Abstract

Reference evapotranspiration (ET0) is a major component of the hydrological cycle. Its use is essential both for the hydrological rainfall–runoff assessment models and determination of water requirements in agricultural and forest ecosystems. This study investigates the performance of 24 different methods, which produce ET0 or potential evapotranspiration estimates above a grass-covered ground in a Mediterranean forest environment in Greece and compares the derived results with those of the presumed most accurate and scientifically acceptable Penman–Monteith method (ETP-M). Their performance was evaluated on a daily basis for a period of 17 years, using 17 different statistical parameters of goodness of fit. The results showed that some empirical methods could serve as suitable alternatives. More specifically, Copais (ETCOP), Hargreaves original (ETHAR), and Valiantzas2 (ETVA2) methods, exhibited very good values of the model efficiency index, EF (0.934, 0.932, and 0.917, respectively) and the index of agreement, d (0.984, 0.982, and 0.977, respectively). Additionally, the differences of the estimated mean daily value against the respective ETP-M value (rt index) for all methods had a range of −27.8% (Penman – ETPEN) to +59.5% (Romanenko – ETROM), while Copais (ETCOP), Hargreaves–Samani modified1 (ETHS1), and STU (ETSTU) yielded the best values (−0.06%, +0.06%, and 0.22%, respectively).

INTRODUCTION

Evapotranspiration (ET) is an important component of both the water and energy cycles. ET is used in agricultural and forest hydrometeorology and in urban planning. It is also used in many rainfall–runoff and ecosystem models (Vörösmarty et al. 1998; Hay & McCabe 2002; Oudin et al. 2005a, 2005b), even for the estimation of ecosystem productivity (Currie 1991). ET also affects significantly regional water availability and use (Zhang et al. 2001; Sun et al. 2006). In order to carry out a long-term study of hydrological, environmental, and ecological processes, reliable estimates and/or accurate measurements of ET are required (Rosenberry et al. 2007; Tabari et al. 2011).

The concept of ‘reference evapotranspiration’ (ET0) was defined by Doorenbos & Pruitt (1977) as ‘the rate of evapotranspiration from an extensive surface of 8 to 15 cm tall, green grass cover of uniform height, actively growing, completely shading the ground and not short of water’. Allen et al. (1998) evolved an ET0 definition based on a reference surface (a hypothetical grass and/or alfalfa reference crop) to define unique evaporation parameters for each crop and growth stage. Hence, the FAO Expert Consultation on Revision of FAO Methodologies for Crop Water Requirements accepted the following unambiguous definition for the reference surface: ‘A hypothetical crop with an assumed height of 0.12 m having a surface resistance of 70 s m−1 and an albedo of 0.23, closely resembling the evaporation of an extension surface of green grass of uniform height, actively growing and adequately watered’ (Allen et al. 1998). The method proposed by Allen et al. (1998) was the FAO56 Penman–Monteith (ETP-M) equation, which was accepted worldwide as the best estimator of ET0 in many regions and in different weather conditions (Droogers & Allen 2002; Xu & Singh 2002; Oudin et al. 2005a, 2005b; Alexandris et al. 2006; Gavilán et al. 2006; Tabari et al. 2011; Rahimikhoob et al. 2012; Khoshravesh et al. 2015; Valipour 2015a, 2015b).

As ET0 is considered to be the most difficult component to estimate, the wealth of ET0 methods and empirical equations proposed by many researchers have certain strong points and limitations depending on the methods' applications and assumptions (Rana & Katerji 2000; Grismer et al. 2002; Valipour 2014a, 2014b). Additionally, past studies at various scales proved that different ET0 methods gave widely different values at particular locations (Federer et al. 1996; Vörösmarty et al. 1998). This means that all these methods cannot be used globally as they need calibration for regional application (Kolka & Wolf 1998; Grismer et al. 2002; Xu & Singh 2002; Rosenberry et al. 2004; Lu et al. 2005; Tabari et al. 2011; Rahimikhoob et al. 2012; Xu et al. 2013; Bogawski & Bednorz 2014; Samaras et al. 2014; Valipour & Eslamian 2014; Valipour 2015c). The selection of the appropriate method based on the availability of data, its cost, estimation accuracy, operational time and space scales, is challenging.

There are many methods in the literature used for the estimation of ET0. These methods can be grouped into categories depending on the variables needed for input. The main categories reported in the literature are: mass-transfer, temperature-based, radiation-based, pan-evaporation, and combination. Many researchers reported overviews by using these methods and categories (Jensen et al. 1990; Xu & Singh 2002; Rosenberry et al. 2004, 2007; Oudin et al. 2005a; Alexandris et al. 2008; Trajkovic & Kolakovic 2009; Tabari et al. 2011; Xystrakis & Matzarakis 2011; Xu et al. 2013; Valipour 2014c) in different areas and environments.

It would be really interesting to investigate the performance of the ET0 methods in a forested area because: (1) forests affect the climatic status variability since they influence the hydrological and carbon cycles at regional and global scale (Houghton 1991; Musselman & Fox 1991; Nepstad et al. 1994) and (2) it is well established that forested sites and catchments have higher ET rates than grassed catchments (Zhang et al. 2001). In the literature there is a lack of studies dealing with ET0 in forests. This is due to the costly equipment requirements (lysimeters, eddy covariance towers, etc.) and to the fact that the main interest of the scientific community focuses on agriculture (Fisher et al. 2005; Alexandris et al. 2008).

Such studies have been performed mainly in coniferous species. Indicatively, McNaughton & Black (1973) measured the ET in a Douglas fir forest for 18 days and came up with a proposed estimation method. Scholl (1976) determined the ET in a Chaparral stand. Spittlehouse & Black (1980) used the Bowen ratio/energy balance method to measure the ET of a thinned Douglas fir forest. Riekerk (1985) measured the ET of a young splash pine stand (Pinus elliottii) with lysimeters for 2 years. Stannard (1993) evaluated three ET models in a sparsely vegetated, semi-arid rangeland. Federer et al. (1996) used specific coefficients to estimate the potential evapotranspiration (PET) in different forested areas. Farahani & Ahuja (1996) worked in partial canopy/residue-covered fields. Kolka & Wolf (1998) modified the Thornthwaite model in order to estimate the actual ET in 29 forested sites. Fisher et al. (2005) compared five models of PET in a mixed (dominant species Pinus ponderosa) coniferous forest. Ha et al. (2015) worked in semi-arid high-elevation disturbed ponderosa pine forests and compared ET between eddy covariance measurements and meteorological and remote sensing-based models.

To our knowledge, except for Gebhart et al. (2012) who studied some temperature-based and radiation-based methods in northern Greece, there have been no reports for comparative evaluation of the behavior of ET0 methods in forested areas of Greece. Other studies conducted in Greece used meteorological data from the Greek National Meteorological Service (Xystrakis & Matzarakis 2011; Samaras et al. 2014) exclusively for urban and agricultural areas. The meteorological stations that provided the data did not always follow the protocols imposed by the FAO (Alexandris et al. 2013). Moreover, there has not been such a study in the Mediterranean forests containing evergreen sclerophyllous broadleaved species.

