation and actual vapor pressures, respectively, in kPa, z is the altitude and φ is the geographical latitude in degrees.

Temperature-Based Methods | Equation PET = f (T) * | Equation | Ref. |
---|---|---|---|

Thornthwaite 1948 | $\mathrm{PET}=16{\left(\frac{10\mathrm{T}}{\mathrm{I}}\right)}^{\mathrm{a}}\frac{\mathrm{N}}{360}$, $\mathrm{I}={\displaystyle \sum}_{1}^{12}{\left(0.2\mathrm{T}\right)}^{1.514}$ | (13) | [51,70] |

Blaney and Criddle 1950 | $\mathrm{PET}=\left\{\begin{array}{c}0.85p\left(0.46\mathrm{T}+8.13\right),\mathrm{from}\mathrm{April}\mathrm{to}\mathrm{September}\\ 0.45p\left(0.46\mathrm{T}+8.13\right),\mathrm{from}\mathrm{October}\mathrm{to}\mathrm{March}\end{array}\right.$ | (14) | [71] |

McCloud 1955 | $\mathrm{PET}=0.254\xb7{1.07}^{1.8\mathrm{T}}$ | (15) | [72] |

Hamon 1963 | $\mathrm{PET}=29.8\mathrm{N}\left(\frac{{\mathrm{e}}_{\mathrm{s}}}{\mathrm{T}+273.2}\right)$, for T > 0 | (16) | [73,74] |

Baier and Robertson 1965 | $\mathrm{PET}=0.157{\mathrm{T}}_{\mathrm{max}}+0.158\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)+0.109{\mathrm{R}}_{\mathrm{a}}-5.39$ | (17) | [30] |

Malmstrom 1969 | $\mathrm{PET}=40.9{\mathrm{e}}_{\mathrm{s}}\frac{\mathrm{N}}{360}$ | (18) | [73] |

Siegert and Schrodter 1975 | $\mathrm{PET}=0.533{\left(\frac{10\mathrm{T}}{33.617}\right)}^{1.033}\frac{\mathrm{N}}{12}$ | (19) | [75] |

Blaney and Criddle (Mid.Eu,. ver.) | $\mathrm{PET}=-1.55+0.96\mathrm{p}\left(0.457\mathrm{T}+8.128\right)$ | (20) | [19] |

Smith and Stopp 1978 | $\mathrm{PET}=0.16\mathrm{T}$ | (21) | [76] |

Hargreaves and Samani 1985 | $\mathrm{PET}=0.0023{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+17.8\right){\mathrm{R}}_{\mathrm{a}}$ | (22) | [77] |

Kharrufa 1985 | $\mathrm{PET}=0.34{\mathrm{p}\mathrm{T}}^{1.3}$ | (23) | [78] |

Mintz and Walker 1993 | $\mathrm{PET}=0.17\frac{\mathrm{N}}{12}\mathrm{T}$ | (24) | [79] |

Camargo et al. 1999 | $\mathrm{PET}=16{\left(\frac{10{\mathrm{T}}_{\mathrm{ef}}}{\mathrm{I}}\right)}^{\mathrm{a}}\frac{\mathrm{N}}{360}$, $\mathrm{I}={\displaystyle \sum}_{1}^{12}{\left(0.2{\mathrm{T}}_{\mathrm{ef}}\right)}^{1.514}$, ${\mathrm{T}}_{\mathrm{ef}}=0.36\left(3{\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)$ | (25) | [80] |

Samani 2000 | $\mathrm{PET}=0.0135{\mathrm{KT}\mathrm{R}}_{\mathrm{a}}{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+17.8\right)$ $\mathrm{KT}=0.00185{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{2}-0.0433\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)+0.4023$ | (26) | [77,81,82] |

Xu and Singh 2001 (1) | $\mathrm{PET}=20{\left(\frac{10\mathrm{T}}{\mathrm{I}}\right)}^{\mathrm{a}}\frac{\mathrm{N}}{360}$, $\mathrm{I}={\displaystyle \sum}_{1}^{12}{\left(0.2\mathrm{T}\right)}^{1.514}$ | (27) | [83] |

Xu and Singh 2001 (2) | $\mathrm{PET}=20.5{\left(\frac{10\mathrm{T}}{\mathrm{I}}\right)}^{\mathrm{a}}\frac{\mathrm{N}}{360}$, $\mathrm{I}={\displaystyle \sum}_{1}^{12}{\left(0.2\mathrm{T}\right)}^{1.514}$ | (28) | [83] |

Xu and Singh 2001 (3) | $\mathrm{PET}=0.37{\mathrm{p}\mathrm{T}}^{1.3}$ | (29) | [83] |

Xu and Singh 2001 (4) | $\mathrm{PET}=0.0028{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+17.8\right){\mathrm{R}}_{\mathrm{a}}$ | (30) | [83] |

Droogers and Allen 2002 (1) | $\mathrm{PET}=0.0030{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.4}\left(\mathrm{T}+20\right){\mathrm{R}}_{\mathrm{a}}$ | (31) | [84] |

Droogers and Allen 2002 (2) | $\mathrm{PET}=0.0025{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+16.8\right){\mathrm{R}}_{\mathrm{a}}$ | (32) | [84] |

Pereira and Pruitt 2004 | $\mathrm{PET}=16{\left(\frac{10{\mathrm{T}}_{\mathrm{ef}}^{\ast}}{\mathrm{I}}\right)}^{\mathrm{a}}\frac{\mathrm{N}}{360}$, $\mathrm{I}={\displaystyle \sum}_{1}^{12}{\left(0.2{\mathrm{T}}_{\mathrm{ef}}\right)}^{1.514}$ ${\mathrm{T}}_{\mathrm{ef}}^{\ast}=0.345\left(3{\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)\frac{\mathrm{N}}{24-\mathrm{N}}$ for $\mathrm{T}\le {\mathrm{T}}_{\mathrm{ef}}^{\ast}\le {\mathrm{T}}_{\mathrm{max}}$ | (33) | [70] |

Trajcovic 2005 (1) | $\mathrm{PET}=0.88\left[16{\left(\frac{10\mathrm{T}}{\mathrm{I}}\right)}^{\mathrm{a}}\frac{\mathrm{N}}{360}\right]+0.565$, $\mathrm{I}={\displaystyle \sum}_{1}^{12}{\left(0.2\mathrm{T}\right)}^{1.514}$ | (34) | [85] |

Trajcovic 2005 (2) | $\mathrm{PET}=0.817\left[0.0023{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+17.8\right){\mathrm{R}}_{\mathrm{a}}\right]+0.320$ | (35) | [85] |

Oudin 2005 | $\mathrm{PET}={\mathrm{R}}_{\mathrm{a}}\frac{\mathrm{T}+5}{100}$, for T + 5 > 0 | (36) | [86] |

Castañeda and Rao 2005 (1) | $\mathrm{PET}=\left\{\begin{array}{c}0.9\mathrm{p}\left(0.46\mathrm{T}+8.13\right),\mathrm{from}\mathrm{April}\mathrm{to}\mathrm{September}\\ 0.6\mathrm{p}\left(0.46\mathrm{T}+8.13\right),\mathrm{from}\mathrm{October}\mathrm{to}\mathrm{March}\end{array}\right.$ | (37) | [87] |

Trajkovic 2007 | $\mathrm{PET}=0.0023{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.424}\left(\mathrm{T}+17.8\right){\mathrm{R}}_{\mathrm{a}}$ | (38) | [31] |

Tabari and Talaee 2011 (1) | $\mathrm{PET}=0.0031{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+17.8\right){\mathrm{R}}_{\mathrm{a}}$ | (39) | [88] |

Tabari and Talaee 2011 (2) | $\mathrm{PET}=0.0028{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+17.8\right){\mathrm{R}}_{\mathrm{a}}$ | (40) | [88] |

Ravazzani et al. 2012 | $\mathrm{PET}=\left(0.817+0.00022\mathrm{z}\right)0.0023{\mathrm{R}}_{\mathrm{a}}\left(\mathrm{T}+17.8\right){\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}$ | (41) | [89] |

Berti et al. 2014 | $\mathrm{PET}=0.00193{\mathrm{R}}_{\mathrm{a}}\left(\mathrm{T}+17.8\right){\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.517}$ | (42) | [90] |

Heydari and Heydari 2014 | $\mathrm{PET}=0.0023{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.611}\left(\mathrm{T}+9.519\right){\mathrm{R}}_{\mathrm{a}}$ | (43) | [91] |

Dorji et al. 2016 | $\mathrm{PET}=0.002{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.296}\left(\mathrm{T}+33.9\right){\mathrm{R}}_{\mathrm{a}}$ | (44) | [92] |

Lobit et al. 2018 | $\mathrm{PET}=0.1555{\mathrm{R}}_{\mathrm{a}}\left(0.00428\mathrm{T}+0.09967\right){\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}$ | (45) | [93] |

Althoff et al. 2019 | $\mathrm{PET}=0.0135\xb70.166{\mathrm{R}}_{\mathrm{a}}{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}\right)}^{0.5}\left(\mathrm{T}+15.3\right)$ | (46) | [94] |

Equation PET = f (T, RH) * | |||

Romanenko 1961 | $\mathrm{PET}=0.0018{\left(25+\mathrm{T}\right)}^{2}\left(100-\mathrm{RH}\right)\frac{\mathrm{N}}{360}$ | (47) | [95] |

Papadakis 1965 | $\mathrm{PET}=2.5\left[{\mathrm{e}}_{\mathrm{ma}}-{\mathrm{e}}_{\mathrm{d}}\right]$ | (48) | [96] |

Schendel 1967 | $\mathrm{PET}=16\frac{\mathrm{T}}{\mathrm{RH}}$ | (49) | [29] |

Antal 1968 | $\mathrm{PET}=0.736{\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)}^{0.7}{\left(1+\frac{\mathrm{T}}{273}\right)}^{4.8}$ | (50) | [97,98] |

Linacre 1977 | $\mathrm{PET}=\left[\frac{500\left(\mathrm{T}+0.006\mathrm{z}\right)}{100-\mathsf{\phi}}+15\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{d}}\right)\right]/\left(80+\mathrm{T}\right)$ | (51) | [99] |

Naumann 1987 | $\mathrm{PET}=0.18\mathrm{N}\left({\mathrm{e}}_{\mathrm{s}}^{14}-{\mathrm{e}}_{\mathrm{a}}^{14}\right)$ | (52) | [100] |

Xu and Singh 2001 (5) | $\mathrm{PET}=0.0020{\left(25+\mathrm{T}\right)}^{2}\left(100-\mathrm{RH}\right)\frac{\mathrm{N}}{360}$ | (53) | [83] |

Xu and Singh 2001 (6) | $\mathrm{PET}=\left[\frac{488\left(\mathrm{T}+0.006\mathrm{z}\right)}{100-\mathsf{\phi}}+15\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{d}}\right)\right]/\left(80+\mathrm{T}\right)$ | (54) | [83] |

Xu and Singh 2001 (7) | $\mathrm{PET}=\left[\frac{615\left(\mathrm{T}+0.006\mathrm{z}\right)}{100-\mathsf{\phi}}+15\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{d}}\right)\right]/\left(80+\mathrm{T}\right)$ | (55) | [83] |

Ahooghalaandari et al. 2016 (1) | $\mathrm{PET}=0.252{\mathrm{R}}_{\mathrm{a}}+0.221\mathrm{T}\left(1-\frac{\mathrm{RH}}{100}\right)$ | (56) | [101] |

Ahooghalaandari et al. 2016 (2) | $\mathrm{PET}=0.29{\mathrm{R}}_{\mathrm{a}}+0.15{\mathrm{T}}_{\mathrm{max}}\left(1-\frac{\mathrm{RH}}{100}\right)$ | (57) | [101] |

Ahooghalaandari et al. 2016 (3) | $\mathrm{PET}=0.369{\mathrm{R}}_{\mathrm{a}}+0.139{\mathrm{T}}_{\mathrm{max}}\left(1-\frac{\mathrm{RH}}{100}\right)-1.95$ | (58) | [101] |

Ahooghalaandari et al. 2016 (4) | $\mathrm{PET}=0.34{\mathrm{R}}_{\mathrm{a}}+0.182\mathrm{T}\left(1-\frac{\mathrm{RH}}{100}\right)-1.55$ | (59) | [101] |

Equation PET = f (T, PR) * | |||

Droogers and Allen 2002 (3) | $\mathrm{PET}=0.0013{\left({\mathrm{T}}_{\mathrm{max}}-{\mathrm{T}}_{\mathrm{min}}-0.0123\mathrm{PR}\right)}^{0.76}\left(\mathrm{T}+17\right){\mathrm{R}}_{\mathrm{a}}$ | (60) | [84] |

^{−7}I

^{3}− 7.71 × 10

^{−5}I

^{2}+1.7912 × 10

^{−2}I + 0.49239 (Equations (13), (25), (27), (28), (33) and (34)), p represents the daily percentage (%) of annual daytime hours for each day of the year, N represents the maximum sunshine daily hours, T, T

_{max}and T

_{min}are the daily mean, maximum and minimum air temperatures in °C, T

_{d}is the dewpoint in °C, RH is the relative humidity in %, φ is the latitude in degrees, z is the altitude in m, PR is the monthly precipitation in mm, Ra is the extraterrestrial radiation in mm day

^{−1}in all equations except those from Baier and Robertson 1965 (Equation (17)) and Lobit et al. 2018 (Equation (45)), where Ra is in MJ m

^{−2}d

^{−1}, e

_{s}and e

_{a}are the saturation and actual vapor pressures in kPa in all equations except those from Antal 1968 (Equation (50)), where they are in hPa, e

_{ma}is the saturation vapor pressure at daily maximum temperature in kPa and e

_{s}

^{14}and e

_{a}

^{14}are the e

_{s}and e

_{a}values in kpa at 14 h local time.

