Water Resour Manage (2012) 26:2867–2881 DOI 10.1007/s11269-012-0054-9
An Evaluation of Four Reference Evapotranspiration Models in a Subtropical Climate Ali Rahimikhoob & Mahmood Reza Behbahani & Javad Fakheri
Received: 15 September 2010 / Accepted: 8 May 2012 / Published online: 24 May 2012 # Springer Science+Business Media B.V. 2012
Abstract This paper describes a detailed evaluation of the performance and characteristic behaviour of four equations for estimating reference evapotranspiration (ET0) at eight meteorological sites in a subtropical climate. The equations assessed were: Makkink (MK), Turc (TC), Priestley–Taylor (PT) and Hargreaves (HG). The sites were distributed throughout the north of Iran and represent an intermediate humidity regime. The Penman– Monteith (PM) method was chosen as the standard for comparison and calibration of the above—mentioned four equations. Good correlation was found between the ET0 values estimated by each of the four empirical equations and the PM method for all the locations; however MK and TC equations produced considerable underestimations. The performance of the PT and HG equations improved slightly after region-specific coefficients were developed for each equation, and the TC and MK equations were improved greatly. The modified PT equation turned out to be the most precise method, demonstrating superiority over the other methods evaluated (0.48 mm d−1 of root mean square error (RMSE)). Good performance from the modified HG equation (0.53 mm d−1 of RMSE) must be emphasized, given the simplicity of that method, which only requires maximum and minimum air temperature data. Keywords Reference evapotranspiration . ET0 equations . Estimation . Subtropical climate . Iran
1 Introduction Accurate estimation of reference evapotranspiration (ET0) is needed for water resources management, farm irrigation scheduling, and environmental assessment. A large number of methods have been developed for assessing ET0 from meteorological data. The Penman– Monteith (PM) method is recommended by FAO as the sole method to calculate reference A. Rahimikhoob (*) : M. R. Behbahani : J. Fakheri Department of Irrigation and Drainage Engineering, Aburaihan Campus, University of Tehran, Tehran, Iran e-mail:
[email protected]
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evapotranspiration wherever the required input data are available (Allen et al. 1998; Droogers and Allen 2002). The PM is a physically based approach, which requires air temperature, relative humidity, solar radiation, and wind speed. The details of the PM equation are provided in the FAO’s Irrigation and Drainage Paper no. 56 (Allen et al. 1998). Unfortunately, there is a limited number of meteorological stations even in developed countries where these climatic variables are accurately measured. The weather input data for the FAO-56 Penman–Monteith (PM56) equation are expensive and often difficult to obtain for practical applications (Di Stefano and Ferro 1997). The weather variables that are used in PM equation can potentially introduce certain amounts of measurement and/ or computational errors, resulting in cumulative errors in the calculated ET0. Systematic and/or random errors in weather variables can lead to significant errors in estimated ET0 (Meyer et al. 1989). Under these conditions, simplified or empirical equations, which require fewer input parameters, should be considered. Empirical ET0 models that require fewer variables exist. Estimates made by these models, particularly in site-specific studies when using weather data as input, are influenced by the inter-relationships between the weather variables. In the past decade, considerable attention has been focused on the evaluation of these models. Suleiman and Hoogenboom (2007) evaluated Priestley–Taylor (PT) ET0 estimation method by comparing the estimates with results from the PM56 method under the humid climatic conditions in Georgia. They found that significantly difference in ET0 values exist among PT method, especially in the coastal and mountainous areas. Douglas et al. (2009) compared the performance of Turk (TC), Priestley–Taylor (PT) and the PM56 methods for estimating potential evapotranspiration in humid climates in Florida. They concluded that the PT performance appears to be superior to the other two methods for a variety of land covers in Florida. Trajkovic and Kolakovic (2009) evaluated five ET0 estimation methods by comparing the estimates with results from the PM56 equation under humid conditions. They showed that Turc’s method gave the best ET0 estimates and ranking first, and other equations ranked in decreasing order are: Priestley–Taylor, Jensen–Haise, Thornthwaite, and Hargreaves (HG). Tabari (2010) evaluated four simpler models based on monthly performance for Various Climates in Iran. The author reported that the Makkink (MK) and PT models estimated ET0 values less accurately than TC and HG models for the all climates. Weather variables as input can have significant impacts on simulation model estimates, particularly when due to introduced errors arising from supplementary estimated data (Rivington et al. 2005). Therefore, to select the most appropriate method for calculating ET0, various forms of existing empirical evapotranspiration formulas should be analyzed and compared, and a calibrated model should be developed from these methods. This paper investigates the performance of four empirical daily ET0 methods (Makkink, Turc, Priestley–Taylor and Hargreaves) by comparing them against the PM56 method using data collected in a subtropical climate of Iran. These models were chosen as they utilise commonly available data and are representative of the best state of such model development. The aim was to determine the performance of each method and identify patterns of characteristic behaviour of estimates. Such information was considered as important when deciding which method to use. The PM56 method was chosen as a standard for comparison in this study because there were no measured ET0 data at any location, as this is the standard procedure used when no measured lysimeter data are available (Irmak et al. 2003; Utset et al. 2004; Vanderlinden et al. 2004). The daily ET0 values estimated by the empirical above methods were compared with estimates by the standard PM56 method.