For the above reasons, the main objective of this study was to test and evaluate the accuracy of different ET0 estimation equations, taking into account the data requirements for each model and making the assumptions that: (1) the ETP-M model is the best estimator for the ET0 and (2) the environmental conditions of the site approximate the conditions for the application of the ETP-M model. The 24 selected equations are very common, extensively used in other studies, and represent the four main categories (mass-transfer, temperature-based, radiation-based, and combination).

The models tested in this work produce ET0 or PET estimates above ground covered with grass in a Mediterranean forest environment in Greece. The results will be useful to other researchers for incorporating them as input into hydrological, environmental, and soil models applied on similar Mediterranean vegetative and climatic conditions.

MATERIALS AND METHODS

Site description

The study was carried out in a small experimental forest watershed (1.23 km2) covered by evergreen sclerophyllous broadleaved vegetation (maquis vegetation) in Western Greece close to Varetada village (Figure 1). This is a multi-layer, dense coppice forest with canopy closure 1.2–1.3 (tree canopies overlap). The understorey is dominated by Phillyrea latifolia, Arbutus unedo, and Erica arborea. Sporadic stems of Cercis siliquastrum and Erica verticilata are also present. In the upper storey there is a number of Quercus ilex stems distributed almost uniformly (Baloutsos et al. 2009). The height of all species varies from 4 to 15 m. The terrain is hilly and the soil is a Haplic Luvisol one (FAO 1988) and its parent material is flysch.

Figure 1

The location of the forest meteorological station in Greece.

Figure 1

The location of the forest meteorological station in Greece.

The site receives a mean annual amount of precipitation of 1,174 mm in the form of rain which ranges from 696 to 2,230 mm, as calculated from climatic data of the period 1996–2012. The wettest months are October (161 mm) and November (130.8 mm) and the driest ones July (46 mm) and June (46.5 mm). The mean annual air temperature is 15.6 °C. The coldest month is January with a mean monthly value of 7.1 °C with August being the hottest (25.5 °C) one. The mean annual relative humidity is 67.5% with an average of 80% during December and 59% during June. The average annual wind speed is 1.9 m/s with a monthly average value of 2.4 m/s during July and 1.5 m/s during December.

The wider area is classified in the Csa climatic type according to the Köppen–Geiger updated world map (Kottek et al. 2006), which shows seasonal variability (warm temperate rainy climates with mild winters and very hot dry summers).

The particular site was selected for forest research purposes for two reasons: (1) the maquis vegetation is one of the most representative vegetations in Mediterranean forest ecosystems and (2) the watershed is a long way from urban and industrial areas, so it is not likely that it receives any kind of pollution. Additionally, the entire existing forest has not been managed by the local Forest Service for over 40 years; therefore, there has not been any land use change for the same period of time.

Meteorological data (evaluation and processing)

The meteorological data were collected from an automatic meteorological station (latitude 38 ° 50′ 35″, longitude 21 ° 18′ 25″, elevation 332 m a.s.l.) installed in a natural forest opening inside the watershed. The main advantage of the location and the ground vegetation of the meteorological station is that they meet the specifications imposed by the FAO to avoid (as much as possible) significant and systematic cumulative errors in determining ET0 (from 27% up to 47% during the warm season – Alexandris et al. 2013). Meteorological variables, such as air temperature (Taver, Tmax, Tmin), relative humidity (RHaver, RHmax, RHmin), solar radiation (Rs), wind speed (u2), and precipitation (PR) were continuously recorded for a time period of 17 years (1996–2012). All sensors were set at 2 m above the ground level except for the rain gauge which was at a height of 1.3 m. The sampling period for all the monitored variables was set up to 15 min and the collected data were stored in a digital datalogger connected to the sensors. The data were periodically downloaded to be summarized and provide hourly, daily, monthly, and annual averages. These values constituted the input data used for the estimation of the daily values of ET0 in all of the equations.

For the present study, daily data covering the 87.5% of the total length of the 17-year period (5,433 days) were used. The existing gaps (12.5% or 777 daily values: 356 in winters, 114 in springs, 100 in summers, and 207 in autumns) were randomly distributed and were excluded from the statistical analysis, since any gap filling could possibly affect the reliability of the results. The gaps were due to the lack of measurements of some parameters that made the application of the ETP-M equation prohibitory. In some cases, some of the methods included in this study estimated a negative ET0 daily value. These values were also excluded from the statistical analysis. A summary of the notations, definitions, and the units of the symbols used are shown in Table 1.

Table 1

Notations, definitions, and units used in all equations for the estimation of the ET0

Notation Definition Unit 
ET Evapotranspiration mm/day 
Δ Slope of vapor pressure curve kPa/°C 
λ Latent heat of vaporization MJ/kg 
ρ Water density =1.0 kg/l 
γ Psychrometric constant kPa/°C 
es Saturation vapor pressure kPa 
ea Actual vapor pressure kPa 
u2 Wind speed at 2 m above ground surface m/s 
Taver Mean daily air temperature °C 
Rn Net solar radiation MJ/m2/day 
C1 and C2 Functions of the attributes Rs, Taver and RHaver mm/day 
Soil heat flux density =0 MJ/m2/day for daily computations (ASCE-EWRI 2005
Rs Incident shortwave solar radiation flux MJ/m2/day 
Ra Extraterrestrial solar radiation MJ/m2/day 
Tmax Maximum daily air temperature °C 
Tmin Minimum daily air temperature °C 
PR Precipitation mm 
Maximum possible duration hrs 
RHaver Mean daily relative humidity 
φ Latitude Rad 
α Albedo =0.23 
Notation Definition Unit 
ET Evapotranspiration mm/day 
Δ Slope of vapor pressure curve kPa/°C 
λ Latent heat of vaporization MJ/kg 
ρ Water density =1.0 kg/l 
γ Psychrometric constant kPa/°C 
es Saturation vapor pressure kPa 
ea Actual vapor pressure kPa 
u2 Wind speed at 2 m above ground surface m/s 
Taver Mean daily air temperature °C 
Rn Net solar radiation MJ/m2/day 
C1 and C2 Functions of the attributes Rs, Taver and RHaver mm/day 
Soil heat flux density =0 MJ/m2/day for daily computations (ASCE-EWRI 2005
Rs Incident shortwave solar radiation flux MJ/m2/day 
Ra Extraterrestrial solar radiation MJ/m2/day 
Tmax Maximum daily air temperature °C 
Tmin Minimum daily air temperature °C 
PR Precipitation mm 
Maximum possible duration hrs 
RHaver Mean daily relative humidity 
φ Latitude Rad 
α Albedo =0.23 

Note: For details needed for the computation of the parameters which were not measured directly, refer to Allen et al. (1998).