Radiation-Based Methods | Equation PET = f (Rs) * | Equation | Ref. |
---|---|---|---|

Christiansen 1968 | $\mathrm{PET}=0.385\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}$ | (61) | [102] |

Abtew 1996 (1) | $\mathrm{PET}=0.52\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}$ | (62) | [103] |

Equation PET= f (Rs, T) * | |||

Makkink 1957 | $\mathrm{PET}=0.61\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}-0.12$ | (63) | [104] |

Steph. and Stewart 1963 | $\mathrm{PET}=\left[0.0082\left(\frac{9}{5}\mathrm{T}+32\right)-0.19\right]\frac{23.9{\mathrm{R}}_{\mathrm{s}}}{1500}25.4$ | (64) | [105] |

Jensen and Haise 1963 | $\mathrm{PET}=\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}\left(0.025\mathrm{T}+0.08\right)$ | (65) | [106] |

Stephens 1965 | $\mathrm{PET}=\left(0.0158\mathrm{T}-0.09\right){\mathrm{R}}_{\mathrm{s}}$ | (66) | [107,108] |

McGuin. and Bord. 1972 | $\mathrm{PET}=\left(0.0059685\mathrm{T}+0.02927624\right){\mathrm{R}}_{\mathrm{s}}$ | (67) | [109] |

Ritchie 1972 | $\mathrm{PET}={\mathrm{a}}_{1}0.00387{\mathrm{R}}_{\mathrm{s}}\left(0.6{\mathrm{T}}_{\mathrm{max}}+0.4{\mathrm{T}}_{\mathrm{min}}+29\right)$, ${\mathrm{a}}_{1}=\left\{\begin{array}{c}1.1,\mathrm{for}5\xb0\mathrm{C}{\mathrm{T}}_{\mathrm{max}}35\xb0\mathrm{C}\\ 1.1+0.05\left({\mathrm{T}}_{\mathrm{max}}-35\right),\mathrm{for}{\mathrm{T}}_{\mathrm{max}}35\xb0\mathrm{C}\\ 0.1+{\mathrm{e}}^{0.18\left({\mathrm{T}}_{\mathrm{max}}+20\right)},\mathrm{for}5{\mathrm{T}}_{\mathrm{max}}5\xb0\mathrm{C}\end{array}\right.$ | (68) | [110,111] |

Caprio 1974 | $\mathrm{PET}=6.1{10}^{-3}{\mathrm{R}}_{\mathrm{s}}\left(1.8\mathrm{T}+1\right)$ | (69) | [112] |

Hargreaves 1975 | $\mathrm{PET}=0.0135\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}\left(\mathrm{T}+17.8\right)$ | (70) | [113] |

Hansen 1984 | $\mathrm{PET}=0.7\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}$ | (71) | [114] |

de Bruin 1987 | $\mathrm{PET}=0.65\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}$ | (72) | [115,116,117] |

Wendl. 1991–1995 | $\mathrm{PET}=\left(100{\mathrm{R}}_{\mathrm{s}}+93\mathrm{K}\right)\frac{\mathrm{T}+22}{150\left(\mathrm{T}+123\right)}$ | (73) | [118,119] |

Abtew 1996 (2) | $\mathrm{PET}=0.012\frac{\left(23.89{\mathrm{R}}_{\mathrm{s}}+50\right){\mathrm{T}}_{\mathrm{max}}}{{\mathrm{T}}_{\mathrm{max}}+15}$ | (74) | [103] |

Abtew 1996 (3) | $\mathrm{PET}=\frac{1}{56}\frac{{\mathrm{T}}_{\mathrm{max}}{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}$ | (75) | [103] |

Irmak et al. 2003 (1) | $\mathrm{PET}=0.149{\mathrm{R}}_{\mathrm{s}}+0.079\mathrm{T}-0.611$ | (76) | [120] |

Irmak et al. 2003 (2) | $\mathrm{PET}=0.286{\mathrm{R}}_{\mathrm{s}}+0.134\mathrm{T}-2.959$ | (77) | [120] |

Irmak et al. 2003 (3) | $\mathrm{PET}=0.264{\mathrm{R}}_{\mathrm{s}}-0.052{\mathrm{T}}_{\mathrm{max}}+0.233{\mathrm{T}}_{\mathrm{min}}-1.110$ | (78) | [120,121] |

Castañeda and Rao 2005 (2) | $\mathrm{PET}=0.70\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}-0.12$ | (79) | [87] |

Valiantzas 2013 (1) | $\mathrm{PET}=0.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-0.19{\mathrm{R}}_{\mathrm{s}}^{0.6}{\mathsf{\phi}}^{0.15}+0.0061\left(\mathrm{T}+20\right){\left(1.12\mathrm{T}-{\mathrm{T}}_{\mathrm{min}}-2\right)}^{0.7}$ | (80) | [122,123] |

Tabari et al. 2013 (1) | $\mathrm{PET}=-0.642+0.174{\mathrm{R}}_{\mathrm{s}}+0.0353\mathrm{T}$ | (81) | [124] |

Tabari et al. 2013 (2) | $\mathrm{PET}=-0.478+0.156{\mathrm{R}}_{\mathrm{s}}-0.0112{\mathrm{T}}_{\mathrm{max}}+0.0733{\mathrm{T}}_{\mathrm{min}}$ | (82) | [124] |

Ahooghal. et al. 2017 (1) | $\mathrm{PET}=0.79\xb70.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-0.94\xb70.19{\mathrm{R}}_{\mathrm{s}}^{0.6}{\mathsf{\phi}}^{0.15}+2.21\xb70.0061\left(\mathrm{T}+20\right){\left(1.12\mathrm{T}-{\mathrm{T}}_{\mathrm{min}}-2\right)}^{0.7}$ | (83) | [125] |

Equation PET = f (Rs, T, RH) * | |||

Turc 1961 | $\mathrm{PET}=\left\{\begin{array}{c}0.013\left(23.9{\mathrm{R}}_{\mathrm{s}}+50\right)\frac{\mathrm{T}}{\mathrm{T}+15},\mathrm{for}\mathrm{RH}50\\ 0.013\left(23.9{\mathrm{R}}_{\mathrm{s}}+50\right)\frac{\mathrm{T}}{\mathrm{T}+15}\left(1+\frac{50-\mathrm{RH}}{70}\right),\mathrm{for}\mathrm{RH}\le 50\end{array}\right.$ | (84) | [126] |

Priestley and Taylor 1972 | $\mathrm{PET}=1.26\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{n}}-\mathrm{G}}{\mathsf{\lambda}}$ | (85) | [127] |

Abtew 1996 (4) | $\mathrm{PET}=1.18\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{n}}-\mathrm{G}}{\mathsf{\lambda}}$ | (86) | [103,128] |

Xu and Singh 2000 | $\mathrm{PET}=0.98\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{n}}-\mathrm{G}}{\mathsf{\lambda}}-0.94$ | (87) | [129] |

Irmak et al. 2003 (4) | $\mathrm{PET}=0.289{\mathrm{R}}_{\mathrm{n}}+0.023\mathrm{T}+0.489$ | (88) | [120] |

Irmak et al. 2003 (5) | $\mathrm{PET}=0.435{\mathrm{R}}_{\mathrm{n}}+0.095\mathrm{T}-1.149$ | (89) | [120] |

Irmak et al. 2003 (6) | $\mathrm{PET}=0.432{\mathrm{R}}_{\mathrm{n}}+0.043{\mathrm{T}}_{\mathrm{max}}+0.055{\mathrm{T}}_{\mathrm{min}}-1.077$ | (90) | [120,121] |

Bereng. and Gavil. 2005 | $\mathrm{PET}=1.65\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{n}}-\mathrm{G}}{\mathsf{\lambda}}$ | (91) | [130] |

Copais | $\mathrm{PET}={\mathrm{m}}_{1}+{\mathrm{m}}_{2}{\mathrm{C}}_{2}+{\mathrm{m}}_{3}{\mathrm{C}}_{1}+{\mathrm{m}}_{4}{\mathrm{C}}_{1}{\mathrm{C}}_{2}$, where m _{1} = 0.057, m_{2} = 0.277, m_{3} = 0.643, m_{4} = 0.0124${\mathrm{C}}_{1}=0.6416-0.00784\mathrm{RH}+0.372{\mathrm{R}}_{\mathrm{s}}-0.00264{\mathrm{R}}_{\mathrm{s}}\mathrm{RH}$ ${\mathrm{C}}_{2}=-0.0033+0.00812\mathrm{T}+0.101{\mathrm{R}}_{\mathrm{s}}+0.00584{\mathrm{R}}_{\mathrm{s}}\mathrm{T}$ | (92) | [131] |

Valiantzas 2006 (1) | $\mathrm{PET}=0.038{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-2.4{\left(\frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{a}}}\right)}^{2}+0.075\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)$ | (93) | [132] |

Tabari and Talaee 2011 (3) | $\mathrm{PET}=2.14\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{n}}-\mathrm{G}}{\mathsf{\lambda}}$ | (94) | [88] |

Tabari and Talaee 2011 (4) | $\mathrm{PET}=1.82\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{n}}-\mathrm{G}}{\mathsf{\lambda}}$ | (95) | [88] |

Valiantzas 2013 (2) | $\mathrm{PET}=0.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-0.19{\mathrm{R}}_{\mathrm{s}}^{0.6}{\mathsf{\phi}}^{0.15}+0.078\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)$ | (96) | [122,123] |

Valiantzas 2013 (3) | $\mathrm{PET}=0.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-2.4{\left(\frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{a}}}\right)}^{2}-0.024\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)+0.1{\mathrm{W}}_{\mathrm{aero}}\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)$ ${\mathrm{W}}_{\mathrm{aero}}=\left\{\begin{array}{c}0.78,\mathrm{for}\mathrm{RH}65\%\\ 1.067,\mathrm{for}\mathrm{RH}\le 65\%\end{array}\right.$ | (97) | [133] |

Milly and Dunne 2016 | $\mathrm{PET}=0.8\frac{{\mathrm{R}}_{\mathrm{n}}-\mathrm{G}}{\mathsf{\lambda}}$ | (98) | [134] |

Ahooghal. et al. 2017 (2) | $\mathrm{PET}=0.79\xb70.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-1.15\xb72.4{\left(\frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{a}}}\right)}^{2}-\left(-3.23\right)\xb70.024\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)+0.32\xb70.1{\mathrm{W}}_{\mathrm{aero}}\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)$, ${\mathrm{W}}_{\mathrm{aero}}=\left\{\begin{array}{c}0.78,\mathrm{for}\mathrm{RH}65\%\\ 1.067,\mathrm{for}\mathrm{RH}\le 65\%\end{array}\right.$ | (99) | [125] |

Ahooghal. et al. 2017 (3) | $\mathrm{PET}=0.79\xb70.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-0.94\xb70.19{\mathrm{R}}_{\mathrm{s}}^{0.6}{\mathsf{\phi}}^{0.15}+1.37\xb70.078\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)$ | (100) | [125] |

_{max}and T

_{min}represent the average, maximum and minimum daily air temperatures in °C, RH is the relative humidity in %, φ is the latitude in radians, Rs, Rn and Ra are the global solar, the net and the extraterrestrial radiation fluxes, respectively, in MJ m

^{−2}day

^{−1}, G is the soil heat flux in MJ m

^{−2}day

^{−1}(G = 0), Δ is the slope of the vapor pressure curve (kPa °C

^{−1}), γ is the psychrometric constant (kPa °C

^{−1}) and λ = 2.501–0.002361 Τ, in MJ kg

^{−1}.

Combination Methods | Equation PET = f (Rs, u, T, RH) * | Equation | Ref. |
---|---|---|---|

FAO56-PM | $\mathrm{PET}=\frac{0.408\Delta \left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+\mathsf{\gamma}\frac{900}{\mathrm{T}+273}\mathrm{u}\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)}{\Delta +\mathsf{\gamma}\left(1+0.34\mathrm{u}\right)}$ | Benchmark method | [11] |

Penman 1963 | $\mathrm{PET}=\left[\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+6.43\frac{\mathsf{\gamma}}{\mathsf{\Delta}+\mathsf{\gamma}}\left(1+0.537\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)\right]\frac{1}{\mathsf{\lambda}}$ | (101) | [135] |

Kimberly Penman 1972 | $\mathrm{PET}=\left[\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+6.43\frac{\mathsf{\gamma}}{\mathsf{\Delta}+\mathsf{\gamma}}\left(0.75+0.993\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)\right]\frac{1}{\mathsf{\lambda}}$ | (102) | [24] |

mod. Makkink (Door. and Pr. 1977) | $\mathrm{PET}=\mathrm{b}\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\frac{{\mathrm{R}}_{\mathrm{s}}}{\mathsf{\lambda}}-0.3$, b = 1.165 + 0.043 u_{b} − 0.00575 RH | (103) | [19] |

FAO24 Penman | $\mathrm{PET}=\left[\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+6.43\frac{\mathsf{\gamma}}{\mathsf{\Delta}+\mathsf{\gamma}}\left(1+0.862\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)\right]\frac{1}{\mathsf{\lambda}}$ | (104) | [19] |

FAO24 Radiation | $\mathrm{PET}=\mathrm{b}\left(\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}{\mathrm{R}}_{\mathrm{s}}\right)-0.3$ b = 1.066 − 0.0013 RH + 0.045 u − 0.0002 RH u − 0.0000315 RH ^{2} − 0.0011 u^{2} | (105) | [19,136] |

Jensen et al. 1990 | $\mathrm{PET}=\left[\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+6.43\frac{\mathsf{\gamma}}{\mathsf{\Delta}+\mathsf{\gamma}}\left({\mathrm{a}}_{\mathrm{w}}+{\mathrm{b}}_{\mathrm{w}}\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)\right]\frac{1}{\mathsf{\lambda}}$. ${\mathrm{a}}_{\mathrm{w}}=0.4+1.4{\mathrm{e}}^{-{\left(\frac{\mathrm{J}-173}{58}\right)}^{2}}$, ${\mathrm{b}}_{\mathrm{w}}=0.605+0.345{\mathrm{e}}^{-{\left(\frac{\mathrm{J}-243}{80}\right)}^{2}}$ | (106) | [21,22] |

