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O R I G I N A L P A P E R
Evaluation of radiation methods to study potentialevapotranspiration of 31 provinces
Mohammad Valipour
Received: 24 April 2014 / Accepted: 6 October 2014
Springer-Verlag Wien 2014
Abstract The present study aims to calibrate radiation-
based methods to determine the best method under differ-ent weather conditions. For this purpose, weather data was
collected from different synoptic stations in all of prov-
inces of Iran. The potential evapotranspiration was esti-
mated using common radiation-based methods and a
sensitive analysis was done for investigating variations of
the methods. The results show that the Stephens method
estimates the potential evapotranspiration better than other
methods in the most provinces of Iran (10 provinces).
However, the values of R2 were less than 0.98 for 15
provinces of Iran. The calibrated methods estimated the
potential evapotranspiration in the south east of Iran better
than other provinces. Precision of the methods calibrated
has been increased in all provinces. The R2 values are less
than 0.98 for only six provinces (WA, EA, GO, NK, AL,
and QO). In the methods calibrated, the Abtew (for YA)
estimated the potential evapotranspiration better than the
other methods.
1 Introduction
It is possible to calculate the actual evapotranspiration
using crop coefficients and potential evapotranspiration.
To this end, FAO PenmanMonteith method (Allen et al.
1998) is presented. Although this method has been applied
in various regions of the world (Chiew et al. 1995;
Estevez et al. 2009; Ley et al. 2009; Moeletsi et al. 2013;Sahoo et al.2012; Valiantzas2013; Valipour2012a,b), it
needs too many parameters to estimate the potential
evapotranspiration. In the most regions, as weather data is
limited, it is not possible to use FPM. Therefore, empirical
methods including mass transfer, radiation, temperature,
and pan evaporation-based methods have been developed
for estimation of the potential evapotranspiration using
limited data. The radiation-based method is one of the
most widely used methods for estimating potential
evapotranspiration. The common radiation-based methods
include the Abtew (1996), Makkink (1957), Priestley-
Taylor (1972), Turc (1961), Xu et al. (2008), Modified
Copais (Alexandris and Kerkides 2003; Alexandris et al.
2006, Jensen-Haise 1963, Doorenbos-Pruitt 1977,
McGuinness and Bordne 1972, Stephens-Stewart Jensen
1966, Stephens and Stewart 1963, Jones-Ritchie1990and
Irmak et al. 2003). A thorough review should be done to
find weakness points of the previous studies. Table1
summarizes these studies.
In addition there are a lot of investigations that com-
pared different methods of estimation of evapotranspiration
in Iran (Rahimi et al.2014; Valipour2014k,l,m,n,o,p,q,
r, s; Valipour and Eslamian 2014). However, in the pre-
vious studies (Table1), one or more of the radiation-based
methods are compared with temperature, mass transfer, or
pan evaporation-based methods. In other cases, there are
some methods which can estimate the potential evapo-
transpiration better than the radiation-based methods. This
is because the previous studies focus on specific weather
conditions and/or do not consider radiation-based methods.
Furthermore, the results of the previous studies are not
useable for estimating potential evapotranspiration in other
regions, because they are recommended for one or more
Responsible Editor: L. Gimeno.
M. Valipour (&)
Young Researchers and Elite Club, Kermanshah Branch, Islamic
Azad University, Kermanshah, Iran
e-mail: [email protected]
1 3
Meteorol Atmos Phys
DOI 10.1007/s00703-014-0351-3
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7/23/2019 Evaluation of radiation methods to study potential evapotranspiration of 31 provinces
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Table 1 Summarization of the previous studies
References Methods compared/evaluated Study
region
Main conclusion
Gunston and
Batchelor
(1983)
Priestley-Taylor and FPM Tropical
countries
The Priestley-Taylor equation offers a satisfactory
alternative to the Penman equation for estimating in
humid tropical climates
Green et al.
(1984)
Lysimeter and Priestley-Taylor New
Zealand
Daily measurements of the potential evapotranspiration
by the lysimeter agreed reasonably well with
Priestley-Taylor estimates
Al-Shalan and
Salih (1987)
Jensen-Haise, Ivanov, Behnke-Maxey, Stephens-
Stewart
Saudi
Arabia
The top six ranked methods obtained are ranked in the
following order of merit: Jensen-Haise, class A pan,
Ivanov, adjusted class A pan, Behnke-Maxey,
Stephens-Stewart
Foroud et al.