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2 Materials and Methods 2.1 Study Area This study was conducted on the southern coast of the Caspian Sea (SCCS) situated in the north of Iran, which lies between latitudes 36.1°N and 38.4°N and between longitudes 48.6°E and 53.7°E. The Caspian Sea, which is the largest continental water body on earth, is situated in west Asia, east of Caucasus and north of the Alburz Mountains. Its elevation is approximately 28 m below sea level. The southern coast of the Caspian Sea has a subtropical climate characterized by warm summers and mild winters (Rodionov 1994; Kosarev and Yablonskaya 1994). The average annual rainfall ranges from 530 mm in the east to 1,350 mm in the west and occasionally reaches as high as 2,000 mm in the west. Based on the climatic data from meteorological stations, the maximum rainfall is experienced during spring and late fall and winter. Additionally, the relative humidity is constantly high, with an average value that fluctuates from 74.6 % in the east to 84.6 % in the west, and that rarely drops below 60 %. The air temperature reaches its maximum in August and its minimum in January. According to the climatic data from meteorological stations, the average annual temperature along the Caspian coast over the past decade has varied from 15 °C in the west to 17.5 °C in the east. The maximum daily temperature of the warmest month ranges from 28 °C to 35 °C, while that of the coldest month ranges from 1.5 °C to 4 °C. Summer temperature ranges from 20 °C to 30 °C. The most important irrigated crop in this region is rice, which encompasses 560 thousand ha. 2.2 Data Meteorological data were obtained from eight manual weather stations in the study area with varying latitudes, longitudes and elevations (Fig. 1). Information regarding the sites, years for which complete weather data are available for each location, and mean annual values of relevant weather variables are given in Table 1. The sites include the daily maximum and minimum air temperature (Tx and Tn), relative humidity (RH), windspeed and daily sunshine hours (n). Measurements were made at a height of 2 m (air temperature and relative humidity) and 10 m (windspeed) above the soil surface. Wind speed data at 2 m (U2) were
Fig. 1 Spatial distribution of the eight meteorological stations used in the study (see Table 1 for weather station codes)
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Table 1 Summary of weather station sites and mean observation data Tx (°C) Tn (°C) RH (%) U (m/s)
Station
Code Lat. (°N) Lon. (°E) Alt. (m) Period
Amol
AM
36.48
52.38
23.7
2001–2004
22.5
14.6
77.2
1.6
Astara
AS
38.42
48.87
−18.0
1996–2005
19.5
12.6
83.0
0.9
Babolsar
BA
36.71
52.65
−21.0
1996–2005
21.5
14.6
81.5
1.6
Ghaemshahr GH Noshahr NO
36.45 36.65
52.77 51.50
14.7 −20.9
1996–2004 1996–2005
22.5 20.2
14.0 13.7
83.2 84.4
1.5 1.7
Ramsar
RM
36.90
50.67
−20.0
1996–2005
19.7
13.7
81.9
1.7
Rasht
RA
37.2
49.65
36.7
1996–2005
21.6
13.6
84.5
0.9
Sari
SA
36.55
53.50
23.0
2000–2005
22.3
13.8
79.1
1.4
obtained from those taken at 10 m using the log-wind profile equation. Data integrity was evaluated using methods similar to those suggested by Allen (1996). Daily Tx , Tn, RH, U2 and n values were compared with the long-term extremes and did not indicate any major deviations. 2.3 The FAO Penman–Monteith and Empirical Methods In this study, the performance of empirical methods were compared with the conventional FAO-56 Penman–Monteith method. Although in practice, the best way to test the performance of the empirical methods would be to compare their performances against lysimetermeasured data; this type of data set is not available in the study area. The following equation was applied for the PM (Allen et al. 1998): ET0 ¼
0:408ΔðRn GÞ þ g Ta900 þ273 U2 ðes ea Þ Δ þ g ð1 þ 0:34U2 Þ
ð1Þ