ET0 estimation equations

The 24 different equations used in this study were categorized in the following groups: five mass-transfer (Albrecht, Mahringer, Penman, Romanenko, and WMO), four combination (Copais, Solar Thermal Unit, Valiantzas (1) and (2)), ten radiation-based (Abtew, Caprio, De Bruin–Keijman, FAO24 Radiation, Jensen–Haise, Hansen, Makkink, McGuiness–Bordne, Priestley–Taylor and Turc), and five temperature-based (Hargreaves original, Hargreaves–Samani, two modified Hargreaves–Samani, and modified Thornthwaite) methods. The formulas of the equations are presented in Table 2 along with their references. The conversion of the units is in agreement with the units shown in Table 1.

Table 2

Formulas, symbols, and references of the ET0 equations

  Method Symbol Equation References 
Benchmark equation 
FAO56 Penman–Monteith ETP-M  Allen et al. (1998)  
Mass-transfer equations 
Albrecht ETALB , where F=0.4 if u2 ≥ 1 m/s and F= 0.1005 + 0.297 u2 if u2 < 1 m/s Albrecht (1950) and Friesland et al. (1998)  
Mahringer ETMAH  Mahringer (1970) and Tabari et al. (2011)  
Penman ETPEN  Penman (1948) and Tabari et al. (2011) a 
Romanenko ETROM  Oudin et al. (2005a, 2005b) and Xystrakis & Matzarakis (2011)  
WMO ETWMO  WMO (1966) and Tabari et al. (2011) b 
Combinations equations 
Copais ETCOP  where m1 = 0.057, m2 = 0.277, m3 = 0.643, m4 = 0.0124 Alexandris et al. (2006, 2008) c,d 
Solar Thermal Unit ETSTU  Caprio (1974)  
Valiantzas (1) ETVA1  Valiantzas (2013)  
10 Valiantzas (2) ETVA2  Valiantzas (2013)  
Radiation-based equations 
11 Abtew ETABT  Abtew (1996) and Samaras et al. (2014)  
12 Caprio ETCAP  Caprio (1974) and Samaras et al. (2014)  
13 De Bruin– Keijman ETDBK  DeBruin & Keijman (1979) and Rosenberry et al. (2007)  
14 FAO24 Radiation ETF24  Doorenbos & Pruitt (1977) and Frevert et al. (1983) e 
15 Hansen ETHAN  Hansen (1984) and Xu & Singh (2002)  
16 Jensen–Haise ETJ-H  Rosenberg et al. (1983) and Xystrakis & Matzarakis (2011)  
17 Makkink ETMAK  Rosenberry et al. (2004) and Alexandris et al. (2008)  
18 McGuinness–Bordne ETMGB  McGuinness & Bordne (1972) and Oudin et al. (2005a, 2005b)  
19 Priestley–Taylor ETP-T  Priestley & Taylor (1972) f 
20 Turc ETTUR , for RHaver > 50% , for RHaver < 50%  Turc (1961) and Lu et al. (2005)  
21 Hargreaves (original) ETHAR  Hargreaves (1975)  
22 Hargreaves–Samani ETH-S  Hargreaves & Samani (1985)  
23 Hargreaves–Samani (modified 1) ETHS1  Droogers & Allen (2002)  
24 Hargreaves–Samani (modified 2) ETHS2  Droogers & Allen (2002)  
25 Thornthwaite (modified) ETTHO , where WI = 33.617 and A = 1.033 Siegert & Schrodter (1975)  
  Method Symbol Equation References 
Benchmark equation 
FAO56 Penman–Monteith ETP-M  Allen et al. (1998)  
Mass-transfer equations 
Albrecht ETALB , where F=0.4 if u2 ≥ 1 m/s and F= 0.1005 + 0.297 u2 if u2 < 1 m/s Albrecht (1950) and Friesland et al. (1998)  
Mahringer ETMAH  Mahringer (1970) and Tabari et al. (2011)  
Penman ETPEN  Penman (1948) and Tabari et al. (2011) a 
Romanenko ETROM  Oudin et al. (2005a, 2005b) and Xystrakis & Matzarakis (2011)  
WMO ETWMO  WMO (1966) and Tabari et al. (2011) b 
Combinations equations 
Copais ETCOP  where m1 = 0.057, m2 = 0.277, m3 = 0.643, m4 = 0.0124 Alexandris et al. (2006, 2008) c,d 
Solar Thermal Unit ETSTU  Caprio (1974)  
Valiantzas (1) ETVA1  Valiantzas (2013)  
10 Valiantzas (2) ETVA2  Valiantzas (2013)  
Radiation-based equations 
11 Abtew ETABT  Abtew (1996) and Samaras et al. (2014)  
12 Caprio ETCAP  Caprio (1974) and Samaras et al. (2014)  
13 De Bruin– Keijman ETDBK  DeBruin & Keijman (1979) and Rosenberry et al. (2007)  
14 FAO24 Radiation ETF24  Doorenbos & Pruitt (1977) and Frevert et al. (1983) e 
15 Hansen ETHAN  Hansen (1984) and Xu & Singh (2002)  
16 Jensen–Haise ETJ-H  Rosenberg et al. (1983) and Xystrakis & Matzarakis (2011)  
17 Makkink ETMAK  Rosenberry et al. (2004) and Alexandris et al. (2008)  
18 McGuinness–Bordne ETMGB  McGuinness & Bordne (1972) and Oudin et al. (2005a, 2005b)  
19 Priestley–Taylor ETP-T  Priestley & Taylor (1972) f 
20 Turc ETTUR , for RHaver > 50% , for RHaver < 50%  Turc (1961) and Lu et al. (2005)  
21 Hargreaves (original) ETHAR  Hargreaves (1975)  
22 Hargreaves–Samani ETH-S  Hargreaves & Samani (1985)  
23 Hargreaves–Samani (modified 1) ETHS1  Droogers & Allen (2002)  
24 Hargreaves–Samani (modified 2) ETHS2  Droogers & Allen (2002)  
25 Thornthwaite (modified) ETTHO , where WI = 33.617 and A = 1.033 Siegert & Schrodter (1975)  

aes and ea are in mmHg and u2 is in miles/day.

bes and ea are in hPa.

cIn the original paper (Alexandris et al. 2006) the coefficient m2 is 0.227 due to a misprint and should be replaced with the correct value 0.277 (Alexandris et al. 2008).

dC1 = 0.6416 − 0.00784 RHaver + 0.372 RS–0.00264 RHaver; C2 = −0.0033 + 0.00812 Taver + 0.101 RS + 0.00584 RsTaver.

eb = 1.066–0.13 × 10−2 (RHaver) + 0.045 (u2)–0.20 × 10−3 (RHaver × u2)–0.135 × 10−4 (RHaver)2–0.11 × 10−2 (u2)2.

fa = 1.26 = Priestley–Taylor's empirically constant, dimensionless.

Statistical analysis

There are many widely used statistical indices and coefficients to evaluate the systematic quantification of the accuracy of compared models (Willmott 1982; Berengena & Gavilán 2005; Alexandris et al. 2008; Valiantzas 2013). A great number of them was selected in this study aiming to facilitate further comparison of the results with those of other studies.