Linacre 1993 | $\mathrm{PET}=\left(0.015+0.00042\mathrm{T}+0.000001\mathrm{z}\right)\left[9.26\mathrm{Rs}-40+2.5\left(1-0.000087\mathrm{z}\right)\mathrm{u}\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{d}}\right)\right]$ | (107) | [137] |

Wright 1996 | $\mathrm{PET}=\left[\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\mathsf{\gamma}}\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+6.43\frac{\mathsf{\gamma}}{\mathsf{\Delta}+\mathsf{\gamma}}\left({\mathrm{a}}_{\mathrm{w}}+{\mathrm{b}}_{\mathrm{w}}\mathrm{u}\right)\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)\right]\frac{1}{\mathsf{\lambda}}$ ${\mathrm{a}}_{\mathrm{w}}=0.3+0.58{\mathrm{e}}^{-{\left(\frac{\mathrm{J}-170}{45}\right)}^{2}}$, ${\mathrm{b}}_{\mathrm{w}}=0.32+0.54{\mathrm{e}}^{-{\left(\frac{\mathrm{J}-228}{67}\right)}^{2}}$ | (108) | [23] |

Valiantzas 2006 (2) | $\mathrm{PET}=0.038{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-2.4{\left(\frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{a}}}\right)}^{2}+0.048\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)\left(0.5+0.536\mathrm{u}\right)+0.00012\mathrm{z}$ | (109) | [132] |

Valiantzas 2013 (4) | $\mathrm{PET}=0.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-0.19{\mathrm{R}}_{\mathrm{s}}^{0.6}{\mathsf{\phi}}^{0.15}+0.048\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right){\mathrm{u}}^{0.7}$ | (110) | [122,123] |

Valiantzas 2013 (5) | $\mathrm{PET}=0.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-2.4{\left(\frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{a}}}\right)}^{2}-0.024\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right)+0.066{\mathrm{W}}_{\mathrm{aero}}\left(\mathrm{T}+20\right)\left(1-\frac{\mathrm{RH}}{100}\right){\mathrm{u}}^{0.6}$, ${\mathrm{W}}_{\mathrm{aero}}=\left\{\begin{array}{c}0.78,\mathrm{for}\mathrm{RH}65\%\\ 1.067,\mathrm{for}\mathrm{RH}\le 65\%\end{array}\right.$ | (111) | [133] |

PET = f (Rs, u, T) * | |||

Valiantzas 2013 (6) | $\mathrm{PET}=0.0393{\mathrm{R}}_{\mathrm{s}}\sqrt{\mathrm{T}+9.5}-0.19{\mathrm{R}}_{\mathrm{s}}^{0.6}{\mathsf{\phi}}^{0.15}+0.0037\left(\mathrm{T}+20\right){\left(1.12\mathrm{T}-{\mathrm{T}}_{\mathrm{min}}-2\right)}^{0.7}{\mathrm{u}}^{0.7}$ | (112) | [122,123] |

_{min}are the average and minimum daily air temperatures in °C, T

_{d}is the dewpoint in °C, RH is the relative humidity in %, φ is the latitude in radians, z is the altitude in m, Rs, Rn and Ra are the global solar, the net and the extraterrestrial radiation fluxes in MJ m

^{−2}day

^{−1}, G is the soil heat flux in MJ m

^{−2}day

^{−1}(G = 0), Δ is slope of the vapor pressure curve (kPa °C

^{−1}), γ is the psychrometric constant (kPa °C

^{−1}), J is the day of the year, λ= 2.501 − 0.002361 Τ, in MJ kg

^{−1}, e

_{s}and e

_{a}are the saturation and actual vapor pressures in kPa, u is the windspeed at height 2m in m/s and u

_{b}is the windspeed in Beaufort.

#### 2.3. Statistical Indices and Ranking

^{2}. Four additional statistical measures recommended by Fox [140] were applied: the mean bias error (MBE) to assess the bias, the variance of the differences distribution ${\mathrm{s}}_{\mathrm{d}}^{2}$ to evaluate the variability of the differences between the PET values around the MBE, the mean absolute error (MAE) and the root mean square error (RMSE) to express the average difference. The index of agreement (d) was also used to make the cross-comparison between the models [141,142,143]. The analytic equations for the estimation of the indices are presented in Appendix A (Equations (A1)–(A5)).

## 3. Results

^{−1}, which is slightly higher compared to the respective values of Amaroussion (3.10 ± 1.92 mm d

^{−1}). Both sites present high seasonal variability with ET values ranging from 1.44 ± 0.49 mm d

^{−1}in winter to 5.87 ± 0.77 mm d

^{−1}in summer in Heraklion and from 1.05 ± 0.41 mm d

^{−1}in winter to 5.48 ± 1.00 mm d

^{−1}in summer in Amaroussion. The day-to-day and monthly values are even more variable, as depicted in Figure 3.

#### 3.1. Mass Transfer-Based Methods

^{−1}) and the best slope a value (1.015) compared to all other mass transfer methods, whereas its mean value (3.234 ± 2.264 mm d

^{−1}) is quite close to FAO56-PM (3.266 ± 1.910 mm d

^{−1}) and only underestimated by −0.98%. Trabert 1886 (Equation (3)) had the best d index (0.974) and Linacre 1992 (Equation (12)) had the smallest RMSE (0.977 mm d

^{−1}), smallest MAE (0.801), smallest sd

^{2}(0.789 mm d

^{−1}), and best R

^{2}(0.796) among all mass transfer-based method in Heraklion.

^{−1}), RMSE (0.923 mm d

^{−1}) and the best sd

^{2}(0.592 mm d

^{−1}) and d (0.982) values, but its average PET estimate (2.465 ± 1.905 mm d

^{−1}) was −17% smaller compared to FAO56-PM (2.969 ± 1.904 mm d

^{−1}). Linacre 1992 (Equation (12)) had the best slope a value (1.062).

#### 3.2. Temperature-Based Methods

^{−1}) and the best d (0.966) values, and they produced an average PET (3.609 ± 2.451 mm d

^{−1}) +10% higher compared to FAO56-PM. The worst temperature-based methods for the site were by Antal 1968 (Equation (50)) and Smith and Stopp 1978 (Equation (21)), which ranked 109th and 108th among the 112 models.

^{−1}, which was +21% higher compared to FAO56-PM.

#### 3.3. Radiation-Based Methods

^{−1}), MAE (0.416 mm d

^{−1}) and sd

^{2}(0.178), whereas Castañeda and Rao 2005 (2) (Equation (79)) had the minimum offset b (−0.007 mm d

^{−1}) and Priestley and Taylor 1972 (Equation (85)) had the minimum MBE (−0.014 mm d

^{−1}) and the best d (0.986) among the radiation-based models. The worst methods of this category in Heraklion were Tabari and Talaee 2011 (3) (Equation (94)) ranking 110th sRPI = 0.495 and Xu and Singh 2000 (Equation (87)) ranking 103rd with sRPI = 0.603, producing PET means −30.7% and +67.6% different compared to FAO56-PM. In general, however, the radiation methods in Heraklion had a good performance in most cases, since the produced PET means were less than 10% different from FAO56-PM in 19 out of the 40 methods.

^{−1}), RMSE (0.486 mm d

^{−1}) and d (0.992) values, whereas Abtew 1996 (4) (Equation (86)) had the best MAE (0.374 mm d

^{−1}) and sd

^{2}(0.229 mm d

^{−1}) and Ahooghalaandari et al. 2017 (2) (Equation (99)) presented the minimum offset b (−0.045 mm d

^{−1}) among all radiation-based methods. The worst models in Amaroussion were Tabari and Talaee 2011 (3) (Equation (94)) and Xu and Singh 2000 (Equation (87)), ranking 103rd and 99th, respectively, among all examined 112 methods, with sRPI values of 0.591 and 0.621. These methods’ mean PET values were +71.7% and −28.7% different compared to FAO56-PM. The overall performance of radiation-based methods in Amaroussion can be considered satisfactory, considering that 28 out of the 40 equations presented sRPI values higher than 0.800, whereas 15 of them had sRPI > 0.900.

#### 3.4. Combination Methods

^{−1}) and MAE (0.315 mm d

^{−1}) and also the best slope a (1.005) and d (0.989) values. Valiantzas 2006 (2) (Equation (109)) and Jensen et al. 1990 (Equation (106)) methods were ranked 2nd and 3rd, respectively, among all 112 examined models and had also high sRPI values (0.970 and 0.963). However, the produced mean PET values were about +11% higher compared to FAO56-PM. However, Valiantzas 2006 (2) (Equation (109)) presented the minimum offset b (−0.008 mm d

^{−1}) and sd

^{2}(0.078 mm d

^{−1}) in Heraklion not only among the combination but among all 112 methods. The worst-performing methods for the site were FAO24 Radiation (Equation (105)) followed by the modified Makkink by Doorenbos and Pruitt 1977 (Equation (103)), which were ranked 58th and 53rd with sRPI values of 0.792 and 0.813, respectively. The mean PET values of these methods were +25.3% and +20.4% higher compared to FAO56-PM.

^{−1}), MAE (0.264 mm d

^{−1}) and sd

^{2}(0.159 mm d

^{−1}) values, producing a mean PET estimate +0.97% higher compared to FAO56-PM. Also, in Amaroussion, Jensen et al. 1990 (Equation (106)) had the best offset b (0.003), but its mean PET was +12.3% higher compared to FAO56-PM. As in Heraklion, the worst combination methods for Amaroussion were also FAO24 Radiation (Equation (105)) followed by the modified Makkink by Doorenbos and Pruitt 1977 (Equation (103)), which ranked 54th and 49th, respectively, among the 112 models, presenting relatively low sRPI values (0.819 and 0.828) and also mean PET values +37.3% and +33.1% higher compared to FAO56-PM.

#### 3.5. Models Adjustment

_{s}– e

_{a}). The adjusted values of a and b, based on the data from the two stations, are presented in Table 9. Similarly, other widely used models were adjusted for local use, and the new models are also presented in Table 9. The performance of the adjusted equations (Equations (113)–(127)) is evaluated following the estimation of statistical indices and ranking as above. The daily PET estimates for the new models are presented for the two sites along with the respective PET values by the FAO56-PM method in Figure 8.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

- Slope a, intercept b and coefficient of determination R
^{2}of the linear regression y = ax + b. - Mean bias error (MBE):$$\mathrm{MBE}={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}}{\mathrm{N}}$$
- Mean absolute error (MAE):$$\mathrm{MAE}={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{N}}\frac{\left|{\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}\right|}{\mathrm{N}}$$
- Differences distribution ${\mathrm{s}}_{\mathrm{d}}^{2}$ around the MBE:$${\mathrm{s}}_{\mathrm{d}}^{2}={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}-\mathrm{MBE}\right)}^{2}}{\mathrm{N}-1}$$
- Root mean square error (RMSE):$$\mathrm{RMSE}=\sqrt{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}\right)}^{2}}{\mathrm{N}}}$$
- Index of agreement (d):$$\mathrm{d}=1-\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}\right)}^{2}}{\mathrm{N}}}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\left(\left|\stackrel{\prime}{{\mathrm{P}}_{\mathrm{i}}}\right|+\left|\stackrel{\prime}{{\mathrm{O}}_{\mathrm{i}}}\right|\right)}^{2}}{\mathrm{N}}}$$
_{i}is the estimated PET by FAO56-PM, and P_{i}is the PET by the compared methods, $\stackrel{\prime}{{\mathrm{P}}_{\mathrm{i}}}={\mathrm{P}}_{\mathrm{i}}-\mathrm{O}$ and $\stackrel{\prime}{{\mathrm{O}}_{\mathrm{i}}}={\mathrm{O}}_{\mathrm{i}}-\mathrm{O}$.

_{i}is each statistical index and k is the number of the statistical indices used for the RPI and sRPI estimations.

## Appendix B

**Figure A1.**Correlation between daily PET values estimated by different mass transfer methods (x-axis) and the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure A2.**Correlation between daily PET values estimated by different temperature-based methods (x-axis) of the general forms PET = f (T) and the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure A3.**Correlation between daily PET values estimated by different temperature-based methods (x-axis) of the general forms PET = f (T, RH or PR) and the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure A4.**Correlation between daily ET values estimated by different radiation-based methods (x-axis) of the general forms PET = f (Rs) and PET = f (Rs, T) with the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure A5.**Correlation between daily ET values estimated by different radiation-based methods (x-axis) of the form PET = f (Rs, T, RH) with the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure A6.**Correlation between daily ET values estimated by different combination methods (x-axis) and the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

## Appendix C

**Table A1.**Statistical indices (mean, slope a, intercept b, and coefficient of determination R

^{2}of the linear regression y = ax + b, mean bias error (MBE), root mean square error (RMSE), mean absolute error (MAE), standard deviation square (sd

^{2}), and index of agreement d) and ranking (sRPI Score and Rank) based on the optimum values of the statistical indices for the 12 mass transfer-based modes (Equations (1)–(12)) for the estimation of PET compared to the benchmark method of FAO56-PM in the two urban green sites of Heraklion and Amaroussion.