where ET0 is reference crop evapotanspiration (mm d−1), Rn is the daily net radiation (MJ m−2 d−1), G is the daily soil heat flux (MJ m−2 d−1), Ta is the mean daily air temperature at a height of 2 m (°C), U2 is the daily mean wind speed at a height of 2 m (m s−1), es is the saturation vapor pressure (kPa), ea is the actual vapor pressure (kPa), Δ is the slope of the saturation vapor pressure versus the air temperature curve (kPa °C−1), and γ is the psychrometric constant (kPa °C−1). The terms in the numerator on the right-hand side of the equation are the radiation term and aerodynamic term, respectively. In this study, the daily values of Δ, Rn, es and ea were calculated using the equations given by Allen et al. (1998). For Rn, an albedo of 0.23 (green vegetation surface) was used. Since G is usually small compared with Rn and is difficult to measure, it was assumed to be zero over the calculation time step period (daily and monthly) (Allen et al. 1998). The measured RH, Tx and Tn values were used to calculate ea and es. The daily solar or shortwave radiation (Rs) was calculated using the Angstrom formula, which relates solar radiation to extraterrestrial radiation and relative sunshine duration. Eq. (39) in Allen et al. (1998) was used to calculate the net outgoing longwave radiation. Empirical ET0 models generally rely on micrometeorological data such as air temperature, radiation, wind speed and humidity. Of the great variety of ET0 models, four equations were chosen for evaluation in this study: the Makkink (MK) method (Makkink 1957), the Turc (TC) method (Turc 1961), the Priestley–Taylor (PT) method (Priestley and Taylor 1972), and the Hargreaves (HG) method (Hargreaves and Samani 1985). The MK model
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was designed in 1957 in the Netherlands as a modification of Penman (1948) after comparing the Penman model to lysimetric data (Allen 2003; Makkink 1957). Currently, MK is popular in Western Europe (Allen 2003) and has been used successfully in the U.S. (see Amatya et al. 1995). Allen (2003) gives the operational form of the MK model as: ET0 ¼ 0:61
Δ Rs 0:12 Δþg l
ð2Þ
where Rs is solar radiation (MJ m−2 day−1) and λ is the latent heat of vaporization (MJ kg−1). The Turc (1961) model was also designed for use in Western Europe and was a simplification of an older equation (Jensen et al. 1990). Turc equation has been used to some extent in the United States (e.g., Amatya et al. 1995). As defined for operational use by Allen (2003): ET0 ¼ aT 0:013
Ta 23:8856Rs þ 50 Ta þ 15 l
ð3Þ
The coefficient aT is a humidity-based value. If the mean daily relative humidity (RH) is greater than or equal to 50 %, then aT 01.0. If the mean daily relative humidity is less than 50 %, then aT has the value of: 50 RH ð4Þ aT ¼ 1 þ 70
Fig. 2 Variation of daily net radiation for the eight meteorological stations used in the study, during the years studied. Vertical dashed lines delineate the beginning of each season. (see Table 1 for weather station codes)
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The Priestley-Taylor model is essentially a shortened version of the original Penman (1948) combination equation (Jensen et al. 1990). Priestley and Taylor (1972) showed that, when large land areas become saturated, net radiation is the dominant factor affecting evapotranspiration. They showed that under equilibrium conditions, the advection or mass transfer (aerodynamic) term of the original Penman equation tends toward a constant fraction of the radiation term. The equation according to Priestley and Taylor (1972) takes the following form: ET0 ¼
a Δ ðRn GÞ l Δþg
ð5Þ