The computational formulas for all indices and coefficients except of mean value (MV), standard deviation (SD), coefficient of determination (R2), and the coefficients of the linear trend line a (slope) and b (intercept) are the following:  
formula
 
formula
 
formula
 
formula
 
formula
 
formula
 
formula
 
formula
 
formula
 
formula
 
formula
 
formula

where Ei and Eaver are the predicted daily and the average of the ET0 method values, respectively, Oi and Oaver are the calculated daily and the average of the ETP-M values, respectively, and n is the total number of data.

Specifically, Correl, R2, a and b indices, of the least squared regression analysis, are commonly used correlation measures. The MV and SD indices provide a general view of the models' performance. For more efficient model assessment, Krause et al. (2005) suggest the use of the combined index wR2. For the mean error evaluation, MBE, Sd2, and rMSE indices were used (Fox 1981; Berengena & Gavilán 2005). For the absolute and/or relative errors' estimation, MAE, AAE, RMSE, and RMAE indices were also calculated, so as to facilitate the discussion in this work, since they are widely reported in the literature (Xystrakis & Matzarakis 2011; Gebhart et al. 2012; Kisi 2014; Samaras et al. 2014). The descriptive d index was used for the cross-comparison between the models, expressing the degree to which a model's predictions are error free (Willmott 1982). Finally, the EF index specifies the relationship between calculated and predicted mean deviations (Greenwood et al. 1985), while rt returns a long-term value of the predicted against the calculated MVs.

RESULTS AND DISCUSSION

On an annual basis, the average observed ET0 rate calculated from the ETP-M for the period 1996–2012, was found to be 1,190 mm. This value is a little different from the mean annual precipitation (1,174 mm) and specifically indicates that the water requirements of a reference crop are totally sufficed. Additionally, the mean seasonal values of ET0 showed seasonal variation, as expected for the Mediterranean climate (Csa), varying from 99 mm (winter) to 558 mm (summer) and moderate values during the transitional periods of spring and autumn (307 mm and 226 mm, respectively).

From the analysis of the annual values, the best approaches seem to give the ETHS2, ETCOP, and ETSTU methods, in which the percentages of ET0 average annual values diverge by +0.47%, −0.69%, and −2.27%, respectively. In contrast, the largest annual deviations appeared in the ETROM (+60.85%), ETMAK (−26.47%), and ETPEN (−26.23%) methods. These results were in line with Federer et al. (1996), who reported that different methods gave widely differing estimates of annual ET0 at particular locations which sometimes were up to several hundreds of millimeters.

From the analysis of 5,433 daily values with 18 different statistical parameters and indices, the 24 tested methods were evaluated comparatively. Their performance against the ETP-M method is shown in Figure 2 and Table 3 and the obtained results are the following.

Figure 2

R2 coefficient, slope, and intercept of the daily values of ET0 (in mm) estimated by various methods (x axis) vs. the standardized ETP-M (y axis). The continuous line in all figures indicates the trendline of the scatter and the dashed line indicates the 1:1 slope trend. The point shapes for each category differ.

Figure 2

R2 coefficient, slope, and intercept of the daily values of ET0 (in mm) estimated by various methods (x axis) vs. the standardized ETP-M (y axis). The continuous line in all figures indicates the trendline of the scatter and the dashed line indicates the 1:1 slope trend. The point shapes for each category differ.

Table 3

Statistical analysis of the 24 methods versus the FAO56 PM model for estimating daily ET0 during the study period (1996–2012)