(1989)
Jensen-Haise and FPM Canada Incorporating the wind parameter in the Jensen-Haise
equation significantly improved the potential
evapotranspiration estimates
Abbaspour
(1991)
Priestley-Taylor, Jensen-Haise, Hargreaves,
Thornthwaite
USA After calibration, six of the eight methods had
predictive power and fit that were not significantly
different at the 5 % level
McKenney and
Rosenberg
(1993)
Thornthwaite, Blaney-Criddle, Hargreaves, Samani-
Hargreaves, Jensen-Haise, Priestley-Taylor,
Penman
North
American
Great
Plains
The results indicate that the methods differ, in some
cases significantly, in their sensitivities to
temperature and other climate inputs. The differences
among methods can be attributed both to differences
in their sensitivities to climate, to differences in the
climatic factors they consider
Garatuza-Payan
et al. (1998)
Makkink and FPM Mexico The good performance of the Makkink formulation is
particularly encouraging because this equation
requires only incoming solar radiation, which can be
readily estimated from remotely sensed data
de Bruin and
Stricker
(2000)
Makkink and FPM Netherlands T he Makkink method appears to be attractive for
practical applications
Xu and Singh
(2000)
Abtew, Hargreaves, Makkink, Priestley-Taylor, Turc Switzerland The Makkink and modified Priestley-Taylor equations
resulted in monthly evaporation values that agreed
most closely with pan evaporation
Al-Ghobari
(2000)
Jensen-Haise and Blaney-Criddle Saudi
Arabia
No one method provided the best results under all
weather conditions
Xu and Singh
(2002)
Priestley-Taylor, Makkink, Hargreaves, Blaney-
Criddle, Rohwer
Switzerland Further examination of the performance resulted in the
following rank of preciseness as compared with the
FPM estimates: Priestley-Taylor, Makkink,
Hargreaves, Blaney-Criddle, Rohwer
Howell et al.
(2005)
Priestley-Taylor and the Hargreaves-Samani USA Both the Priestley-Taylor and the Hargreaves-Samani
methods under estimated the potential
evapotranspiration computed by the FPM
Liu and Lin
(2005)
Priestley-Taylor and FPM China Care should be taken when applying the Priestley
Taylor equation in the semiarid climate in north
China
Lu et al. (2005) Thornthwaite, Hamon, Hargreaves-Samani, Turc,
Makkink, Priestley-Taylor
USA The Priestley-Taylor, Turc, Hamon methods are
recommended for regional applications in thesoutheastern US
Xu et al. (2006) FPM and pan evaporation China The reference evapotranspiration is most sensitive to
the net total radiation, followed by relative humidity,
air temperature and wind speed
Alexandris
et al. (2006)
Modified Copais, ASCE PenmanMonteith, CIMIS
Penman, HargreavesSamani
Greece The Modified Copais method may become a useful tool
for routine daily potential evapotranspiration
estimations
Kisi (2007) Penman, Hargreaves, Turc USA The Hargreaves method provides better performance
than the Penman and Turc methods in estimation of
the potential evapotranspiration
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Table 1 continued
References Methods compared/evaluated Study
region
Main conclusion
Suleiman and
Hoogenboom
(2007)
Priestley-Taylor and FPM USA The Priestley-Taylor method overestimated the
potential evapotranspiration and was less precise than
the FAO PenmanMonteith
Guven et al.
(2008)
CIMIS PenmanMonteith, FPM, Hargreaves-
Samani, Jensen-Haise, Jones-Ritchie, Turc
USA Genetic programming produces quite satisfactorily
results and can be used as an alternative to the
conventional models
Bois et al.
(2008)
Turc, PriestleyTaylor, Hargreaves France Radiation-based methods were more accurate and more
precise than Hargreaves method
Shi et al. (2008) PriestleyTaylor, KaterjiPerrier, Todorovic China The PriestleyTaylor method was effective enough to
estimate large time-scale evapotranspiration
Trajkovic and
Kolakovic
(2009a)
Turc, PriestleyTaylor, JensenHaise, Thornthwaite USA Turc method is most suitable for estimating potential
evapotranspiration at humid locations when weather
data are insufficient to apply the FPM
Douglas et al.