α is the Priestley–Taylor constant and equal 1.26, which accounts for the fact that the atmosphere does not generally attain saturation (Priestley and Taylor 1972). The HG equation is the simplest one for practical use, among the above—mentioned ET0 equations, because only air temperature data are required. Allen et al. (1998) have proposed that when sufficient or reliable data to solve the PM equation are not available then the HG equation can be used. The HG equation (Hargreaves et al. 1985) requires only daily maximum and minimum air temperature, usually available at most weather stations worldwide, and an estimate of extraterrestrial radiation (Droogers and Allen 2002). Extraterrestrial radiation can be calculated for a certain day and location, therefore only minimum and maximum
Fig. 3 Variation of daily reference evapotranspiration for the eight meteorological stations used in the study, during the years studied. Vertical dashed lines delineate the beginning of each season. (see Table 1 for weather station codes)
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temperatures require observation. This method behaves best for weekly or longer predictions although some accurate ET0 daily estimations have been reported in the literature (Hargreaves and Allen 2003). The form of the HG equation presented in FAO 56 by Allen et al. (1998) is: ð6Þ ET0 ¼ 0:0023 Ra ðTa þ 17:8Þ ðTx Tn Þ0:5 where Ra is the water equivalent of the extraterrestrial radiation (mm d−1) computed according to Allen et al. (1998). All of the terms are the same as for the PM equation (Eq. 1). Allen et al. (1998) recommended local calibration of the empirical ET0 equations in monthly or annual basis to produce reliable estimates. They suggest performing a linear regression. In it, ET0 values obtained by empirical models are compared with ET0 values measured by lysimeters or with PM56 estimated ET0 value. Landeras et al. (2008) used the above calibration on a daily basis for Northern Spain. Here, daily data from several stations are grouped, so as to produce patterns with higher spatial applicability. The regression equations computed are of the form: Y¼mXþC
ð7Þ
Where Y represents the PM56 daily ET0; X is the daily ET0 estimated from each of the other four methods; and m and C are the regression constants. In this study, to calibrate the
Fig. 4 Variation of daily relative humidity for the eight meteorological stations used in the study, during the years studied. Vertical dashed lines delineate the beginning of each season. (see Table 1 for weather station codes)
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empirical ET0 equations, data from Amol, Astara, Ghaemshahr, and Ramsar with a wide range of latitudes, longitudes, and elevations were collected into one group to produce regional regression coefficients that could be applied to estimate ET0 for different locations in the SCCS. After the calibrating process, data from four other sites, Noshahr, Babolsar, Rasht, and Sari, were used to validate the regression coefficients. 2.4 Statistical Parameters The results from the ET0 estimates obtained from the calibrated equations were compared with the ET0 results obtained using the PM equation. This comparison was conducted by using four statistical indices: The coefficient of determination (R2), the root mean square error (RMSE), the relative error (RelRMSE) and the ratio between average ET0 estimations (R). These indices are defined as follows: N 2 P Pi P Oi O R2 ¼
i¼1
N P i¼1
N 2 P 2 Pi P Oi O
ð8Þ
i¼1
Fig. 5 Variation of daily wind speed for the eight meteorological stations used in the study, during the years studied. Vertical dashed lines delineate the beginning of each season. (see Table 1 for weather station codes)
An Evaluation of Four Reference Evapotranspiration Models
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMSE ¼ t ðPi Oi Þ2 N i¼1
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ð9Þ
RelRMSE ¼ RMSE=O
ð10Þ
R ¼ P=O
ð11Þ
where N is the number of observations, P is the ET0 estimated using the empirical equations and O is ET0 calculated using the PM method, overbars are average values. The lower the value for RMSE, the better the agreement.