A/A Categories Symbol Mean (mm) SD (mm) rt Correl MBE (mm) MAE (mm) rMSE (mm) rMAE (mm) RMSE (mm) RMAE (mm) d wR2 Sd2 (mm) EF 
 ETP-M 5,433 3.380 2.196             
Mass-transfer methods ETALB 5,414 3.687 2.900 1.091 0.911 0.379 0.901 1.348 0.949 1.381 0.863 0.928 0.567 1.673 0.625 
ETMAH 5,414 3.821 3.265 1.131 0.927 0.523 0.984 1.593 0.992 1.066 1.078 0.914 0.531 2.265 0.475 
ETPEN 5,414 2.440 1.895 0.722 0.909 −0.897 0.990 1.283 0.995 0.757 0.737 0.905 0.654 0.843 0.660 
ETROM 5,414 5.392 3.611 1.595 0.919 2.046 2.099 2.642 1.449 0.293 0.604 0.811 0.478 3.117 −0.437 
ETWMO 5,414 3.046 2.635 0.901 0.925 −0.270 0.773 1.080 0.879 2.026 1.278 0.949 0.652 1.094 0.759 
Combination methods ETCOP 5,428 3.360 2.241 0.994 0.968 0.022 0.442 0.564 0.665 0.438 0.325 0.984 0.921 0.318 0.934 
ETSTU 5,426 3.306 2.681 0.978 0.977 −0.079 0.569 0.715 0.755 1.940 0.704 0.978 0.764 0.513 0.894 
ETVA1 5,425 3.763 2.423 1.113 0.978 0.375 0.523 0.649 0.723 1.214 0.294 0.980 0.849 0.281 0.913 
10 ETVA2 5,367 3.051 2.023 0.903 0.972 −0.355 0.468 0.635 0.684 2.024 0.364 0.977 0.847 0.278 0.917 
11 Radiation-based methods ETABT 5,430 2.783 2.186 0.824 0.976 −0.600 0.623 0.766 0.789 1.857 0.827 0.970 0.926 0.227 0.878 
12 ETCAP 5,433 3.772 2.579 1.116 0.953 0.391 0.697 0.913 0.835 0.183 0.259 0.963 0.737 0.681 0.827 
13 ETDBK 5,433 2.930 1.959 0.867 0.949 −0.452 0.597 0.836 0.773 0.337 0.318 0.959 0.762 0.495 0.855 
14 ETF24 5,260 3.763 2.668 1.114 0.976 0.296 0.622 0.783 0.788 2.676 0.975 0.974 0.753 0.526 0.877 
15 ETHAN 5,433 2.974 1.884 0.880 0.961 −0.408 0.556 0.765 0.746 0.714 0.339 0.965 0.762 0.418 0.879 
16 ETJ-H 5,431 3.488 2.719 1.032 0.978 0.105 0.575 0.740 0.758 1.697 0.475 0.977 0.755 0.537 0.886 
17 ETMAK 5,399 2.487 1.635 0.736 0.901 −0.912 0.926 1.192 0.962 2.603 0.731 0.907 0.662 0.590 0.707 
18 ETMGB 5,432 3.876 2.361 1.147 0.930 0.618 0.815 1.063 0.903 0.133 0.264 0.945 0.863 0.749 0.766 
19 ETP-T 5,433 2.881 1.969 0.852 0.953 −0.501 0.608 0.843 0.780 0.407 0.345 0.959 0.775 0.460 0.853 
20 ETTUR 5,419 2.970 1.956 0.879 0.974 −0.414 0.513 0.674 0.716 0.316 0.397 0.974 0.819 0.283 0.906 
21 Temperature-based methods ETHAR 5,433 3.139 2.116 0.929 0.972 −0.244 0.427 0.572 0.653 0.780 0.321 0.982 0.884 0.268 0.932 
22 ETH-S 5,433 3.123 1.910 0.924 0.931 −0.167 0.603 0.832 0.777 0.171 0.248 0.958 0.701 0.664 0.856 
23 ETHS1 5,433 3.400 1.969 1.006 0.932 0.116 0.615 0.808 0.784 0.111 0.231 0.961 0.726 0.640 0.865 
24 ETHS2 5,433 3.300 2.034 0.976 0.931 0.016 0.590 0.802 0.768 0.154 0.237 0.963 0.748 0.643 0.867 
25 ETTHO 5,423 2.777 1.608 0.822 0.915 −0.532 0.895 1.111 0.946 0.942 0.593 0.913 0.558 0.951 0.744 
A/A Categories Symbol Mean (mm) SD (mm) rt Correl MBE (mm) MAE (mm) rMSE (mm) rMAE (mm) RMSE (mm) RMAE (mm) d wR2 Sd2 (mm) EF 
 ETP-M 5,433 3.380 2.196             
Mass-transfer methods ETALB 5,414 3.687 2.900 1.091 0.911 0.379 0.901 1.348 0.949 1.381 0.863 0.928 0.567 1.673 0.625 
ETMAH 5,414 3.821 3.265 1.131 0.927 0.523 0.984 1.593 0.992 1.066 1.078 0.914 0.531 2.265 0.475 
ETPEN 5,414 2.440 1.895 0.722 0.909 −0.897 0.990 1.283 0.995 0.757 0.737 0.905 0.654 0.843 0.660 
ETROM 5,414 5.392 3.611 1.595 0.919 2.046 2.099 2.642 1.449 0.293 0.604 0.811 0.478 3.117 −0.437 
ETWMO 5,414 3.046 2.635 0.901 0.925 −0.270 0.773 1.080 0.879 2.026 1.278 0.949 0.652 1.094 0.759 
Combination methods ETCOP 5,428 3.360 2.241 0.994 0.968 0.022 0.442 0.564 0.665 0.438 0.325 0.984 0.921 0.318 0.934 
ETSTU 5,426 3.306 2.681 0.978 0.977 −0.079 0.569 0.715 0.755 1.940 0.704 0.978 0.764 0.513 0.894 
ETVA1 5,425 3.763 2.423 1.113 0.978 0.375 0.523 0.649 0.723 1.214 0.294 0.980 0.849 0.281 0.913 
10 ETVA2 5,367 3.051 2.023 0.903 0.972 −0.355 0.468 0.635 0.684 2.024 0.364 0.977 0.847 0.278 0.917 
11 Radiation-based methods ETABT 5,430 2.783 2.186 0.824 0.976 −0.600 0.623 0.766 0.789 1.857 0.827 0.970 0.926 0.227 0.878 
12 ETCAP 5,433 3.772 2.579 1.116 0.953 0.391 0.697 0.913 0.835 0.183 0.259 0.963 0.737 0.681 0.827 
13 ETDBK 5,433 2.930 1.959 0.867 0.949 −0.452 0.597 0.836 0.773 0.337 0.318 0.959 0.762 0.495 0.855 
14 ETF24 5,260 3.763 2.668 1.114 0.976 0.296 0.622 0.783 0.788 2.676 0.975 0.974 0.753 0.526 0.877 
15 ETHAN 5,433 2.974 1.884 0.880 0.961 −0.408 0.556 0.765 0.746 0.714 0.339 0.965 0.762 0.418 0.879 
16 ETJ-H 5,431 3.488 2.719 1.032 0.978 0.105 0.575 0.740 0.758 1.697 0.475 0.977 0.755 0.537 0.886 
17 ETMAK 5,399 2.487 1.635 0.736 0.901 −0.912 0.926 1.192 0.962 2.603 0.731 0.907 0.662 0.590 0.707 
18 ETMGB 5,432 3.876 2.361 1.147 0.930 0.618 0.815 1.063 0.903 0.133 0.264 0.945 0.863 0.749 0.766 
19 ETP-T 5,433 2.881 1.969 0.852 0.953 −0.501 0.608 0.843 0.780 0.407 0.345 0.959 0.775 0.460 0.853 
20 ETTUR 5,419 2.970 1.956 0.879 0.974 −0.414 0.513 0.674 0.716 0.316 0.397 0.974 0.819 0.283 0.906 
21 Temperature-based methods ETHAR 5,433 3.139 2.116 0.929 0.972 −0.244 0.427 0.572 0.653 0.780 0.321 0.982 0.884 0.268 0.932 
22 ETH-S 5,433 3.123 1.910 0.924 0.931 −0.167 0.603 0.832 0.777 0.171 0.248 0.958 0.701 0.664 0.856 
23 ETHS1 5,433 3.400 1.969 1.006 0.932 0.116 0.615 0.808 0.784 0.111 0.231 0.961 0.726 0.640 0.865 
24 ETHS2 5,433 3.300 2.034 0.976 0.931 0.016 0.590 0.802 0.768 0.154 0.237 0.963 0.748 0.643 0.867 
25 ETTHO 5,423 2.777 1.608 0.822 0.915 −0.532 0.895 1.111 0.946 0.942 0.593 0.913 0.558 0.951 0.744 

The two best fitted methods for each index or coefficient are in bold and underlined.

N: Sample days; Mean: Time series average; SD: Standard deviation; rt: long-term average ratio; Correl: Pearson's correlation; MBE: Mean bias error; MAE: Mean absolute error; rMSE: Root mean square error; rMAE: Root mean absolute error; RMSE: Relative mean square error; RMAE: Relative mean absolute error; d: Index of agreement; wR2: Weighted determination; Sd2: Coefficient variance of distribution of differences; EF: Model efficiency.

Mass-transfer equations

Among the five examined methods, the ETPEN showed average daily ET0 equal to 2.44 mm, a value significantly lower (−27.8%, rt = 0.722) compared to the corresponding ETP-M. Simultaneously, it displayed the smallest correlation coefficient (R2 = 0.826). The approaches of the average daily ET0 of the ETALB, ETWMO, and ETMAH were very similar, with deviations of +9.1% (rt = 1.091), −9.9% (rt = 0.901), and +13.0% (rt = 1.131), respectively. However, their R2s are not considered satisfactory (0.830, 0.855, and 0.860 respectively). Finally, the ETROM method displayed the worst statistics for almost all of the evaluation indices.

It is worth noting that this category of methods resulted in the smallest EF index ranging from −0.437 (ETROM) to 0.759 (ETWMO). Overall, the statistical indices of the mass-transfer equations were not satisfactory (Table 3). Hence, these methods cannot be recommended for use without calibration, in models that need the input of ET0 daily values. Similar results were reported by Valipour (2014b, 2015c), who examined R2 and MBE and suggested new calibrated mass-transfer equations for the provinces of Iran which relatively improved the performance of the original models.