(2009)
Priestley-Taylor, Turc, PenmanMonteith USA The Priestley-Taylor performance appears to be
superior to the Turc and PenmanMonteith methods
Ye et al. (2009) Priestley-Taylor and FPM China The Priestley-Taylor method was more suitable for
Tibetan Plateau in the absence of the parameters
necessary for the calculation of the FPMMartinez and
Thepadia
(2010)
Turc, Hargreaves and FPM USA The Turc equation is recommended for estimating
potential evapotranspiration using measured
maximum and minimum temperature and estimated
radiation
Jacobs et al.
(2010)
Makkink and FPM Netherlands The authors estimated the potential evapotranspiration
by the Makkink method successfully
Zhai et al.
(2010)
Hargreaves, Makkink, Turc, PriestleyTaylor,
JensenHaise, Doorenbos-Pruitt, Abtew,
McGuinness-Bordne, Rohwer, BlaneyCriddle
China Calibration can be used to modify the potential
evapotranspiration equations
Kisi (2011) wavelet regression, CIMIS Penman, Hargreaves,
Ritchie, Turc
USA The wavelet regression models were found to perform
better than the empirical models
Li et al. (2011) Priestley-Taylor and FPM Central
Asia
The PriestleyTaylor model was only able to yield a
fair estimation of the referenceevapotranspiration
during some periods of the growing season
Thepadia and
Martinez
(2012)
Turc and HargreavesSamani USA Using the regionally calibrated radiation estimates, the
original Turc method was found to underestimate
potential evapotranspiration
Medeiros et al.
(2012)
Camargo and Jensen-Haise Brazil Both proposed methodologies showed good agreement
with the standard method indicating that the
methodology can be used for local potential
evapotranspiration estimates
Er-Raki et al.
(2012)
Makkink, PriestleyTaylor, HargreavesSamani Morocco
and
Mexico
The HargreavesSamani model is the most precise one
for estimating the spatio-temporal variability of the
potential evapotranspiration
Le et al. (2012) Hamon, PriestleyTaylor, Thornthwaite, Blaney
Criddle, Turc, FPM
Vietnam In highly structured (land use and elevation) regions,
not all methods provide satisfying results
Li et al. (2013) Temporal variations in reference evapotranspiration China The wind speed was the main likely influence factor inthe river
Ngongondo
et al. (2013)
HargreavesSamani and PriestleyTaylor Malawi The FPM method computed with estimated climate
variables instead of observed climate variables still
outperformed both the methods if their original
parameters and estimated radiation were used
Jakimavicius
et al. (2013)
Dalton, Trabert, Meyer, WMO, Mahringer,
Thornthwaite, Schendel, Hargreaves-Samani
Baltic The Thornthwaite and Schendel gave the most precise
assessment
Cammalleri and
Ciraolo
(2013)
The Makkink (MAK) method and a deterministic
procedure for estimating air temperature inputs
used in the MAK method (named RS)
Italy The differences between MAK and RS approaches
were negligible at all analyzed temporal scales
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climatic conditions. However, a climatic condition contains
various values of weather parameters and results of each
research is not applicable for other regions without deter-
mining specified ranges of each weather parameter even if
climatic conditions are the same for both regions. In
addition, the governments cannot schedule for irrigationand agricultural water management when the potential
evapotranspiration is estimated for a basin, wetland,
watershed, or catchment instead a state or province and/or
number of weather station used is low. Therefore, this
study aims to estimate potential evapotranspiration for all
of provinces of Iran by using common radiation-based
methods to determine the best method based on the weather
conditions of each province as well as analysing sensitivity
of the methods.
2 Study area and Methodology
In this study, monthly weather information (from 1951 to
2010) is collected from 181 synoptic stations of 31 prov-
inces in Iran. Table 2shows the position of each province,
number of years that data was measured, and number of
stations.
In each station, average monthly weather data in years
measured is considered as value of that weather parameter in
each month (e.g. value of solar radiation in June for NK is
average of 24 data collected). A spatial interpolation method
is usually used to obtain an averaged value from stations.