3 Results and Discussion Before comparing ET0 models, the characteristics of the climatic and ET0 values estimated by PM method were evaluated. Figures 2, 3, 4 and 5 show the variation of daily net radiation, reference evapotranspiration, wind speed and relative humidity for all eight sites. In these figures seasons were demarcated by the Julian day (JD) of their calendar start and end dates (winter: December 21 through March 20 (JD 355–79); spring: March 21 through June 20 (JD 80–171); summer: June 21 through September 20 (JD 172–263); and fall: September 21 through December 20 (JD 264–354)). It may be observed, that these sites
Fig. 6 Scatter plots of the ET0 values estimated using the PM and four empirical equations at eight locations in the SCCS. a Makkink method, b Turc method, c Priestley–Taylor method and d Hargreaves method. The 1:1 line is shown for reference. (see Table 1 for weather station codes)
−1
0.82
0.77
1.03
0.72
0.85
0.90
0.64 0.76
AS
BA
GH
NO
RM
RA SA
26.30 29.68
39.12
36.31
27.44
39.11
33.19
30.66
RMSE (mm d ) RelRMSE (%)
Makkink
AM
Station code
0.90 0.91
0.89
0.89
0.92
0.91
0.92
0.90
R
2
−1
1.71 1.84
1.76
1.76
1.85
2.03
1.76
1.89
70.42 71.92
76.35
75.04
70.81
77.06
75.87
70.85
RMSE (mm d ) RelRMSE (%)
Turc
Table 2 Evaluation of the various methods of calculating daily ET0 before calibration
0.90 0.91
0.89
0.88
0.91
0.91
0.92
0.90
R
2
0.66 0.52
0.48
0.51
0.59
0.46
0.47
0.51
27.12 20.52
20.87
21.68
22.50
17.63
20.27
18.89
RMSE (mm d ) RelRMSE (%)
−1
Priestley– Taylor
0.90 0.90
0.89
0.88
0.90
0.93
0.92
0.89
R
2
0.75 0.60
0.45
0.51
0.68
0.49
0.51
0.56
31.14 23.44
19.69
21.88
25.93
18.68
21.87
20.78
RMSE (mm d−1) RelRMSE (%)
Hargreaves
0.92 0.92
0.91
0.89
0.93
0.92
0.93
0.90
R2
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exhibit same climatic characteristics. In general, the highest daily Rn was observed during late spring to mid summer, not surprisingly, the highest ET0 values also occurred in this period with an average of 4.5 mm d−1. At all sites the majority of RH values lies above 75 % and rarely drops below 50 % implying an intermediate humidity regime. As for the wind velocity regime, all sites have constantly low velocities ranging little from 0.5 m s−1 to 3 ms−1. Figure 6 shows scatter plots of the ET0 values estimated using the PM56 and different empirical models (Makkink, Turc, Priestley–Taylor and Hargreaves) at eight locations in the SCCS. As seen from the scatter plots, site location has little effect on the performance of each equation. This indicates that differences between equations rather than differences in data collected are the sites dominate differences in the ET0 estimates. PT and HG methods compared very well with PM56 values, with all ET0 data appear to be well distributed along the 1:1 line. TC and MK methods compared less favourably, and underestimated the ET0 PM56 at all locations. This underestimation was constant throughout the study area. The statistical summary of a comparison between the daily ET0 estimated by the PM56 method and by four empirical models at eight locations in the SCCS is presented in Table 2. The results revealed that all methods produced only slight variability from one location to another. Among these methods, the TC method had the largest error, at 70–77 %, and the PT and HG methods had the lowest error, at 17–31 %. Moreover, comparison indicated that all methods yield large coefficient of determination (R2 >0.88), which means calibration of the equations using simple linear regression improves the equations performances. The four empirical methods were calibrated using data from calibration data (data set from Amol, Astara, Ghaemshahr, and Ramsar). The resulted regression equations together with the determination coefficient are presented in Fig. 7. The high values of coefficient of determination (R2 >0.90) for all methods showed that there was good linear regression between these methods and PM56 method. When slope values of the straight regression lines are concerned, PT and HG had the lowest value with m00.94 and TC had the highest value with m02.77. Concerning the intercept of the Fig. 7 Scatter plots of the ET0 values estimated using the PM and four empirical equations for whole data set of calibration locations. a Makkink method, b Turc method, c Priestley–Taylor method and d Hargreaves method. Resulted regression equations together with the determination coefficient are presented
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Table 3 Evaluation of the various methods of calculating daily ET0 after calibration
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R2
R
24.49
0.89
0.89
23.67
0.89
0.90
0.48
19.04
0.91
0.93
0.53
20.85
0.90
0.91
Impirical methods
RMSE (mm d−1)
RelRMSE (%)
Makkink
0.60
Turc
0.58
PT HAR