In our study (forest environment with warm humid Mediterranean climate), except for ETPPEN, the high summer daily values (>5 mm) are overestimated with the mass-transfer equations. Although Tabari et al. (2011) reported that the majority of the mass-transfer empirical equations they tested, had also the worst performances but at the same time underestimated ETP-M in humid environments. This could be attributed to the fact that VPD (es – ea) presents significant variations among locations, as stated by Irmak et al. (2006), who performed a sensitivity analysis of the Penman–Monteith method for several regions with different climate types, in the USA.

Combination equations

Combination methods, in general, showed much better statistical indices compared to the methods of all other categories (Table 3). The four methods examined here presented sufficiently strong correlations (R2 is ranging from 0.937 in ETCOP to 0.958 in ETVA1), compared to ETP-M. However, the rt was significantly lower in ETCOP deviating only by −0.6% (rt = 0.994), compared to the other three methods, while ETVA1 presented the greatest divergence (+11.3%, rt = 1.113). Impressive was the finding that despite the relatively small R2 of ETCOP, most of the other statistical indices outweighed the respective indices which derived from the analysis of all 24 tested methods (Table 3). Similar results for the ETCOP, ETVA1, and ETVA2 equations were presented by Kisi (2014) in a Mediterranean environment in Turkey. The findings of Valipour (2015b) in Iran for the Valiantzas' equations are also in line with the results presented here.

The ETSTU method also gave satisfactory results (rt = 0.978, R2 = 0.955) despite the small requirements in input data. These methods are strongly recommended for use in models which need the input of ET0 daily values because they have a very satisfactory EF index ranging from 0.894 (ETSTU) to 0.934 (ETCOP).

Radiation-based equations

In this category ten methods were tested. The radiation-based equations overall performed better than the mass-transfer equations, since a more important role is expected for Rs when estimating ET0 in humid climates (Irmak et al. 2006) and in forest environments (Gebhart et al. 2012). ETJ-H and ETABT (R2 = 0.956 and 0.953, respectively) methods presented satisfactory correlations. Additionally, the ETJ-H method showed the lowest deviation from the daily MV (+3.2%, rt = 1.032), while ETABT had the best indices, wR2 and Sd2, over all of the 24 tested methods. These findings for ETJ-H are in contrast to Tabari et al. (2011), who worked in humid environments.

ETTUR can be considered as the best performing equation in this category, in terms of its EF (0.906), rMAE (0.716), RMSE (0.674), and MAE (0.513). The best performance of the equation was also found by Lu et al. (2005) in forest watersheds with warm and humid climates in the southeastern USA, and by Trajkovic & Kolakovic (2009) who recommended ETTUR for use under humid conditions, and by Gebhart et al. (2012) who suggested the use of ETTUR for the southern regions of Central Macedonia in Greece.

In contrast, the ETMGB and ETDBK methods gave the worst correlations among all the radiation-based equations (R2 = 0.865 and R2 = 0.901, respectively). Under humid conditions, similar results were reported for ETMGB by Tabari et al. (2011). The largest deviations from the daily MV were displayed by ETMAK (−26.4%, rt = 0.736) and ETABT (−17.6%, rt = 0.824). The EF index ranged from 0.707 (ETMAK) to 0.886 (ETJ-H). The poor performance of ETMAK was also reported by Lu et al. (2005).

From the above, it can be concluded that some methods (ETTUR, ETJ-H, and ETABT) of this category can be satisfactorily accepted for use in models needing the input of ET0 daily values.

Temperature-based equations

In this category five methods were tested. The best correlation was exhibited by ETHAR with R2 = 0.945 and the worst by ETTHO (R2 = 0.837). Concerning the deviation from the daily MV, the ETHS1 gave the best of all 24 tested methods (along with ETCOP), with rt = 1.006. These findings were similar to those of Valipour & Eslamian (2014) and Valipour (2015a) who gave specific ranges of the meteorological parameters used in 11 temperature-based equations for Iran's provinces and found a better performance of ETH-S, ETHS1, and ETHS2 against ETTHO. The results in our study indicated a slight underestimation in ET0 daily values for all of the tested temperature-based equations (except of ETTHO which underestimated by 17.8%). Valipour (2015a) also found a slight underestimation in ET0 daily values with ETH-S and ETHS1 equations, while the ETHS2 equation showed overestimation but not a significant one.

Contrary to these results, Trajkovic & Kolakovic (2009) and Tabari et al. (2011) found overestimation when using ETHS1, ETHS2, and ETH-S equations, on a monthly time-step analysis and under humid conditions. They also found very poor performance of the ETTHO equation. Additionally, Lu et al. (2005) suggested careful calibration and verification when applying the ETTHO equation.

The ETHAR method, despite the small data requirements, exhibited in general impressive statistical indices (e.g., best MAE, rMSE, rMAE, d, Sd2, and EF values) compared to all tested methods of all categories (Table 3). Gebhart et al. (2012) also proposed the ETHAR equation as a good alternative for ET0 estimations in northern regions of Central Macedonia in Greece. From the above mentioned, it can be concluded that this category of equations seems to have similar performance (with the exception of ETTHO) and they are recommended for use in forest environments.

CONCLUSIONS

This study attempted to investigate and evaluate the best-fit methods for the estimation of daily ET0 in a humid Mediterranean evergreen broadleaved forest environment. Twenty-four different equations classified in four categories were tested and seventeen different statistical indices were used for the evaluation.

At the category level, the combination equations seem to have the best performance followed by temperature-based and radiation-based methods. The mass-transfer methods have the worst coefficients and overestimate ET0, especially for the high summer daily values (>5 mm).

At the method level, the most accurate and consistent estimates of ET0 derived from ETCOP and ETHAR, followed by ETVA1 and ETVA2. The methods ETTUR, ETHS2, ETSTU, and ETJ-H are also proposed for use because their ET0 estimations compared quite well with those of the ETP-M method. The latter ones can also be used for the annual estimation of the ET0. Concerning the rest of the tested methods, it is suggested that calibration should be made for local conditions, mainly at a seasonal time-step to obtain more reliable daily estimates. Especially, calibration is necessary for all the mass-transfer equations and the ETMAK and ETTHO methods. There is an ongoing work by the authors, in which new coefficients will be proposed for some of these methods. The results of this study will be useful to a multidisciplinary community working on similar climates. More specifically, the best performing equations in Figure 2 could be tested further in order to optimize the ET0 obtaining values of the empirical models in the Mediterranean. Further research is needed in order to evaluate the performance of the proposed modified equations in other areas with different climates. Finally, evaluation is needed for the performance of the models on a different time scale (monthly and seasonal).

ACKNOWLEDGEMENTS

The authors would like to express their sincere thanks to the Greek ‘Ministry of Agriculture and Rural Development’ and the European Union that funded various research projects from which the data used in this work were derived. The contribution of the anonymous reviewers is also greatly acknowledged.