PET Method | N | Mean | a | b | MBE | RMSE | MAE | sd^{2} | d | R^{2} | sRPI | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Heraklion | ||||||||||||

FAO56-PM | 1139 | 3.266 | ||||||||||

1. Dalton 1802 | 1139 | 4.692 | 1.287 | 0.491 | 1.429 | 2.126 | 1.528 | 2.477 | 0.810 | 0.735 | 0.603 | 102 |

2. Fitzgerald 1886 | 1139 | 6.767 | 1.989 | 0.274 | 3.504 | 4.573 | 3.511 | 8.634 | 0.729 | 0.740 | 0.177 | 112 |

3. Trabert 1896 | 1139 | 3.470 | 1.091 | −0.094 | 0.207 | 1.270 | 0.882 | 1.569 | 0.974 | 0.738 | 0.825 | 47 |

4. Meyer 1926 | 1139 | 4.501 | 1.207 | 0.558 | 1.238 | 1.925 | 1.360 | 2.177 | 0.868 | 0.724 | 0.654 | 95 |

5. Rohwer 1931 | 1139 | 4.570 | 1.279 | 0.392 | 1.307 | 2.017 | 1.435 | 2.367 | 0.890 | 0.741 | 0.657 | 94 |

6. Penman 1948 | 1139 | 4.546 | 1.342 | 0.163 | 1.280 | 2.095 | 1.459 | 2.749 | 0.891 | 0.739 | 0.652 | 96 |

7. Albrecht 1950 | 1139 | 3.634 | 1.080 | 0.105 | 0.371 | 1.255 | 0.830 | 1.437 | 0.898 | 0.750 | 0.796 | 56 |

8. Br. and Wen. 1963 | 1139 | 6.054 | 1.876 | −0.073 | 2.791 | 3.865 | 2.830 | 7.174 | 0.715 | 0.745 | 0.292 | 111 |

9. WMO 1966 | 1139 | 2.594 | 0.785 | 0.025 | −0.670 | 1.212 | 0.913 | 1.002 | 0.964 | 0.729 | 0.798 | 55 |

10. Mahringer 1970 | 1139 | 3.234 | 1.015 | −0.087 | −0.029 | 1.158 | 0.834 | 1.332 | 0.919 | 0.738 | 0.827 | 46 |

11. Szász 1973 | 1139 | 4.325 | 0.964 | 1.170 | 1.062 | 1.422 | 1.155 | 0.904 | 0.897 | 0.790 | 0.726 | 74 |

12. Linacre 1992 | 1138 | 3.669 | 0.895 | 0.738 | 0.403 | 0.977 | 0.801 | 0.789 | 0.946 | 0.796 | 0.813 | 52 |

Amaroussion | ||||||||||||

FAO56-PM | 1195 | 2.969 | ||||||||||

1. Dalton 1802 | 1195 | 4.904 | 1.694 | −0.121 | 1.429 | 2.753 | 1.967 | 3.828 | 0.767 | 0.833 | 0.547 | 106 |

2. Fitzgerald 1886 | 1195 | 6.639 | 2.410 | −0.514 | 3.504 | 4.942 | 3.674 | 10.937 | 0.764 | 0.849 | 0.189 | 112 |

3. Trabert 1896 | 1195 | 3.225 | 1.259 | −0.514 | 0.207 | 1.197 | 0.786 | 1.368 | 0.981 | 0.836 | 0.817 | 56 |

4. Meyer 1926 | 1195 | 4.791 | 1.630 | −0.049 | 1.238 | 2.617 | 1.862 | 3.531 | 0.830 | 0.821 | 0.597 | 102 |

5. Rohwer 1931 | 1195 | 4.690 | 1.642 | −0.185 | 1.307 | 2.510 | 1.764 | 3.341 | 0.893 | 0.841 | 0.631 | 97 |

6. Penman 1948 | 1196 | 4.441 | 1.617 | −0.361 | 1.280 | 2.285 | 1.537 | 3.065 | 0.906 | 0.849 | 0.651 | 95 |

7. Albrecht 1950 | 1195 | 3.647 | 1.398 | −0.506 | 0.371 | 1.562 | 0.981 | 1.985 | 0.902 | 0.834 | 0.740 | 84 |

8. Br. and Wen. 1963 | 1195 | 5.716 | 2.203 | −0.828 | 2.791 | 4.003 | 2.772 | 8.492 | 0.762 | 0.844 | 0.300 | 111 |

9. WMO 1966 | 1195 | 2.465 | 0.915 | −0.259 | −0.670 | 0.923 | 0.693 | 0.592 | 0.982 | 0.844 | 0.853 | 40 |

10. Mahringer 1970 | 1195 | 3.005 | 1.171 | −0.478 | −0.029 | 1.042 | 0.726 | 1.085 | 0.943 | 0.836 | 0.826 | 50 |

11. Szász 1973 | 1195 | 4.286 | 1.301 | 0.417 | 1.062 | 1.714 | 1.349 | 1.222 | 0.893 | 0.874 | 0.732 | 86 |

12. Linacre 1992 | 1187 | 3.620 | 1.062 | 0.446 | 0.403 | 1.076 | 0.903 | 0.761 | 0.957 | 0.847 | 0.831 | 44 |

**Table A2.**Statistical indices (mean, slope a, intercept b, and coefficient of determination R

^{2}, of the linear regression y = ax + b, mean bias error (MBE), root mean square error (RMSE), mean absolute error (MAE), standard deviation square (sd

^{2}), and index of agreement d) and ranking (sRPI Score and Rank) based on the optimum values of the statistical indices for the 48 temperature-based PET models (Equations (13)–(60)) compared to the benchmark method of FAO56-PM in the two urban green sites of Heraklion and Amaroussion.

PET Method | N | Mean | a | b | MBE | RMSE | MAE | sd^{2} | D | R^{2} | sRPI | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Heraklion | ||||||||||||

FAO56-PM | 1139 | 3.266 | ||||||||||

13. Thornthwaite 1948 | 1139 | 2.652 | 0.867 | −0.187 | −0.611 | 1.015 | 0.794 | 0.631 | 0.926 | 0.829 | 0.832 | 45 |

14. Blaney and Criddle 1950 | 1139 | 4.637 | 0.637 | 2.548 | 1.374 | 1.582 | 1.400 | 0.637 | 0.789 | 0.904 | 0.585 | 104 |

15. McCloud 1955 | 1139 | 3.362 | 1.065 | −0.126 | 0.099 | 1.325 | 0.981 | 1.735 | 0.894 | 0.706 | 0.780 | 63 |

16. Hamon 1963 | 1139 | 2.988 | 0.640 | 0.887 | −0.275 | 0.919 | 0.758 | 0.746 | 0.939 | 0.845 | 0.794 | 57 |

17. Baier and Robert. 1965 | 1042 | 3.025 | 0.823 | 0.170 | −0.426 | 1.051 | 0.826 | 0.894 | 0.880 | 0.754 | 0.787 | 60 |

18. Malmstrom 1969 | 1139 | 3.406 | 0.758 | 0.918 | 0.143 | 0.805 | 0.667 | 0.616 | 0.945 | 0.839 | 0.822 | 49 |

19. Sieg. and Schrodt. 1975 | 1139 | 3.319 | 0.685 | 1.069 | 0.056 | 0.806 | 0.685 | 0.631 | 0.927 | 0.864 | 0.808 | 54 |

20. Bl. and Criddle (m. Eu.) | 1139 | 2.895 | 0.609 | 0.892 | −0.368 | 0.928 | 0.751 | 0.696 | 0.877 | 0.908 | 0.781 | 62 |

21. Smith and Stopp 1978 | 1139 | 3.067 | 0.422 | 1.674 | −0.196 | 1.245 | 1.069 | 1.487 | 0.688 | 0.707 | 0.552 | 108 |

22. Hargr. and Samani 1985 | 1139 | 2.970 | 0.663 | 0.788 | −0.293 | 1.050 | 0.776 | 0.986 | 0.807 | 0.737 | 0.706 | 81 |

23. Kharrufa 1985 | 1139 | 4.499 | 1.079 | 0.959 | 1.236 | 1.503 | 1.304 | 0.761 | 0.841 | 0.852 | 0.714 | 76 |

24. Mintz and Walker 1993 | 1139 | 3.356 | 0.677 | 1.126 | 0.093 | 0.815 | 0.697 | 0.639 | 0.955 | 0.866 | 0.814 | 50 |

25. Camargo et al. 1999 | 1139 | 2.618 | 0.695 | 0.329 | −0.645 | 1.235 | 0.972 | 1.059 | 0.829 | 0.710 | 0.707 | 80 |

26. Samani 2000 | 1139 | 3.126 | 0.683 | 0.874 | −0.137 | 0.826 | 0.658 | 0.635 | 0.926 | 0.864 | 0.814 | 51 |

27. Xu and Singh 2001 (1) | 1139 | 3.114 | 0.926 | 0.068 | −0.149 | 0.869 | 0.706 | 0.702 | 0.931 | 0.821 | 0.869 | 37 |

28. Xu and Singh 2001 (2) | 1139 | 3.171 | 0.934 | 0.100 | −0.092 | 0.877 | 0.718 | 0.731 | 0.950 | 0.816 | 0.876 | 34 |

29. Xu and Singh 2001 (3) | 1139 | 4.899 | 1.174 | 1.043 | 1.636 | 1.899 | 1.671 | 0.985 | 0.835 | 0.852 | 0.652 | 97 |

30. Xu and Singh 2001 (4) | 1139 | 3.619 | 0.807 | 0.959 | 0.356 | 1.058 | 0.881 | 0.984 | 0.946 | 0.737 | 0.767 | 66 |

31. Dr. and Allen 2002 (1) | 1139 | 3.316 | 0.723 | 0.929 | 0.053 | 0.915 | 0.735 | 0.809 | 0.927 | 0.782 | 0.787 | 59 |

32. Dr. and Allen 2002 (2) | 1139 | 3.152 | 0.707 | 0.816 | −0.111 | 1.001 | 0.770 | 0.956 | 0.898 | 0.739 | 0.757 | 68 |

33. Pereira and Pruit 2004 | 1139 | 2.474 | 0.631 | 0.385 | −0.790 | 1.340 | 1.057 | 1.096 | 0.818 | 0.707 | 0.678 | 86 |

34. Trajkovic 2005 (1) | 1139 | 2.918 | 0.763 | 0.400 | −0.345 | 0.902 | 0.725 | 0.644 | 0.921 | 0.829 | 0.822 | 48 |

35. Trajcovic 2005 (2) | 1139 | 2.761 | 0.542 | 0.964 | −0.502 | 1.209 | 0.893 | 1.148 | 0.823 | 0.737 | 0.669 | 90 |

36. Oudin 2005 | 1139 | 3.013 | 0.755 | 0.516 | −0.251 | 0.709 | 0.578 | 0.392 | 0.935 | 0.923 | 0.869 | 38 |

37. Castañ. and Rao 2005 (1) | 1139 | 3.602 | 0.800 | 0.960 | 0.339 | 0.743 | 0.610 | 0.426 | 0.943 | 0.893 | 0.841 | 43 |

38. Trajkovic 2007 | 1139 | 2.542 | 0.562 | 0.676 | −0.721 | 1.279 | 0.940 | 1.034 | 0.803 | 0.775 | 0.679 | 85 |

39. Tabari and Tal. 2011 (1) | 1139 | 4.012 | 0.894 | 1.062 | 0.748 | 1.275 | 1.098 | 1.082 | 0.847 | 0.737 | 0.701 | 83 |

40. Tabari and Tal. 2011 (2) | 1139 | 3.628 | 0.807 | 0.959 | 0.364 | 1.062 | 0.890 | 0.985 | 0.927 | 0.737 | 0.758 | 67 |

41. Ravazzani et al. 2012 | 1139 | 2.499 | 0.553 | 0.658 | −0.764 | 1.342 | 0.980 | 1.126 | 0.813 | 0.737 | 0.665 | 91 |

42. Berti et al.2014 | 1139 | 2.605 | 0.577 | 0.684 | −0.658 | 1.275 | 0.924 | 1.105 | 0.812 | 0.728 | 0.672 | 88 |

43. Heydari and Heyd. 2014 | 1139 | 2.973 | 0.716 | 0.598 | −0.290 | 1.104 | 0.817 | 1.075 | 0.873 | 0.705 | 0.736 | 71 |

44. Dorji et al. 2016 | 1139 | 2.403 | 0.478 | 0.806 | −0.860 | 1.426 | 1.073 | 1.187 | 0.761 | 0.812 | 0.639 | 99 |

45. Lobit et al. 2018 | 1139 | 2.432 | 0.517 | 0.705 | −0.832 | 1.421 | 1.043 | 1.221 | 0.744 | 0.724 | 0.617 | 101 |

46. Althoff et al. 2019 | 1139 | 2.728 | 0.616 | 0.677 | −0.535 | 1.178 | 0.857 | 1.017 | 0.837 | 0.743 | 0.704 | 82 |

47. Romanenko 1961 | 1139 | 4.550 | 1.374 | 0.024 | 1.286 | 1.918 | 1.349 | 2.088 | 0.937 | 0.814 | 0.715 | 75 |

48. Papadakis 1965 | 1139 | 4.104 | 0.872 | 1.217 | 0.841 | 1.653 | 1.216 | 2.052 | 0.906 | 0.582 | 0.635 | 100 |

49. Schendel 1967 | 1139 | 5.037 | 1.069 | 1.506 | 1.773 | 2.214 | 1.792 | 1.863 | 0.820 | 0.693 | 0.556 | 107 |

50. Antal 1968 | 1139 | 5.232 | 1.158 | 1.411 | 1.969 | 2.392 | 1.983 | 1.972 | 0.851 | 0.722 | 0.550 | 109 |

51. Linacre 1977 | 1139 | 4.634 | 0.881 | 1.715 | 1.370 | 1.650 | 1.414 | 0.919 | 0.912 | 0.766 | 0.660 | 93 |

52. Naumann 1987 | 1139 | 2.963 | 0.810 | 0.276 | −0.300 | 1.370 | 1.048 | 1.714 | 0.884 | 0.602 | 0.710 | 77 |

53. Xu and Singh 2001 (5) | 1139 | 5.056 | 1.527 | 0.027 | 1.793 | 2.461 | 1.818 | 2.959 | 0.785 | 0.814 | 0.567 | 105 |

54. Xu and Singh 2001 (6) | 1139 | 4.574 | 0.870 | 1.689 | 1.311 | 1.599 | 1.366 | 0.912 | 0.927 | 0.765 | 0.671 | 89 |

55. Xu and Singh 2001 (7) | 1139 | 5.230 | 0.987 | 1.962 | 1.967 | 2.188 | 1.969 | 1.054 | 0.820 | 0.772 | 0.563 | 106 |

56. Ahoogh. et al. 2016 (1) | 1139 | 4.550 | 0.837 | 1.769 | 1.287 | 1.376 | 1.289 | 0.314 | 0.921 | 0.922 | 0.727 | 72 |