regression equations, HG method resulted in an intercept close to zero (C0−0.11). As has been noticed in Fig. 6, again Fig. 7 shows that the TC estimate is the worst when the regression equation’s slope and intercept are concerned. The calibrated equations were used on the data set from validation locations (Noshahr, Babolsar, Rasht, and Sari) and compared with the daily ET0 values estimated by PM56
Fig. 8 Scatter plots of the ET0 values estimated using the PM and four calibrated empirical equations at four test locations. a Makkink method, b Turc method, c Priestley–Taylor method and d Hargreaves method. (see Table 1 for weather station codes)
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method. This comparison was conducted with whole data set of test locations. Table 3 shows the results of this comparison, through simple regression analysis, between the values calculated by various methods and PM56 estimations, indicating the calculation of error. The four methods of calculation were taken as independent variables and the estimations made using PM56 method, as the dependent variable. The PT offers the best performance, although it gives a slight underestimation (approximately 7 %), with a RMSE of 0.48 mm d−1, equivalent to a relative error under 19.04 %. It presents a coefficient of determination (R2) over 0.90. Next to PT equation, the best performance was shown by the HG method. It gave way to a slight underestimation and showed the second lowest RMSE value (0.53 mm d−1), which means a relative error of approximately 20.85 %. The good performance that this method presents must be emphasized, since it deals with a very simple equation that only requires measuring maximum, minimum and mean air temperatures. The TC method underestimated daily ET0 values during the entire period studied, with a RMSE of 0.58 mm d−1, which is equivalent to a relative error under 24 %. The MK method is the one that demonstrated the worst performance, due to the highest underestimations it presented, with a RMSE of 0.60 mm d−1, equivalent to a relative error near 24.49 %. Good coefficients of determination (R2) were obtained in all cases, with values above 0.89. Figure 8 shows graphs of the regressions from the four methods compared to PM estimations for test locations. It can be seen that after modification all methods provided quite good agreement with the evapotranspiration obtained using the PM method and provided reliable estimates for all locations. All empirical methods gave a small underestimation when ET0 was over 3.5 mm d−1 approximately; under this value the slope of the straight line is near 1 and coincides perceptibly to the intercept, which indicates the correct performance of the all
Fig. 9 Comparison of monthly ET0 calculated by PM56 and four calibrated empirical equations at four test locations. a Makkink method, b Turc method, c Priestley–Taylor method and d Hargreaves method. (see Table 1 for weather station codes)
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empirical methods in this interval. The results revealed that after calibration these methods produced only slight variability from one location to another and based on these results, the four empirical methods, after modification, can be recommended for utilization in a regional study. The comparison of monthly total ET0 estimations calculated using the PM56 and the four calibrated methods and for the four test sites are shown in Fig. 9. These monthly data computed using the daily ET0 were combined to produce monthly averages for the entire year for each site. It can be seen that, Although there is a little underestimation ET0 during the summer season, but in general the evolution of ET0 values estimated using all four calibrated models agreed well over time with the ET0 estimated using the PM56 method.
4 Conclusions Four equations for calculating daily ET0 were computed using daily meteorological data from eight stations in a subtropical climate (north of iran). The evaluation and comparison were made based on both the original equations and the calibrated equations. When using the original equations, the TC and MK equations produced large errors, underestimating the evapotranspiration rates. The comparison results show that before calibration, the PT and HG equations are more applicable in an intermediate humidity region. The performance of the PT and HG equations improved slightly after the calibration; however the TC and MK equations improved greatly. Considering the limitations associated with the availability and reliability of the climatological data, especially in developing countries, the good performance of HG method must be emphasized, since it deals with a very simple equation that only requires measuring maximum and minimum air temperature. Acknowledgments The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved the content of the article. This study was done in Department of Irrigation and Drainage Engineering, Aburaihan Campus, University of Tehran.
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An Evaluation of Four Reference Evapotranspiration Models
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