However, the most of synoptic stations have been distributedin north, south, west, and east of each province based on
different weather conditions and considering equal spatial
distances to skip spatial interpolation method. Therefore,
average of data in all stations has been considered as value
of that weather parameter in each month for provinces with
more than one station (e.g. value of relative humidity in June
for KH is average of 55 9 14 = 770 data collected). All of
the data mentioned were used for estimating the potential
evapotranspiration using 22 radiation-based methods and
compared with FAO PenmanMonteith (FPM) method to
determine the best method based on the weather conditions
of each province (Table3).
The best method for each province and the best per-
formance of each method were determined using the belowerror indices:
R2 1
P12i1
ETFPMi ETmi 2
P12i1
ETFPMiP12i1
ETFPMi
12
0B@
1CA
2 1
MBE P12i1
ETFPMi ETmi 12
2
In which, i indicates month, ETFPM indicates thepotential evapotranspiration calculated for FAO Penman
Monteith (FPM) method, ETm indicates the potential
evapotranspiration calculated for radiation-based methods,
and MBE is mean bias error (MBE).
The best method for each province was modified to
increase precision of estimating by calibration of the
coefficients (Table3) similar to the studies of Irmak
et al. (2003) and Xu and Singh (2000) and using mul-
tiplication linear regressions in which the FPM values
were used as the dependent variable and other parame-
ters (Table3) were independent variables. In each
province, two-third of the data was used for develop-ment of the equations and one-third of the data were
applied for validation.
Then, the potential evapotranspiration calculated using
new formulas was compared with FPM and variations of
the errors were investigated.
For better evaluation, a sensitive analysis was done for
investigating variations of the methods and the map of the
error calculated for each province is presented.
Table 1 continued
References Methods compared/evaluated Study
region
Main conclusion
Ding et al.
(2013)
Priestley-Taylor and FPM China The modified Priestley-Taylor model can be used to
estimate the potential evapotranspiration
Xu et al. (2013) Turc and PriestleyTaylor, HargreavesSamani,
lysimeter
China Serious local calibration is strongly recommended
before applying HargreavesSamani for daily
evapotranspiration estimation
Kisi (2014) Modified Copais, Turc, Hargreaves-Samani,
Hargreaves, Ritchie, Valiantzas, Irmak
Turkey The worst estimates are generally obtained from the
Turc method
Ye et al. (2014) Linear regression, attribution analysis, Mann
Kendall
China Sunshine is the most sensitive climatic variable to the
variability of reference evapotranspiration on annual
basis
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3 Results and discussion
3.1 Estimating the potential evapotranspiration for all
of provinces of Iran using common radiation
methods
Table4 shows the average of errors in 31 provinces.
Table4 and Eq. (2) indicate that in the Caprio, Cas-taneda-Rao, McGuinness-Bordne, Modified Priestley-
Taylor, Priestley-Taylor, Stephens-Stewart, and Xu and
Singh methods (in the most cases) the estimations are
more than the potential evapotranspiration calculated
using the FPM. The overestimation of the potential
evapotranspiration values by the radiation-based methods
was also found in the other researches (Martinez and
Thepadia 2010; Suleiman and Hoogenboom 2007; Tra-
jkovic and Kolakovic 2009b; Yoder et al. 2005).