57. Ahoogh. et al. 2016 (2) | 1139 | 4.719 | 0.801 | 2.058 | 1.455 | 1.556 | 1.458 | 0.396 | 0.863 | 0.904 | 0.660 | 92 |

58. Ahoogh. et al. 2016 (3) | 1139 | 3.609 | 0.916 | 0.569 | 0.346 | 0.717 | 0.562 | 0.379 | 0.966 | 0.897 | 0.889 | 27 |

59. Ahoogh. et al. 2016 (4) | 1139 | 4.028 | 0.951 | 0.874 | 0.765 | 0.959 | 0.800 | 0.362 | 0.939 | 0.904 | 0.838 | 44 |

60. Dr. and Allen 2002 (3) | 1132 | 2.808 | 0.691 | 0.493 | −0.465 | 1.304 | 0.971 | 1.381 | 0.867 | 0.628 | 0.689 | 84 |

Amaroussion | ||||||||||||

FAO56-PM | 1195 | 2.969 | ||||||||||

13. Thornthwaite 1948 | 1195 | 2.578 | 0.959 | −0.278 | −0.611 | 0.951 | 0.725 | 0.745 | 0.949 | 0.821 | 0.831 | 45 |

14. Blaney and Criddle 1950 | 1195 | 4.552 | 0.745 | 2.332 | 1.374 | 1.725 | 1.596 | 0.500 | 0.807 | 0.888 | 0.590 | 104 |

15. McCloud 1955 | 1195 | 3.311 | 1.251 | −0.412 | 0.099 | 1.692 | 1.158 | 2.752 | 0.878 | 0.693 | 0.680 | 90 |

16. Hamon 1963 | 1195 | 2.958 | 0.752 | 0.714 | −0.275 | 0.819 | 0.671 | 0.670 | 0.966 | 0.825 | 0.816 | 57 |

17. Baier and Robert. 1965 | 1044 | 3.432 | 0.978 | 0.235 | −0.426 | 1.029 | 0.827 | 1.033 | 0.919 | 0.766 | 0.797 | 62 |

18. Malmstrom 1969 | 1195 | 3.387 | 0.895 | 0.716 | 0.143 | 0.929 | 0.745 | 0.700 | 0.948 | 0.818 | 0.817 | 55 |

19. Sieg. and Schrodt. 1975 | 1194 | 3.148 | 0.793 | 0.779 | 0.056 | 0.783 | 0.656 | 0.587 | 0.952 | 0.845 | 0.829 | 47 |

20. Bl. and Criddle (m. Eu.) | 1195 | 2.812 | 0.711 | 0.685 | −0.368 | 0.761 | 0.611 | 0.550 | 0.939 | 0.888 | 0.830 | 46 |

21. Smith and Stopp 1978 | 1194 | 2.902 | 0.514 | 1.360 | −0.196 | 1.119 | 0.959 | 1.245 | 0.811 | 0.719 | 0.628 | 98 |

22. Hargr. and Samani 1985 | 1195 | 3.190 | 0.853 | 0.643 | −0.293 | 0.868 | 0.690 | 0.712 | 0.909 | 0.811 | 0.796 | 63 |

23. Kharrufa 1985 | 1194 | 4.329 | 1.260 | 0.570 | 1.236 | 1.785 | 1.484 | 1.387 | 0.851 | 0.836 | 0.679 | 91 |

24. Mintz and Walker 1993 | 1194 | 3.184 | 0.785 | 0.835 | 0.093 | 0.793 | 0.668 | 0.592 | 0.969 | 0.847 | 0.831 | 43 |

25. Camargo et al. 1999 | 1195 | 2.890 | 0.907 | 0.176 | −0.645 | 1.013 | 0.808 | 1.018 | 0.920 | 0.755 | 0.783 | 70 |

26. Samani 2000 | 1195 | 3.149 | 0.791 | 0.781 | −0.137 | 0.919 | 0.669 | 0.820 | 0.936 | 0.780 | 0.785 | 69 |

27. Xu and Singh 2001 (1) | 1195 | 2.974 | 1.002 | −0.022 | −0.149 | 0.921 | 0.737 | 0.849 | 0.939 | 0.815 | 0.857 | 37 |

28. Xu and Singh 2001 (2) | 1195 | 3.023 | 1.008 | 0.010 | −0.092 | 0.938 | 0.753 | 0.880 | 0.951 | 0.811 | 0.861 | 36 |

29. Xu and Singh 2001 (3) | 1194 | 4.714 | 1.371 | 0.620 | 1.636 | 2.195 | 1.832 | 1.853 | 0.828 | 0.836 | 0.613 | 100 |

30. Xu and Singh 2001 (4) | 1195 | 3.886 | 1.038 | 0.783 | 0.356 | 1.320 | 1.087 | 0.942 | 0.945 | 0.811 | 0.781 | 72 |

31. Dr. and Allen 2002 (1) | 1195 | 3.487 | 0.903 | 0.783 | 0.053 | 0.939 | 0.787 | 0.637 | 0.952 | 0.837 | 0.826 | 51 |

32. Dr. and Allen 2002 (2) | 1195 | 3.384 | 0.910 | 0.659 | −0.111 | 0.951 | 0.776 | 0.752 | 0.941 | 0.812 | 0.814 | 59 |

33. Pereira and Pruit 2004 | 1195 | 2.728 | 0.834 | 0.225 | −0.790 | 1.022 | 0.811 | 0.973 | 0.926 | 0.749 | 0.768 | 78 |

34. Trajkovic 2005 (1) | 1195 | 2.852 | 0.844 | 0.321 | −0.345 | 0.837 | 0.666 | 0.681 | 0.946 | 0.821 | 0.832 | 42 |

35. Trajcovic 2005 (2) | 1195 | 2.940 | 0.697 | 0.845 | −0.502 | 0.881 | 0.670 | 0.774 | 0.924 | 0.811 | 0.769 | 77 |

36. Oudin 2005 | 1195 | 2.878 | 0.831 | 0.382 | −0.251 | 0.642 | 0.501 | 0.399 | 0.957 | 0.904 | 0.885 | 27 |

37. Castañ. and Rao 2005 (1) | 1195 | 3.581 | 0.877 | 0.949 | 0.339 | 0.888 | 0.743 | 0.448 | 0.934 | 0.885 | 0.822 | 53 |

38. Trajkovic 2007 | 1195 | 2.685 | 0.706 | 0.559 | −0.721 | 0.899 | 0.634 | 0.710 | 0.923 | 0.832 | 0.788 | 66 |

39. Tabari and Tal. 2011 (1) | 1195 | 4.308 | 1.149 | 0.866 | 0.748 | 1.715 | 1.423 | 1.231 | 0.822 | 0.811 | 0.673 | 92 |

40. Tabari and Tal. 2011 (2) | 1195 | 3.895 | 1.038 | 0.783 | 0.364 | 1.323 | 1.096 | 0.951 | 0.933 | 0.811 | 0.776 | 74 |

41. Ravazzani et al. 2012 | 1195 | 2.758 | 0.732 | 0.552 | −0.764 | 0.898 | 0.640 | 0.748 | 0.945 | 0.811 | 0.789 | 65 |

42. Berti et al.2014 | 1195 | 2.805 | 0.746 | 0.557 | −0.658 | 0.890 | 0.642 | 0.755 | 0.921 | 0.806 | 0.781 | 71 |

43. Heydari and Heyd. 2014 | 1195 | 3.261 | 0.949 | 0.410 | −0.290 | 0.994 | 0.776 | 0.922 | 0.925 | 0.788 | 0.805 | 60 |

44. Dorji et al. 2016 | 1195 | 2.475 | 0.578 | 0.724 | −0.860 | 1.081 | 0.785 | 0.889 | 0.889 | 0.854 | 0.744 | 83 |

45. Lobit et al. 2018 | 1195 | 2.611 | 0.666 | 0.598 | −0.832 | 0.993 | 0.696 | 0.832 | 0.871 | 0.805 | 0.738 | 85 |

46. Althoff et al. 2019 | 1195 | 2.926 | 0.792 | 0.537 | −0.535 | 0.850 | 0.636 | 0.718 | 0.926 | 0.813 | 0.798 | 61 |

47. Romanenko 1961 | 1195 | 4.883 | 1.933 | −0.891 | 1.286 | 2.904 | 1.977 | 4.911 | 0.914 | 0.887 | 0.559 | 105 |

48. Papadakis 1965 | 1195 | 4.711 | 1.321 | 0.753 | 0.841 | 2.424 | 1.821 | 2.971 | 0.900 | 0.712 | 0.600 | 101 |

49. Schendel 1967 | 1194 | 5.263 | 1.604 | 0.460 | 1.773 | 2.946 | 2.319 | 3.601 | 0.843 | 0.806 | 0.531 | 107 |

50. Antal 1968 | 1195 | 5.566 | 1.597 | 0.786 | 1.969 | 3.197 | 2.604 | 3.679 | 0.852 | 0.797 | 0.489 | 109 |

51. Linacre 1977 | 1195 | 4.859 | 1.217 | 1.206 | 1.370 | 2.169 | 1.899 | 1.281 | 0.914 | 0.834 | 0.646 | 96 |

52. Naumann 1987 | 1195 | 3.877 | 1.418 | −0.376 | −0.300 | 1.882 | 1.238 | 2.793 | 0.908 | 0.775 | 0.699 | 88 |

53. Xu and Singh 2001 (5) | 1195 | 5.426 | 2.147 | −0.990 | 1.793 | 3.573 | 2.492 | 6.936 | 0.802 | 0.887 | 0.407 | 110 |

54. Xu and Singh 2001 (6) | 1195 | 4.798 | 1.203 | 1.184 | 1.311 | 2.104 | 1.839 | 1.237 | 0.931 | 0.834 | 0.662 | 94 |

55. Xu and Singh 2001 (7) | 1195 | 5.470 | 1.351 | 1.418 | 1.967 | 2.806 | 2.506 | 1.834 | 0.830 | 0.831 | 0.518 | 108 |

56. Ahoogh. et al. 2016 (1) | 1195 | 4.542 | 1.059 | 1.353 | 1.287 | 1.624 | 1.575 | 0.302 | 0.933 | 0.944 | 0.746 | 82 |

57. Ahoogh. et al. 2016 (2) | 1195 | 4.749 | 1.004 | 1.724 | 1.455 | 1.826 | 1.782 | 0.328 | 0.877 | 0.929 | 0.682 | 89 |

58. Ahoogh. et al. 2016 (3) | 1195 | 3.607 | 1.118 | 0.240 | 0.346 | 0.917 | 0.719 | 0.493 | 0.964 | 0.920 | 0.887 | 26 |

59. Ahoogh. et al. 2016 (4) | 1195 | 4.068 | 1.196 | 0.472 | 0.765 | 1.299 | 1.106 | 0.581 | 0.929 | 0.930 | 0.815 | 58 |

60. Dr. and Allen 2002 (3) | 1194 | 3.213 | 0.913 | 0.452 | −0.465 | 1.096 | 0.863 | 1.166 | 0.941 | 0.735 | 0.770 | 76 |

**Table A3.**Statistical indices (mean, slope a, intercept b, and coefficient of determination R

^{2}, of the linear regression y = ax + b, mean bias error (MBE), root mean square error (RMSE), mean absolute error (MAE), standard deviation square (sd

^{2}), and index of agreement d) and ranking (sRPI Score and Rank) based on the optimum values of the statistical indices for the 40 radiation-based models (Equations (61)–(100)) for the estimation of PET compared to the benchmark method of FAO56-PM in the two urban green sites of Heraklion and Amaroussion.

PET Method | N | Mean | a | b | MBE | RMSE | MAE | sd^{2} | D | R^{2} | sRPI | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Heraklion | ||||||||||||

FAO56-PM | 1139 | 3.266 | ||||||||||

61. Christiansen 1968 | 1139 | 2.657 | 0.668 | 0.423 | −0.607 | 1.094 | 0.880 | 0.711 | 0.884 | 0.841 | 0.775 | 64 |

62. Abtew 1996 (1) | 1139 | 3.570 | 0.903 | 0.571 | 0.307 | 0.845 | 0.706 | 0.598 | 0.935 | 0.841 | 0.846 | 42 |

63. Makkink 1957 | 1138 | 2.806 | 0.849 | −0.021 | −0.460 | 0.835 | 0.673 | 0.380 | 0.944 | 0.899 | 0.886 | 29 |

64. Stephens and Stewart 1963 | 1139 | 2.659 | 0.898 | −0.329 | −0.605 | 0.877 | 0.742 | 0.279 | 0.943 | 0.925 | 0.878 | 33 |

65. Jensen and Haise 1963 | 1139 | 4.219 | 1.471 | −0.640 | 0.956 | 1.519 | 1.260 | 1.444 | 0.897 | 0.926 | 0.727 | 73 |

66. Stephens 1965 | 1135 | 4.181 | 1.670 | −1.342 | 0.909 | 1.826 | 1.428 | 2.556 | 0.921 | 0.917 | 0.644 | 98 |

67. McGuinness and Bordne 1972 | 1139 | 2.659 | 0.898 | −0.329 | −0.604 | 0.880 | 0.747 | 0.279 | 0.950 | 0.925 | 0.880 | 31 |

68. Ritchie 1972 | 1139 | 3.671 | 1.084 | 0.076 | 0.408 | 0.820 | 0.716 | 0.494 | 0.958 | 0.902 | 0.898 | 24 |

69. Caprio 1974 | 1139 | 4.053 | 1.450 | −0.740 | 0.790 | 1.395 | 1.149 | 1.356 | 0.927 | 0.926 | 0.753 | 70 |

70. Hargreaves 1975 | 1139 | 3.641 | 1.137 | −0.129 | 0.378 | 0.812 | 0.716 | 0.501 | 0.976 | 0.916 | 0.902 | 22 |

71. Hansen 1984 | 1139 | 3.353 | 0.974 | 0.112 | 0.090 | 0.672 | 0.554 | 0.393 | 0.975 | 0.899 | 0.934 | 12 |

72. de Bruin 1987 | 1139 | 3.119 | 0.905 | 0.104 | −0.144 | 0.687 | 0.546 | 0.370 | 0.976 | 0.899 | 0.924 | 14 |