REFERENCES

REFERENCES
Abtew
W.
1996
Evapotranspiration measurements and modeling for three wetland systems in South Florida
.
Journal of American Water Resources Association
32
(
3
),
465
473
.
Alexandris
S.
,
Kerkides
P.
&
Liakatas
A.
2006
Daily reference evapotranspiration estimates by the Copais approach
.
Agricultural Water Management
82
(
3
),
371
386
.
Alexandris
S.
,
Stricevic
R.
&
Petkovic
S.
2008
Comparative analysis of reference evapotranspiration from the surface of rain-fed grass in central Serbia, calculated by six empirical methods against the Penman-Monteith formula
.
European Water
21/22
,
17
28
.
Alexandris
S.
,
Proutsos
N.
,
Caravitis
Ch.
,
Tsiros
I.
&
Stamatakos
D.
2013
Reasons for non-rational estimates of reference evapotranspiration in Greece
. In:
Proceedings of the 8th National Agricultural Conference
,
25–26 September
,
Volos, Greece
, pp.
110
116
(in Greek)
.
Allen
R.
,
Pereira
L.
,
Raes
D.
&
Smith
M.
1998
Crop Evapotranspiration. Guidelines for Computing Crop Water Requirements
.
FAO Irrigation and Drainage Paper No. 56
,
FAO
,
Rome
, p
300
.
ASCE-EWRI
2005
The ASCE Standardized Reference Evapotranspiration Equation. Technical Committee Report to the Environmental and Water Resources Institute of the American Society of Civil Engineers from the Task Committee on Standardization of Reference Evapotranspiration
.
ASCE-EWRI
,
Reston, VA
, p.
173
.
Baloutsos
G.
,
Bourletsikas
A.
&
Baltas
E.
2009
Development of a simplified model for the estimation of hydrological components in areas of maquis vegetation in Greece
.
WSEAS Transactions on Environment and Development
5
(
3
),
310
320
.
Berengena
J.
&
Gavilán
P.
2005
Reference ET estimation in a highly advective semi-arid environment
.
Journal of Irrigation and Drainage Engineering
131
(
2
),
147
163
.
DeBruin
H. A. R.
&
Keijman
J. Q.
1979
The Priestley-Taylor evaporation model applied to a large, shallow lake in the Netherlands
.
Journal of Applied Meteorology
18
,
898
903
.
Doorenbos
J.
&
Pruitt
W. O.
1977
Guidelines for Predicting Crop Water Requirements
.
FAO Irrigation and Drainage Paper No. 24
,
FAO
,
Rome
, pp
144
.
Droogers
P.
&
Allen
R. G.
2002
Estimating reference evapotranspiration under inaccurate data conditions
.
Irrigation and Drainage Systems
16
(
1
),
33
45
.
FAO
1988
FAO/Unesco Soil Map of the World, Legend, World Soil Resources Report 60
.
FAO
,
Rome
.
Farahani
H. J.
&
Ahuja
L. R.
1996
Evapotranspiration modeling of partial canopy/residue-covered fields
.
Transactions of the ASAE
39
(
6
),
2051
2064
.
Federer
C. A.
,
Vörösmarty
C.
&
Fekete
B.
1996
Intercomparison of methods for calculating potential evaporation in regional and global water balance models
.
Water Resources Research
32
,
2315
2321
.
Fisher
J. B.
,
DeBiase
T. A.
,
Ye
O.
,
Ming
X.
&
Goldstein
A. H.
2005
Evapotranspiration models compared on a Sierra Nevada forest ecosystem
.
Environmental Modelling & Software
20
,
783
796
.
Frevert
D. K.
,
Hill
B. W.
&
Braaten
B. C.
1983
Estimation of FAO evapotranspiration coefficients
.
Journal of Irrigation and Drainage Engineering ASCE
109
,
265
270
.
Friesland
H.
,
Kersebaum
K.-C.
&
Löpmeier
F.-J.
1998
Operational use of Irrigation Models Using Medium Range Weather Forecast
.
Report of COST 711: Operational Applications of Meteorology to Agriculture, Including Horticulture
, p
79
.
Gavilán
P.
,
Lorite
I. J.
,
Tornero
S.
&
Berengena
J.
2006
Regional calibration of Hargreaves equation for estimating reference ET in a semiarid environment
.
Agricultural Water Management
81
(
3
),
257
281
.
Gebhart
S.
,
Radoglou
K.
,
Chalivopoulos
G.
,
Matzarakis
A.
2012
Evaluation of potential evapotranspiration in Central Macedonia by EmPEst
. In:
Advances in Meteorology, Climatology and Atmospheric Physics
(
Helmis
C. G.
&
Nastos
P. T.
, eds).
Springer Atmospheric Sciences, Springer-Verlag
,
Berlin Heidelberg
, pp.
451
456
.
Greenwood
D. J.
,
Neteson
J. J.
&
Drayscott
A.
1985
Response of potatoes N fertilizer: dynamic model
.
Plant and Soil
85
,
185
203
.
Grismer
M. E.
,
Orang
M.
,
Snyder
R.
&
Matyac
R.
2002
Pan evaporation to reference evapotranspiration conversion methods
.
Journal of Irrigation and Drainage Engineering
128
(
3
),
180
184
.
Ha
W.
,
Kolb
T. E.
,
Springer
A. E.
,
Dore
S.
,
O'Donnell
F. C.
,
Morales
R. M.
,
Masek Lopez
S.
&
Koch
G. W.
2015
Evapotranspiration comparisons between eddy covariance measurements and meteorological and remote-sensing-based models in disturbed ponderosa pine forests
.
Ecohydrology
8
,
1335
1350
.
Hansen
S.
1984
Estimation of potential and actual evapotranspiration
.
Nordic Hydrology
15
,
205
212
.
Hargreaves
G. H.
1975
Moisture availability and crop production
.
Transactions of the ASAE
18
(
5
),
980
984
.
Hargreaves
G. L.
&
Samani
Z. A.
1985
Reference crop evapotranspiration from temperature
.
Applied Engineering in Agriculture
1
(
2
),
96
99
.
Hay
L. E.
&
McCabe
G. J.
2002
Spatial variability in water balance performance in the conterminous United States
.
Journal of the American Water Resources Association
38
,
847
860
.
Irmak
S.
,
Payero
J. O.
,
Martin
D. L.
,
Irmak
A.
&
Howell
T. A.
2006
Sensitivity analyses and sensitivity coefficients of standardized daily ASCE Penman-Monteith equation
.
Journal of Irrigation and Drainage Engineering
132
(
6
),
564
578
.
Jensen
M. E.
,
Burman
R. D.
&
Allen
R. G.
1990
Evapotranspiration and Water Requirements, ASCE Manual 70, American Society of Civil Engineers
,
New York
, p.
332
.
Khoshravesh
M.
,
Sefidkouhi
M. A. G.
&
Valipour
M.
2015
Estimation of reference evapotranspiration using multivariate fractional polynomial, Bayesian regression, and robust regression models in three arid environments
.
Applied Water Science
,
doi:10.1007/s13201-015-0368-x
.
Kisi
O.
2014