However, the de Bruin, Doorenbos-Pruitt, Hansen, Irmak,
Jensen-Haise, Jones-Ritchie, Modified Copais, and Turc
methods (in the most cases) estimate the potential
evapotranspiration less than the FPM. The underestima-
tion of the potential evapotranspiration values by the
radiation-based methods was also found in the other
studies (Howell et al. 2005; Kisi 2007; Rojas and Shef-
field 2013; Thepadia and Martinez 2012; Trajkovic andKolakovic 2009b). The Xu-Singh method provided the
greatest overestimate 4.11 mm day-1 for KH, while the
Berengena-Gavilan and Irmak methods yielded the least
overestimate 0.02 mm day-1 for KO and QO, respectively
(Table4). In addition, the Doorenbos-Pruitt method pro-
vided greatest underestimate 3.11 mm day-1 for KB,
while the Abtew (for YA) and de Bruin (for EA and HO)
methods yielded the least underestimate 0.01 mm day-1
(Table4). This underlines that radiation-based methods
Table 2 Position of all
provinces and synoptic stationsProvince Latitude (N) Longitude (E) Data measured (year) Number of station
AL 35550 50540 20 1AR 38150 48170 30 4BU 28590 50500 55 5CB 32170 50510 51 4EA 38050 46170 55 10
ES 32370 51400 55 12FA 29320 52360 55 9GH 36150 50030 47 2GI 37150 49360 50 4GO 36510 54160 54 3HA 34520 48320 55 4HO 27130 56220 49 9IL 33380 46260 20 3KB 30500 51410 19 1KE 30150 56580 55 8KH 31200 48400 55 14KO 35200 47000 47 7KS 34210 47090 55 6LO 33260 48170 55 9MA 34060 49460 51 4MZ 36330 53000 55 7NK 37280 57160 24 1QO 34420 50510 20 1RK 36160 59380 55 12SB 29280 60050 55 8SE 35350 53330 55 4SK 32520 59120 51 3TE 35410 51190 55 8
WA 37
320 45
050 55 8YA 31540 54170 54 6ZA 36410 48290 51 4
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should be used carefully in accordance with weather
conditions of each province. Because according to the R2
values, each method estimates the potential evapotrans-
piration for only one or few provinces as acceptable. In
the other words, precision of estimating by radiation-based
methods is very sensitive to variations of the parameters
used in each method (Table3).
3.2 The best and worst performance of the methods
used
Figure1 compares the best and worst performance of the
methods used.
According to Fig. 1 the Berengena-Gavilan for ES
(R2 = 1.00 and MBE = 0.08) yielded the best potential
Table 3 Method used and parameters applied in each method
Model Reference(s) Formula Parameters
FAO Penman-
Monteith
Allen et al. (1998) ETo 0:408RnGc 900T273uesea
Dc 10:34u H, u, T, Tmin, Tmax,
RH, u, n
Abtew Abtew (1996) ETo 0:01786 RsTmaxk T, Tmax, RsBerengena-
Gavilan
Berengena and Gavilan (2005) ETo 1:65 DDcRnG
k T, Tmax, Tmin, n, RH,
u, HCaprio Caprio (1974) ETo 0:01092708T 0:0060706 Rs T, RsCastaneda-Rao Castaneda and Rao (2005) ETo 0:70 DDc Rsk 0:12 T, RsChristiansen Christiansen (1968), Hargreaves and
Allen (2003)ETo 0:0385 Rsk T, Rs
de Bruin de Bruin (1981), de Bruin and Lablans
(1998)ETo 0:65 DDc Rsk T, Rs
Doorenbos-Pruitt Doorenbos and Pruitt (1977) ETo 1:066 0:0013RH 0:045u 0:0002RHu 0:0000315RH2 0:0011u2 D
D cRs
k 0:3
T, Rs, RH, u
Hansen Hansen (1984) ETo 0:7 DDc Rsk T, RsIrmak Irmak et al. (2003) ETo 0:149Rs 0:079T 0:611 T, RsJensen-Haise Jensen and Haise (1963) ETo 0
:
408CT T Tx Rs T, Rs, H, Tmax,TminJones-Ritchie Jones and Ritchie (1990) ET
0 0:002322Tmax 0:001548Tmin 0:11223 Rsa Rs, Tmax,Tmin
Makkink Makkink (1957) ETo 0:61 DDc Rsk 0:12 T, RsMcGuinness-
Bordne
McGuinness and Bordne (1972) ETo 0:00597T 0:0838 Rs T, Rs
Modified Copais Alexandris and Kerkides, (2003),
Alexandris et al. (2006)
ETo 0:057 0:277C2 0:643C1 0:0124C1C2 T, Rs, RH
Modified Jensen-
Haise
Samani and Pesarakli (1986) ETo 0:408CT T Tx KTRaffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiTmax Tmin
p H, T, n, u, Tmax,Tmin
Modified
Priestley-Taylor
Abtew (1996) ETo 1:18 DDc RnGk T, Tmax, Tmin, n, RH,u, H