73. Wendling 1991–1995 | 1139 | 3.466 | 0.975 | 0.220 | 0.203 | 0.692 | 0.582 | 0.399 | 0.967 | 0.898 | 0.919 | 17 |

74. Abtew 1996 (2) | 1139 | 3.380 | 0.876 | 0.457 | 0.117 | 0.705 | 0.590 | 0.434 | 0.965 | 0.882 | 0.891 | 26 |

75. Abtew 1996 (3) | 1139 | 3.165 | 1.065 | −0.376 | −0.099 | 0.747 | 0.606 | 0.469 | 0.967 | 0.902 | 0.907 | 19 |

76. Irmak et al. 2003 (1) | 1138 | 3.433 | 0.836 | 0.639 | 0.168 | 0.688 | 0.586 | 0.401 | 0.965 | 0.895 | 0.880 | 32 |

77. Irmak et al. 2003 (2) | 1047 | 4.846 | 1.467 | −0.292 | 1.395 | 1.851 | 1.641 | 1.612 | 0.854 | 0.900 | 0.676 | 87 |

78. Irmak et al. 2003 (3) | 1123 | 4.899 | 1.444 | 0.071 | 1.603 | 1.945 | 1.730 | 1.366 | 0.910 | 0.921 | 0.709 | 78 |

79. Castañeda and Rao 2005 (2) | 1138 | 3.243 | 0.974 | −0.007 | −0.022 | 0.683 | 0.553 | 0.394 | 0.979 | 0.899 | 0.943 | 8 |

80. Valiantzas 2013 (1) | 1137 | 3.448 | 1.009 | 0.082 | 0.182 | 0.734 | 0.634 | 0.460 | 0.966 | 0.891 | 0.922 | 15 |

81. Tabari et al. 2013 (1) | 1133 | 3.002 | 0.823 | 0.234 | −0.275 | 0.821 | 0.677 | 0.488 | 0.951 | 0.869 | 0.872 | 35 |

82. Tabari et al. 2013 (2) | 1134 | 3.021 | 0.804 | 0.317 | −0.252 | 0.747 | 0.602 | 0.386 | 0.951 | 0.907 | 0.884 | 30 |

83. Ahooghalaan. et al. 2017 (1) | 1137 | 3.576 | 0.917 | 0.508 | 0.311 | 0.854 | 0.755 | 0.605 | 0.941 | 0.842 | 0.851 | 41 |

84. Turc 1961 | 1139 | 3.517 | 0.986 | 0.225 | 0.253 | 0.668 | 0.569 | 0.346 | 0.971 | 0.913 | 0.926 | 13 |

85. Priestley and Taylor 1972 | 1139 | 3.249 | 1.058 | −0.279 | −0.014 | 0.639 | 0.499 | 0.332 | 0.986 | 0.929 | 0.941 | 9 |

86. Abtew 1996 (4) | 1139 | 3.048 | 0.991 | −0.261 | −0.215 | 0.660 | 0.486 | 0.281 | 0.969 | 0.929 | 0.935 | 11 |

87. Xu and Singh 2000 | 839 | 2.262 | 0.799 | −1.012 | −1.705 | 1.923 | 1.912 | 0.331 | 0.691 | 0.905 | 0.603 | 103 |

88. Irmak et al. 2003 (4) | 1139 | 3.556 | 0.807 | 0.845 | 0.292 | 0.700 | 0.612 | 0.373 | 0.955 | 0.911 | 0.862 | 39 |

89. Irmak et al. 2003 (5) | 1139 | 4.581 | 1.374 | 0.018 | 1.318 | 1.630 | 1.407 | 1.047 | 0.932 | 0.928 | 0.769 | 65 |

90. Irmak et al. 2003 (6) | 1139 | 4.655 | 1.371 | 0.100 | 1.391 | 1.682 | 1.465 | 1.033 | 0.922 | 0.929 | 0.755 | 69 |

91. Berengena and Gavilán 2005 | 1139 | 4.237 | 1.386 | −0.365 | 0.974 | 1.400 | 1.165 | 1.086 | 0.944 | 0.929 | 0.783 | 61 |

92. Copais | 1139 | 3.755 | 1.140 | −0.046 | 0.492 | 0.883 | 0.757 | 0.537 | 0.958 | 0.912 | 0.888 | 28 |

93. Valiantzas 2006 (1) | 1139 | 3.809 | 1.079 | 0.207 | 0.546 | 0.714 | 0.630 | 0.219 | 0.974 | 0.957 | 0.921 | 16 |

94. Tabari and Talaee 2011 (3) | 1139 | 5.474 | 1.797 | −0.474 | 2.211 | 2.799 | 2.276 | 3.226 | 0.775 | 0.929 | 0.495 | 110 |

95. Tabari and Talaee 2011 (4) | 1139 | 4.669 | 1.529 | −0.403 | 1.405 | 1.872 | 1.536 | 1.679 | 0.937 | 0.929 | 0.708 | 79 |

96. Valiantzas 2013 (2) | 1139 | 3.851 | 1.117 | 0.123 | 0.588 | 0.828 | 0.741 | 0.354 | 0.965 | 0.938 | 0.900 | 23 |

97. Valiantzas 2013 (3) | 1139 | 3.893 | 1.165 | 0.006 | 0.630 | 0.845 | 0.720 | 0.339 | 0.966 | 0.955 | 0.904 | 20 |

98. Milly and Dunne 2016 | 1139 | 2.969 | 0.850 | 0.109 | −0.294 | 0.787 | 0.610 | 0.397 | 0.974 | 0.895 | 0.903 | 21 |

99. Ahooghalaan. et al. 2017 (2) | 1139 | 3.518 | 0.977 | 0.243 | 0.255 | 0.534 | 0.416 | 0.178 | 0.984 | 0.954 | 0.955 | 4 |

100. Ahooghalaan. et al. 2017 (3) | 1139 | 3.552 | 0.980 | 0.266 | 0.289 | 0.598 | 0.493 | 0.237 | 0.976 | 0.939 | 0.939 | 10 |

Amaroussion | ||||||||||||

FAO56-PM | 1195 | 2.969 | ||||||||||

61. Christiansen 1968 | 1195 | 2.650 | 0.608 | 0.795 | −0.607 | 0.976 | 0.784 | 0.819 | 0.907 | 0.864 | 0.768 | 79 |

62. Abtew 1996 (1) | 1195 | 3.562 | 0.822 | 1.073 | 0.307 | 0.920 | 0.779 | 0.553 | 0.903 | 0.864 | 0.786 | 68 |

63. Makkink 1957 | 1193 | 2.760 | 0.807 | 0.311 | −0.460 | 0.650 | 0.530 | 0.356 | 0.959 | 0.934 | 0.892 | 25 |

64. Stephens and Stewart 1963 | 1195 | 2.566 | 0.883 | −0.106 | −0.605 | 0.688 | 0.574 | 0.270 | 0.959 | 0.945 | 0.907 | 20 |

65. Jensen and Haise 1963 | 1195 | 4.063 | 1.452 | −0.301 | 0.956 | 1.531 | 1.218 | 1.262 | 0.891 | 0.943 | 0.766 | 80 |

66. Stephens 1965 | 1155 | 4.073 | 1.681 | −1.087 | 0.909 | 1.909 | 1.428 | 2.685 | 0.915 | 0.914 | 0.669 | 93 |

67. McGuinness and Bordne 1972 | 1195 | 2.567 | 0.882 | −0.106 | −0.604 | 0.692 | 0.579 | 0.273 | 0.966 | 0.945 | 0.910 | 18 |

68. Ritchie 1972 | 1195 | 3.691 | 1.037 | 0.558 | 0.408 | 1.062 | 0.810 | 0.685 | 0.925 | 0.863 | 0.825 | 52 |

69. Caprio 1974 | 1195 | 3.886 | 1.439 | −0.443 | 0.790 | 1.410 | 1.103 | 1.248 | 0.925 | 0.939 | 0.786 | 67 |

70. Hargreaves 1975 | 1195 | 3.553 | 1.096 | 0.244 | 0.378 | 0.787 | 0.694 | 0.343 | 0.977 | 0.946 | 0.910 | 17 |

71. Hansen 1984 | 1195 | 3.299 | 0.927 | 0.491 | 0.090 | 0.609 | 0.522 | 0.301 | 0.977 | 0.934 | 0.916 | 12 |

72. de Bruin 1987 | 1195 | 3.068 | 0.860 | 0.456 | −0.144 | 0.566 | 0.469 | 0.323 | 0.984 | 0.934 | 0.916 | 13 |

73. Wendling 1991–1995 | 1195 | 3.429 | 0.926 | 0.621 | 0.203 | 0.681 | 0.591 | 0.307 | 0.963 | 0.933 | 0.894 | 24 |

74. Abtew 1996 (2) | 1195 | 3.357 | 0.851 | 0.771 | 0.117 | 0.714 | 0.610 | 0.406 | 0.961 | 0.910 | 0.869 | 32 |

75. Abtew 1996 (3) | 1195 | 3.201 | 1.098 | −0.121 | −0.099 | 0.733 | 0.608 | 0.511 | 0.967 | 0.914 | 0.911 | 16 |

76. Irmak et al. 2003 (1) | 1192 | 3.352 | 0.822 | 0.846 | 0.168 | 0.690 | 0.595 | 0.380 | 0.959 | 0.925 | 0.867 | 33 |

77. Irmak et al. 2003 (2) | 1103 | 4.661 | 1.442 | 0.055 | 1.395 | 1.832 | 1.633 | 1.269 | 0.852 | 0.935 | 0.720 | 87 |

78. Irmak et al. 2003 (3) | 1180 | 4.507 | 1.370 | 0.339 | 1.603 | 1.707 | 1.555 | 0.825 | 0.925 | 0.963 | 0.758 | 81 |

79. Castañeda and Rao 2005 (2) | 1194 | 3.188 | 0.926 | 0.373 | −0.022 | 0.572 | 0.486 | 0.308 | 0.984 | 0.934 | 0.930 | 10 |

80. Valiantzas 2013 (1) | 1185 | 3.419 | 1.002 | 0.361 | 0.182 | 0.727 | 0.634 | 0.399 | 0.964 | 0.917 | 0.905 | 21 |

81. Tabari et al. 2013 (1) | 1183 | 2.974 | 0.772 | 0.599 | −0.275 | 0.702 | 0.590 | 0.490 | 0.961 | 0.903 | 0.863 | 35 |

82. Tabari et al. 2013 (2) | 1190 | 2.898 | 0.764 | 0.556 | −0.252 | 0.644 | 0.531 | 0.398 | 0.956 | 0.945 | 0.885 | 28 |

83. Ahooghalaan. et al. 2017 (1) | 1186 | 3.606 | 0.967 | 0.651 | 0.311 | 0.950 | 0.836 | 0.601 | 0.926 | 0.866 | 0.828 | 48 |

84. Turc 1961 | 1194 | 3.497 | 1.042 | 0.332 | 0.253 | 0.734 | 0.629 | 0.334 | 0.969 | 0.940 | 0.912 | 15 |

85. Priestley and Taylor 1972 | 1195 | 3.027 | 1.018 | −0.065 | −0.014 | 0.486 | 0.375 | 0.241 | 0.992 | 0.958 | 0.972 | 2 |

86. Abtew 1996 (4) | 1195 | 2.841 | 0.954 | −0.061 | −0.215 | 0.513 | 0.374 | 0.229 | 0.979 | 0.958 | 0.956 | 6 |

87. Xu and Singh 2000 | 861 | 2.116 | 0.767 | −0.865 | −1.705 | 1.843 | 1.840 | 0.379 | 0.702 | 0.932 | 0.621 | 99 |

88. Irmak et al. 2003 (4) | 1195 | 3.368 | 0.779 | 0.983 | 0.292 | 0.701 | 0.640 | 0.390 | 0.952 | 0.942 | 0.854 | 39 |

89. Irmak et al. 2003 (5) | 1193 | 4.244 | 1.366 | 0.110 | 1.318 | 1.531 | 1.325 | 0.912 | 0.933 | 0.951 | 0.793 | 64 |

90. Irmak et al. 2003 (6) | 1193 | 4.330 | 1.362 | 0.208 | 1.391 | 1.595 | 1.399 | 0.902 | 0.926 | 0.951 | 0.777 | 73 |

91. Berengena and Gavilán 2005 | 1195 | 3.947 | 1.333 | −0.085 | 0.974 | 1.256 | 1.035 | 0.765 | 0.951 | 0.958 | 0.839 | 41 |

92. Copais | 1195 | 3.859 | 1.205 | 0.206 | 0.492 | 1.128 | 0.975 | 0.614 | 0.940 | 0.933 | 0.854 | 38 |

93. Valiantzas 2006 (1) | 1195 | 3.728 | 1.188 | 0.125 | 0.546 | 0.908 | 0.778 | 0.363 | 0.966 | 0.971 | 0.901 | 23 |

94. Tabari and Talaee 2011 (3) | 1195 | 5.100 | 1.729 | −0.110 | 2.211 | 2.588 | 2.144 | 2.483 | 0.788 | 0.958 | 0.591 | 103 |

95. Tabari and Talaee 2011 (4) | 1195 | 4.350 | 1.471 | −0.093 | 1.405 | 1.710 | 1.413 | 1.230 | 0.942 | 0.958 | 0.775 | 75 |

96. Valiantzas 2013 (2) | 1194 | 3.815 | 1.186 | 0.213 | 0.588 | 1.027 | 0.903 | 0.473 | 0.955 | 0.951 | 0.873 | 31 |

97. Valiantzas 2013 (3) | 1195 | 3.852 | 1.287 | −0.048 | 0.630 | 1.108 | 0.913 | 0.586 | 0.952 | 0.968 | 0.873 | 30 |

98. Milly and Dunne 2016 | 1195 | 2.783 | 0.804 | 0.316 | −0.294 | 0.687 | 0.506 | 0.408 | 0.977 | 0.928 | 0.902 | 22 |

99. Ahooghalaan. et al. 2017 (2) | 1195 | 3.474 | 1.158 | −0.045 | 0.255 | 0.731 | 0.562 | 0.361 | 0.978 | 0.964 | 0.933 | 9 |

100. Ahooghalaan. et al. 2017 (3) | 1194 | 3.548 | 1.102 | 0.192 | 0.289 | 0.785 | 0.663 | 0.377 | 0.970 | 0.946 | 0.913 | 14 |

**Table A4.**Statistical indices (mean, slope a, intercept b, and coefficient of determination R

^{2}, of the linear regression y = ax + b, mean bias error (MBE), root mean square error (RMSE), mean absolute error (MAE), standard deviation square (sd

^{2}), and index of agreement d) and ranking (sRPI Score and Rank) based on the optimum values of the statistical indices for the 12 combination models (Equations (101)–(112)) for the estimation of PET compared to the benchmark method of FAO56-PM in the two urban green sites of Heraklion and Amaroussion.