Comparison of different empirical methods for estimating daily reference evapotranspiration in Mediterranean climate
.
Journal of Irrigation and Drainage Engineering
40
(
1
).
10.1061/(ASCE)IR.1943-4774.0000664
,
04013002
.
Kolka
R. K.
&
Wolf
A. T.
1998
Estimating Actual Evapotranspiration for Forested Sites: Modifications to the Thornthwaite Model. Res. Note SRS-6
,
USDA Forest Service, Southern Research Station
, p.
7
.
Kottek
M.
,
Grieser
J.
,
Beck
C.
,
Rudolf
B.
&
Rubel
F.
2006
World map of the Köppen-Geiger climate classification updated
.
Meteorologische Zeitschrift
15
(
3
),
259
263
.
Krause
P.
,
Boyle
D. P.
&
Base
F.
2005
Comparison of different efficiency criteria for hydrological model assessment
.
Advances in Geosciences
5
,
89
97
.
Lu
J. B.
,
Sun
G.
,
McNulty
S. G.
&
Amatya
D. M.
2005
A comparison of six potential evapotranspiration methods for regional use in the southeastern United States
.
Journal of American Water Resources Association
41
(
3
),
621
633
.
Mahringer
W.
1970
Verdunstungsstudien am Neusiedler See
.
Archiv für Meteorologie, Geophysik und Bioklimatologie, Serie B
18
,
1
20
.
McGuinness
J. L.
&
Bordne
E. F.
1972
A Comparion of Lysimeter-Derived Potential Evapotranspiration with Computed Values. Technical Bulletin 1452
,
Agricultural Research Service, USDA
,
Washington, DC
, p.
71
.
McNaughton
K. G.
&
Black
T. A.
1973
A study of evapotranspiration from a Douglas fir forest using the energy balance approach
.
Water Resources Research
9
(
6
),
1579
1590
.
Musselman
R. C.
&
Fox
D. G.
1991
A review of the role of temperate forests in the global CO2 balance
.
Journal of the Air & Waste Management Association
41
(
6
),
798
807
.
Nepstad
D. C.
,
de Carvalho
C. R.
,
Davidson
E. A.
,
Jipp
P. H.
,
Lefebvre
P. A.
,
Negreiros
G. H.
,
da Silva
E. D.
,
Stone
T. A.
,
Trumbore
S. E.
&
Vieira
S.
1994
The role of deep roots in the hydrological and carbon cycles of Amazonian forests and pastures
.
Nature
372
,
666
669
.
Penman
H. L.
1948
Natural evaporation from open water, bare soil and grass
.
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
193
(
1032
),
120
145
.
Priestley
C. H. B.
&
Taylor
R. J.
1972
On the assessment of surface heat flux and evaporation using large-scale parameters
.
Monthly Weather Review
100
(
2
),
81
92
.
Rahimikhoob
A.
,
Behbahani
M. R.
&
Fakheri
J.
2012
An evaluation of four reference evapotranspiration models in a subtropical climate
.
Water Resources Management
26
(
10
),
2867
2881
.
Riekerk
H.
1985
Lysimetric evaluation of pine forest evapotranspiration for water balances
. In:
The Forest – Atmosphere Interaction
(
Hutchison
B. A.
&
Hicks
B. B.
, eds).
Reidel Publishing Co.
,
Boston, MA
, pp.
293
308
.
Rosenberg
N.
,
Blad
B.
&
Verma
S.
1983
Microclimate: The Biological Environment
,
Wiley
,
New York
, p.
495
.
Rosenberry
D. O.
,
Winter
T. C.
,
Buso
D. C.
&
Likens
G. E.
2007
Comparison of 15 evaporation methods applied to a small mountain lake in the northeastern USA
.
Journal of Hydrology
340
,
149
166
.
Siegert
E.
&
Schrodter
H.
1975
Erfahrungen mit dem Wasserbilanzschreiber nach Klausing (Experiences on the water balance recorder according to Klausing).
Deutsche Gewasserkundliche Mitteilungen
19
,
167
171
.
Sun
G.
,
Zhou
G.
,
Zhang
Z.
,
Wei
X.
,
McNulty
S. G.
&
Vose
J. M.
2006
Potential water yield reduction due to reforestation across China
.
Journal of Hydrology
328
,
548
558
.
Tabari
H.
,
Grismer
M. E.
&
Trajkovic
S.
2011
Comparative analysis of 31 reference evapotranspiration methods under humid conditions
.
Irrigation Science
31
(
2
),
107
117
.
Trajkovic
S.
&
Kolakovic
S.
2009
Evaluation of reference evapotranspiration equations under humid conditions
.
Water Resources Management
23
,
3057
3067
.
Turc
L.
1961
Estimation of irrigation water requirements, potential evapotranspiration: a simple climatic formula evolved up to date
.
Annals of Agronomy
12
,
13
49
.
Valipour
M.
2014a
Analysis of potential evapotranspiration using limited weather data
.
Applied Water Science
,
doi:10.1007/s13201-014-0234-2
.
Valipour
M.
2014b
Application of new mass transfer formulae for computation of evapotranspiration
.
Journal of Applied Water Engineering and Research
2
(
1
),
33
46
.
Valipour
M.
2015a
Temperature analysis of reference evapotranspiration models
.
Meteorological Applications
22
,
385
394
.
Valipour
M.
2015b
Investigation of Valiantzas’ evapotranspiration equation in Iran
.
Theoretical and Applied Climatology
121
(
1
),
267
278
.
Valipour
M.
2015c
Calibration of mass transfer-based models to predict reference crop evapotranspiration
.
Applied Water Science
,
doi:10.1007/s13201-015-0274-2
.
Valipour
M.
&
Eslamian
S.
2014
Analysis of potential evapotranspiration using 11 modified temperature-based models
.
International Journal of Hydrology Science and Technology (IJHST)
4
(
3
),
192
207
.
Willmott
C. J.
1982
Some comments on the evaluation of model performance
.
Bulletin American Meteorological Society
63
(
11
),
1309
1313
.
WMO
1966
Measurement and estimation of evaporation and evapotranspiration
.
Technical Note No. 83, Geneva (WMO)
,
Quarterly Journal of the Royal Meteorological Society
95
,
444
.
Xu
J.
,
Peng
S.
,
Ding
J.
,
Wei
Q.
&
Yu
Y.
2013
Evaluation and calibration of simple methods for daily reference evapotranspiration estimation in humid East China
.
Archives of Agronomy and Soil Science
59
(
6
),
845
858
.
Xystrakis
F.
&
Matzarakis
A.
2011
Evaluation of 13 empirical reference potential evapotranspiration equations on the island of Crete in Southern Greece
.
Journal of Irrigation and Drainage Engineering
137
(
4
),
211
222
.
Zhang
L.
,
Dawes
W. R.
&
Walker
G. R.
2001
Response of mean annual evapotranspiration to vegetation changes at catchment scale
.
Water Resources Research
37
(
3
),
701
708
.