PET Method | N | Mean | a | b | MBE | RMSE | MAE | sd^{2} | D | R^{2} | sRPI | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Heraklion | ||||||||||||

FAO56-PM | 1139 | 3.266 | ||||||||||

101. Penman 1963 | 1139 | 3.959 | 1.112 | 0.240 | 0.695 | 0.727 | 0.695 | 0.079 | 0.969 | 0.994 | 0.918 | 18 |

102. Kimberly Penman 1972 | 1139 | 4.233 | 1.205 | 0.212 | 0.970 | 1.025 | 0.970 | 0.192 | 0.952 | 0.994 | 0.869 | 36 |

103. mod. Makkink (Door. and Pruitt 1977) | 1127 | 3.932 | 1.327 | −0.524 | 0.642 | 1.120 | 0.988 | 0.868 | 0.941 | 0.931 | 0.813 | 53 |

104. FAO24 Penman | 1139 | 4.298 | 1.201 | 0.288 | 1.035 | 1.073 | 1.035 | 0.178 | 0.953 | 0.996 | 0.861 | 40 |

105. FAO24 Radiation | 1127 | 4.094 | 1.370 | −0.507 | 0.804 | 1.260 | 1.119 | 0.997 | 0.942 | 0.932 | 0.792 | 58 |

106. Jensen et al. 1990 | 1139 | 3.629 | 1.104 | −0.067 | 0.365 | 0.524 | 0.377 | 0.116 | 0.989 | 0.985 | 0.963 | 3 |

107. Linacre 1993 | 1095 | 3.636 | 1.219 | −0.558 | 0.276 | 0.704 | 0.641 | 0.375 | 0.975 | 0.964 | 0.896 | 25 |

108. Wright 1996 | 1139 | 3.239 | 1.005 | −0.134 | −0.024 | 0.446 | 0.315 | 0.099 | 0.989 | 0.976 | 0.987 | 1 |

109. Valiantzas 2006 (2) | 1139 | 3.615 | 1.081 | −0.008 | 0.352 | 0.479 | 0.411 | 0.078 | 0.986 | 0.990 | 0.970 | 2 |

110. Valiantzas 2013 (4) | 1138 | 3.590 | 1.120 | −0.164 | 0.324 | 0.553 | 0.499 | 0.167 | 0.983 | 0.977 | 0.947 | 6 |

111. Valiantzas 2013 (5) | 1139 | 3.612 | 1.156 | −0.257 | 0.349 | 0.548 | 0.446 | 0.149 | 0.985 | 0.990 | 0.943 | 7 |

112. Valiantzas 2013 (6) | 1136 | 3.251 | 1.016 | −0.170 | −0.017 | 0.604 | 0.488 | 0.263 | 0.979 | 0.937 | 0.954 | 5 |

Amaroussion | ||||||||||||

FAO56-PM | 1195 | 2.969 | ||||||||||

101. Penman 1963 | 1195 | 3.722 | 1.140 | 0.255 | 0.695 | 0.802 | 0.755 | 0.200 | 0.968 | 0.992 | 0.908 | 19 |

102. Kimberly Penman 1972 | 1195 | 3.868 | 1.212 | 0.187 | 0.970 | 0.965 | 0.901 | 0.272 | 0.958 | 0.997 | 0.883 | 29 |

103. mod. Makkink (Door. and Pruitt 1977) | 1181 | 3.951 | 1.349 | −0.176 | 0.642 | 1.266 | 1.092 | 0.854 | 0.924 | 0.953 | 0.828 | 49 |

104. FAO24 Penman | 1195 | 3.982 | 1.225 | 0.260 | 1.035 | 1.075 | 1.015 | 0.300 | 0.953 | 0.996 | 0.865 | 34 |

105. FAO24 Radiation | 1183 | 4.076 | 1.375 | −0.126 | 0.804 | 1.381 | 1.204 | 0.922 | 0.934 | 0.955 | 0.819 | 54 |

106. Jensen et al. 1990 | 1195 | 3.336 | 1.093 | 0.003 | 0.365 | 0.529 | 0.370 | 0.209 | 0.988 | 0.982 | 0.963 | 3 |

107. Linacre 1993 | 1152 | 3.436 | 1.155 | −0.181 | 0.276 | 0.668 | 0.608 | 0.369 | 0.976 | 0.963 | 0.924 | 11 |

108. Wright 1996 | 1195 | 2.998 | 0.984 | −0.010 | −0.024 | 0.393 | 0.264 | 0.159 | 0.991 | 0.983 | 0.992 | 1 |

109. Valiantzas 2006 (2) | 1195 | 3.391 | 1.114 | −0.006 | 0.352 | 0.528 | 0.443 | 0.176 | 0.983 | 0.993 | 0.962 | 5 |

110. Valiantzas 2013 (4) | 1194 | 3.361 | 1.099 | 0.007 | 0.324 | 0.570 | 0.513 | 0.244 | 0.982 | 0.976 | 0.952 | 7 |

111. Valiantzas 2013 (5) | 1195 | 3.338 | 1.165 | −0.213 | 0.349 | 0.546 | 0.429 | 0.229 | 0.984 | 0.994 | 0.947 | 8 |

112. Valiantzas 2013 (6) | 1185 | 3.098 | 0.969 | 0.110 | −0.017 | 0.502 | 0.422 | 0.260 | 0.985 | 0.957 | 0.962 | 4 |

PET Method | Category | Form | sRPI | Rank |
---|---|---|---|---|

108. Wright 1996 | Combination | PET = f (Rs, u, T, RH) | 0.990 | 1 |

109. Valiantzas 2006 (2) | Combination | PET = f (Rs, u, T, RH) | 0.966 | 2 |

106. Jensen et al. 1990 | Combination | PET = f (Rs, u, T, RH) | 0.963 | 3 |

122. Model 10 | Radiation-based | PET = f (Rs, T, RH) | 0.959 | 4 |

112. Valiantzas 2013 (6) | Combination | PET = f (Rs, u, T) | 0.958 | 5 |

120. Model 8 | Radiation-based | PET =f (Rs, T, RH) | 0.957 | 6 |

85. Priestley and Taylor 1972 | Radiation-based | PET = f (Rs, T, RH) | 0.957 | 7 |

125. Model 13 | Radiation-based | PET = f (Rs, T) | 0.957 | 8 |

123. Model 11 | Radiation-based | PET = f (Rs, T) | 0.952 | 9 |

126. Model 14 | Radiation-based | PET = f (Rs, T, RH) | 0.951 | 10 |

110. Valiantzas 2013 (4) | Combination | PET = f (Rs, u, T, RH) | 0.950 | 11 |

86. Abtew 1996 (4) | Radiation-based | PET = f (Rs, T, RH) | 0.945 | 12 |

111. Valiantzas 2013 (5) | Combination | PET = f (Rs, u, T, RH) | 0.945 | 13 |

99. Ahooghalaandari et al. 2017 (2) | Radiation-based | PET = f (Rs, T, RH) | 0.944 | 14 |

79. Castañeda and Rao 2005 (2) | Radiation-based | PET = f (Rs, T) | 0.936 | 15 |

121. Model 9 | Radiation-based | PET = f (Rs, T) | 0.931 | 16 |

100. Ahooghalaandari et al. 2017 (3) | Radiation-based | PET = f (Rs, T, RH) | 0.926 | 17 |

124. Model 12 | Radiation-based | PET = f (Rs, T) | 0.925 | 18 |

71. Hansen 1984 | Radiation-based | PET = f (Rs, T) | 0.925 | 19 |

72. de Bruin 1987 | Radiation-based | PET = f (Rs, T) | 0.920 | 20 |

84. Turc 1961 | Radiation-based | PET = f (Rs, T, RH) | 0.919 | 21 |

116. Model 4 | Temperature-based | PET = f (T) | 0.915 | 22 |

80. Valiantzas 2013 (1) | Radiation-based | PET = f (Rs, T) | 0.913 | 23 |

101. Penman 1963 | Combination | PET = f (Rs, u, T, RH) | 0.913 | 24 |

93. Valiantzas 2006 (1) | Radiation-based | PET = f (Rs, T, RH) | 0.911 | 25 |

107. Linacre 1993 | Combination | PET = f (Rs, u, T, RH) | 0.910 | 26 |

75. Abtew 1996 (3) | Radiation-based | PET = f (Rs, T) | 0.909 | 27 |

73. Wendling 1991–1995 | Radiation-based | PET = f (Rs, T) | 0.906 | 28 |

70. Hargreaves 1975 | Radiation-based | PET = f (Rs, T) | 0.906 | 29 |

98. Milly and Dunne 2016 | Radiation-based | PET = f (Rs, T, RH) | 0.902 | 30 |

67. McGuinness and Bordne 1972 | Radiation-based | PET = f (Rs, T) | 0.895 | 31 |

64. Stephens and Stewart 1963 | Radiation-based | PET = f (Rs, T) | 0.892 | 32 |

63. Makkink 1957 | Radiation-based | PET = f (Rs, T) | 0.889 | 33 |

97. Valiantzas 2013 (3) | Radiation-based | PET = f (Rs, T, RH) | 0.888 | 34 |

58. Ahooghalaandari et al. 2016 (3) | Temperature-based | PET = f (T, RH) | 0.888 | 35 |

96. Valiantzas 2013 (2) | Radiation-based | PET = f (Rs, T, RH) | 0.886 | 36 |

82. Tabari et al. 2013 (2) | Radiation-based | PET = f (Rs, T) | 0.884 | 37 |

74. Abtew 1996 (2) | Radiation-based | PET = f (Rs, T) | 0.880 | 38 |

36. Oudin 2005 | Temperature-based | PET = f (T) | 0.877 | 39 |

102. Kimberly Penman 1972 | Combination | PET = f (Rs, u, T, RH) | 0.876 | 40 |

76. Irmak et al. 2003 (1) | Radiation-based | PET = f (Rs, T) | 0.874 | 41 |

92. Copais | Radiation-based | PET = f (Rs, T, RH) | 0.871 | 42 |

28. Xu and Singh 2001 (2) | Temperature-based | PET = f (T) | 0.869 | 43 |

81. Tabari et al. 2013 (1) | Radiation-based | PET = f (Rs, T) | 0.867 | 44 |

104. FAO24 Penman | Combination | PET = f (Rs, u, T, RH) | 0.863 | 45 |

27. Xu and Singh 2001 (1) | Temperature-based | PET = f (T) | 0.863 | 46 |

68. Ritchie 1972 | Radiation-based | PET = f (Rs, T) | 0.861 | 47 |

118. Model 6 | Temperature-based | PET = f (T,RH) | 0.860 | 48 |

88. Irmak et al. 2003 (4) | Radiation-based | PET = f (Rs, T, RH) | 0.858 | 49 |

83. Ahooghalaandari et al. 2017 (1) | Radiation-based | PET = f (Rs, T) | 0.839 | 50 |

114. Model 2 | Mass transfer-based | PET = f (u,T,RH) | 0.839 | 51 |

113. Model 1 | Mass transfer-based | PET = f (u,T,RH) | 0.835 | 52 |

119. Model 7 | Radiation-based | PET = f (Rs) | 0.835 | 53 |

13. Thornthwaite 1948 | Temperature-based | PET = f (T) | 0.831 | 54 |

37. Castañeda and Rao 2005 (1) | Temperature-based | PET = f (T) | 0.831 | 55 |

34. Trajkovic 2005 (1) | Temperature-based | PET = f (T) | 0.827 | 56 |

10. Mahringer 1970 | Mass transfer-based | PET = f (u, T, RH) | 0.827 | 57 |

59. Ahooghalaandari et al. 2016 (4) | Temperature-based | PET = f (T, RH) | 0.826 | 58 |

9. WMO 1966 | Mass transfer-based | PET = f (u, T, RH) | 0.826 | 59 |

24. Mintz and Walker 1993 | Temperature-based | PET = f (T) | 0.823 | 60 |

12. Linacre 1992 | Mass transfer-based | PET = f (u, T, RH) | 0.822 | 61 |

3. Trabert 1896 | Mass transfer-based | PET = f (u, T, RH) | 0.821 | 62 |

103. mod. Makkink (Doorenbos and Pruitt 1977) | Combination | PET = f (Rs, u, T, RH) | 0.820 | 63 |

18. Malmstrom 1969 | Temperature-based | PET = f (T) | 0.820 | 64 |

19. Siegert and Schrodter 1975 | Temperature-based | PET = f (T) | 0.818 | 65 |

62. Abtew 1996 (1) | Radiation-based | PET = f (Rs) | 0.816 | 66 |

91. Berengena and Gavilán 2005 | Radiation-based | PET = f (Rs, T, RH) | 0.811 | 67 |

31. Droogers and Allen 2002 (1) | Temperature-based | PET = f (T) | 0.806 | 68 |

105. FAO24 Radiation | Combination | PET = f (Rs, u, T, RH) | 0.806 | 69 |

20. Blaney and Criddle (Mid. Europ. Ver.) | Temperature-based | PET = f (T) | 0.805 | 70 |

16. Hamon 1963 | Temperature-based | PET = f (T) | 0.805 | 71 |

26. Samani 2000 | Temperature-based | PET = f (T) | 0.800 | 72 |

17. Baier and Robertson 1965 | Temperature-based | PET = f (T) | 0.792 | 73 |

32. Droogers and Allen 2002 (2) | Temperature-based | PET = f (T) | 0.786 | 74 |

89. Irmak et al. 2003 (5) | Radiation-based | PET = f (Rs, T, RH) | 0.781 | 75 |

30. Xu and Singh 2001 (4) | Temperature-based | PET = f (T) | 0.774 | 76 |

61. Christiansen 1968 | Radiation-based | PET = f (Rs) | 0.772 | 77 |

43. Heydari and Heydari 2014 | Temperature-based | PET = f (T) | 0.770 | 78 |

69. Caprio 1974 | Radiation-based | PET = f (Rs, T) | 0.769 | 79 |

115. Model 3 | Temperature-based | PET =f (T) | 0.769 | 80 |

127. Model 15 | Radiation-based | PET = f (T, RH) | 0.769 | 81 |

117. Model 5 | Temperature-based | PET = f (T,RH) | 0.768 | 82 |

7. Albrecht 1950 | Mass transfer-based | PET = f (u, T, RH) | 0.768 | 83 |

40. Tabari and Talaee 2011 (2) | Temperature-based | PET = f (T) | 0.767 | 84 |

90. Irmak et al. 2003 (6) | Radiation-based | PET = f (Rs, T, RH) | 0.766 | 85 |

22. Hargreaves and Samani 1985 | Temperature-based | PET = f (T) | 0.751 | 86 |

46. Althoff et al. 2019 | Temperature-based | PET = f (T) | 0.751 | 87 |

65. Jensen and Haise 1963 | Radiation-based | PET = f (Rs, T) | 0.746 | 88 |

25. Camargo et al. 1999 | Temperature-based | PET = f (T) | 0.745 | 89 |

95. Tabari and Talaee 2011 (4) | Radiation-based | PET = f (Rs, T, RH) | 0.742 | 90 |

56. Ahooghalaandari et al. 2016 (1) | Temperature-based | PET = f (T, RH) | 0.737 | 91 |

78. Irmak et al. 2003 (3) | Radiation-based | PET = f (Rs, T) | 0.734 | 92 |

38. Trajkovic 2007 | Temperature-based | PET = f (T) | 0.733 | 93 |

15. McCloud 1955 | Temperature-based | PET = f (T) | 0.730 | 94 |

60. Droogers and Allen 2002 (3) | Temperature-based | PET = f (T, PR) | 0.729 | 95 |

11. Szász 1973 | Mass transfer-based | PET = f (u, T, RH) | 0.729 | 96 |

41. Ravazzani et al. 2012 | Temperature-based | PET = f (T) | 0.727 | 97 |

42. Berti et al.2014 | Temperature-based | PET = f (T) | 0.727 | 98 |

33. Pereira and Pruit 2004 | Temperature-based | PET = f (T) | 0.723 | 99 |

35. Trajcovic 2005 (2) | Temperature-based | PET = f (T) | 0.719 | 100 |

52. Naumann 1987 | Temperature-based | PET = f (T, RH) | 0.704 | 101 |

77. Irmak et al. 2003 (2) | Radiation-based | PET = f (Rs, T) | 0.698 | 102 |

23. Kharrufa 1985 | Temperature-based | PET = f (T) | 0.697 | 103 |

44. Dorji et al. 2016 | Temperature-based | PET = f (T) | 0.691 | 104 |

39. Tabari and Talaee 2011 (1) | Temperature-based | PET = f (T) | 0.687 | 105 |

45. Lobit et al. 2018 | Temperature-based | PET = f (T) | 0.678 | 106 |

57. Ahooghalaandari et al. 2016 (2) | Temperature-based | PET = f (T, RH) | 0.671 | 107 |

54. Xu and Singh 2001 (6) | Temperature-based | PET = f (T, RH) | 0.667 | 108 |

66. Stephens 1965 | Radiation-based | PET = f (Rs, T) | 0.656 | 109 |

51. Linacre 1977 | Temperature-based | PET = f (T, RH) | 0.653 | 110 |

6. Penman 1948 | Mass transfer-based | PET = f (u, T, RH) | 0.651 | 111 |

5. Rohwer 1931 | Mass transfer-based | PET = f (u, T, RH) | 0.644 | 112 |

47. Romanenko 1961 | Temperature-based | PET = f (T, RH) | 0.637 | 113 |

29. Xu and Singh 2001 (3) | Temperature-based | PET = f (T) | 0.632 | 114 |

4. Meyer 1926 | Mass transfer-based | PET = f (u, T, RH) | 0.626 | 115 |

48. Papadakis 1965 | Temperature-based | PET = f (T, RH) | 0.617 | 116 |

87. Xu and Singh 2000 | Radiation-based | PET = f (Rs, T, RH) | 0.612 | 117 |

21. Smith and Stopp 1978 | Temperature-based | PET = f (T) | 0.590 | 118 |

14. Blaney and Criddle 1950 | Temperature-based | PET = f (T) | 0.588 | 119 |

1. Dalton 1802 | Mass transfer-based | PET = f (u, T, RH) | 0.575 | 120 |

49. Schendel 1967 | Temperature-based | PET = f (T, RH) | 0.543 | 121 |

94. Tabari and Talaee 2011 (3) | Radiation-based | PET = f (Rs, T, RH) | 0.543 | 122 |

55. Xu and Singh 2001 (7) | Temperature-based | PET = f (T, RH) | 0.540 | 123 |

50. Antal 1968 | Temperature-based | PET = f (T, RH) | 0.519 | 124 |

53. Xu and Singh 2001 (5) | Temperature-based | PET = f (T, RH) | 0.487 | 125 |

8. Brockamp and Wenner 1963 | Mass transfer-based | PET = f (u, T, RH) | 0.296 | 126 |

2. Fitzgerald 1886 | Mass transfer-based | PET = f (u, T, RH) | 0.183 | 127 |

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**Figure 1.**(

**a**) Map of the sites and (

**b**) photos of the meteorological stations installed in the urban green spaces (UGSs) of (

**a**) Heraklion (S. Greece—Crete island), and (

**c**) Amaroussion (central Greece).

**Figure 2.**Monthly average, minimum and maximum values of (

**a**) air temperature in Heraklion, (

**b**) air temperature in Amaroussion, (

**c**) relative humidity in Heraklion, (

**d**) relative humidity in Amaroussion, (

**e**) wind speed and gust in Heraklion, (

**f**) wind speed and gust in Amaroussion, (

**g**) precipitation in Heraklion and (

**h**) precipitation in Amaroussion.

**Figure 3.**(

**a**) Daily and (

**b**) monthly PET, estimated by the FAO56-PM method at two urban green spaces in the cities of Heraklion and Amaroussion. Vertical lines show the standard deviations.

**Figure 4.**Correlation between daily PET values estimated by the best five mass transfer methods (x-axis) against the benchmark method of FAO56-PM (y-axis) for the two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure 5.**Correlation between daily PET values estimated by the best-performing temperature-based methods (x-axis) of the general forms PET = f (T, RH or PR) against the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure 6.**Correlation between daily ET values estimated by the five best-performing radiation-based methods (x-axis), against the FAO56-PM benchmark method (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure 7.**Correlation between daily PET values estimated by the five better-performing combination methods (x-axis) against the FAO56-PM benchmark method (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line indicates the 1:1 regression.

**Figure 8.**Correlation between daily PET estimated by the adjusted models (x-axis) and the benchmark method of FAO56-PM (y-axis) for two urban green areas in Amaroussion (gray points) and Heraklion (red points) along with the linear regression statistics. The blue line depicts the 1:1 regression.

**Table 5.**Statistical indices (mean, slope a, intercept b, and coefficient of determination R

^{2}, of the linear regression y = ax + b, mean bias error (MBE), root mean square error (RMSE), mean absolute error (MAE), standard deviation square (sd

^{2}), and index of agreement d) and ranking (sRPI score and rank) based on the optimum values of the statistical indices for the five best mass transfer-based PET modes compared to the FAO56-PM base method in the two urban green sites of Heraklion and Amaroussion.

PET Method | N | Mean | a | b | MBE | RMSE | MAE | sd^{2} | d | R^{2} | sRPI | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Heraklion | ||||||||||||

FAO56-PM | 1139 | 3.266 | ||||||||||

10. Mahringer 1970 | 1139 | 3.234 | 1.015 | −0.087 | −0.029 | 1.158 | 0.834 | 1.332 | 0.919 | 0.738 | 0.827 | 46 |

3. Trabert 1896 | 1139 | 3.470 | 1.091 | −0.094 | 0.207 | 1.270 | 0.882 | 1.569 | 0.974 | 0.738 | 0.825 | 47 |

12. Linacre 1992 | 1138 | 3.669 | 0.895 | 0.738 | 0.403 | 0.977 | 0.801 | 0.789 | 0.946 | 0.796 | 0.813 | 52 |

9. WMO 1966 | 1139 | 2.594 | 0.785 | 0.025 | −0.670 | 1.212 | 0.913 | 1.002 | 0.964 | 0.729 | 0.798 | 55 |

7. Albrecht 1950 | 1139 | 3.634 | 1.080 | 0.105 | 0.371 | 1.255 | 0.830 | 1.437 | 0.898 | 0.750 | 0.796 | 56 |

Amaroussion | ||||||||||||

FAO56-PM | 1195 | 2.969 | ||||||||||

9. WMO 1966 | 1195 | 2.465 | 0.915 | −0.259 | −0.670 | 0.923 | 0.693 | 0.592 | 0.982 | 0.844 | 0.853 | 40 |

12. Linacre 1992 | 1187 | 3.620 | 1.062 | 0.446 | 0.403 | 1.076 | 0.903 | 0.761 | 0.957 | 0.847 | 0.831 | 44 |

10. Mahringer 1970 | 1195 | 3.005 | 1.171 | −0.478 | −0.029 | 1.042 | 0.726 | 1.085 | 0.943 | 0.836 | 0.826 | 50 |

3. Trabert 1896 | 1195 | 3.225 | 1.259 | −0.514 | 0.207 | 1.197 | 0.786 | 1.368 | 0.981 | 0.836 | 0.817 | 56 |

7. Albrecht 1950 | 1195 | 3.647 | 1.398 | −0.506 | 0.371 | 1.562 | 0.981 | 1.985 | 0.902 | 0.834 | 0.740 | 84 |

**Table 6.**Statistical indices (mean, slope a, intercept b, and coefficient of determination R

^{2}, of the linear regression y = ax + b, mean bias error (MBE), root mean square error (RMSE), mean absolute error (MAE), standard deviation square (sd

^{2}), and index of agreement d) and ranking (sRPI Score and Rank) based on the optimum values of the statistical indices for the best five temperature-based PET models compared to the benchmark method of FAO56-PM in the two urban green sites of Heraklion and Amaroussion.

PET Method | N | Mean | a | b | MBE | RMSE | MAE | sd^{2} | D | R^{2} | sRPI | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Heraklion | ||||||||||||

FAO56-PM | 1139 | 3.266 | ||||||||||

58. Ahoogh. et al. 2016 (3) | 1139 | 3.609 | 0.916 | 0.569 | 0.346 | 0.717 | 0.562 | 0.379 | 0.966 | 0.897 | 0.889 | 27 |

28. Xu and Singh 2001 (2) | 1139 | 3.171 | 0.934 | 0.100 | −0.092 | 0.877 | 0.718 | 0.731 | 0.950 | 0.816 | 0.876 | 34 |

27. Xu and Singh 2001 (1) | 1139 | 3.114 | 0.926 | 0.068 | −0.149 | 0.869 | 0.706 | 0.702 | 0.931 | 0.821 | 0.869 | 37 |

36. Oudin 2005 | 1139 | 3.013 | 0.755 | 0.516 | −0.251 | 0.709 | 0.578 | 0.392 | 0.935 | 0.923 | 0.869 | 38 |

37. Castañ. and Rao 2005 (1) | 1139 | 3.602 | 0.800 | 0.960 | 0.339 | 0.743 | 0.610 | 0.426 | 0.943 | 0.893 | 0.841 | 43 |

Amaroussion | ||||||||||||

FAO56-PM | 1195 | 2.969 | ||||||||||

58. Ahoogh. et al. 2016 (3) | 1195 | 3.607 | 1.118 | 0.240 | 0.346 | 0.917 | 0.719 | 0.493 | 0.964 | 0.920 | 0.887 | 26 |

36. Oudin 2005 | 1195 | 2.878 | 0.831 | 0.382 | −0.251 | 0.642 | 0.501 | 0.399 | 0.957 | 0.904 | 0.885 | 27 |

28. Xu and Singh 2001 (2) | 1195 | 3.023 | 1.008 | 0.010 | −0.092 | 0.938 | 0.753 | 0.880 | 0.951 | 0.811 | 0.861 | 36 |

27. Xu and Singh 2001 (1) | 1195 | 2.974 | 1.002 | −0.022 | −0.149 | 0.921 | 0.737 | 0.849 | 0.939 | 0.815 | 0.857 | 37 |

34. Trajkovic 2005 (1) | 1195 | 2.852 | 0.844 | 0.321 | −0.345 | 0.837 | 0.666 | 0.681 | 0.946 | 0.821 | 0.832 | 42 |

**Table 7.**Statistical indices (mean, slope a, intercept b, and coefficient of determination R

^{2}, of the linear regression y = ax + b, mean bias error (MBE), root mean square error (RMSE), mean absolute error (MAE), standard deviation square (sd

^{2}), and index of agreement d) and ranking (sRPI Score and Rank) based on the optimum values of the statistical indices for the five better-performing radiation-based models for the estimation of PET compared to the benchmark method of FAO56-PM in the two urban green sites of Heraklion and Amaroussion.

PET Method | N | Mean | a | b | MBE | RMSE | MAE | sd^{2} | d | R^{2} | sRPI | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Heraklion | ||||||||||||

FAO56-PM | 1139 | 3.266 |