Modified Turc Abtew (1996) ETo 0:2868Rs 0:6 TmaxTmax15 Tmax, RsPriestley-Taylor Priestley and Taylor (1972) ETo 1
:
26 DDc RnGk T, Tmax,Tmin, n, RH,u, H
Stephens Stephens (1965) Jensen (1966) ETo 0:0158T 0:09 Rsk T, RsStephens-Stewart Jensen (1966), Stephens and Stewart
(1963)ETo 0:0148T 0:07 Rsk T, Rs
Turc Turc (1961), Xu et al. (2008) ETo 0:3107Rs 0:65 TatT15 T, RsXu-Singh Xu and Singh (2000) ETo 0:98 DDc RnGk 0:94 T, Tmax, Tmin, n, RH,
u, H
ETo is the reference crop evapotranspiration (mm/day), Rn is the net radiation (MJ/m2/day), G is the soil heat flux (MJ/m2/day), c is the
psychrometric constant (kPa/ C), esis the saturation vapor pressure (kPa), ea is the actual vapor pressure (kPa), D is the slope of the saturation
vapor pressuretemperature curve (kPa/ C), T is the average daily air temperature (C), u is the mean daily wind speed at 2 m (m/s), His the
elevation (m), u is the latitude (rad), Tmin is the minimum air temperature (C), Tmax is the maximum air temperature (C), RH is the average
relative humidity (%), n is the actual duration of sunshine (h), Rsis the solar radiation (MJ/m2/day),Ra is the extraterrestrial radiation (MJ/m
2/
day), k is the latent heat of vaporization (MJ/kg), and CT, Tx, a, C1, C2, atand KTare empirical coefficients
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evapotranspiration as compared to that from the FPM.However, the Stephens has been introduced as the best
method in the most provinces (10 provinces). This is
because the weather conditions for which the Stephens
equation has been calibrated are more similar to weather
conditions in Iran (Jensen 1966; Stephens 1965), espe-
cially in those 10 provinces. In general, radiation-based
methods are more suitable (R2 more than 0.98) for ES,
YA, SE, and CB (centre of Iran). However, it is less than
0.98 for 15 provinces of Iran (RK, NK, HO, FA, BU,
KH, QO, KS, HA, ZA, KO, GH, GI, AR, and EA). In
addition, according to Table4, variations of the errors
(the worst and best R2
) for different methods are con-siderable in all provinces. These different values indicate
highly varied performances of the radiation-based meth-
ods for a specific weather condition in each province. In
addition, an impressive difference between the values of
each model is observable. For instance, the R2 values of
the Caprio method ranges from -4.2 to 0.96 for GI and
EA, respectively. However, according to Table3, for
instance, the Berengena-Gavilan, Modified Priestley-
Taylor, Priestley-Taylor, and Xu-Singh methods are a
function of mean, minimum and maximum temperature,
sunshine, elevation, latitude and relative humidity, and
the most methods are a function of temperature and solarradiation. In addition, the only difference among the
Berengena-Gavilan, Modified Priestley-Taylor, Priestley-
Taylor, and Xu-Singh methods is coefficients used in
each method (Table3) as well as the only difference
among the Castaneda-Rao, de Bruin, Hansen, and Mak-
kink methods is also coefficients used in each method
(Table3). This is also true for Stephens and Stephens-
Stewart methods. However, the output of each model is
different from the other models because they have been
Table 4 The average values of the errors in 31 province
Method Error index Average of 31 provinces
Ab. MBE -0.47742
R2 0.712581
BG MBE -0.04419
R2 0.794839
Ca. MBE -0.96871R2 0.082258
CR MBE -0.59484
R2 0.643871
Ch. MBE 0.160968
R2 0.499677
de MBE 0.380323
R2 0.705484
DP MBE 2.456129
R2 0.73806
Ha. MBE 0.716452
R2 0.589677
Ir. MBE 0.311613
R2 0.670323
JH MBE 0.729355
R2 0.358065
JR MBE 1.148387
R2 0.376452
Ma. MBE -0.00484
R2 0.756452
MB MBE -0.63032
R2 0.801613
MC MBE 1.964839
R2 0.07484
MJH MBE -0.04871
R2 0.623871
MPT MBE -1.09065
R2 0.631935
MT MBE 0.533871
R2 0.642903
PT MBE -0.89839
R2 0.71871
St. MBE -0.2371
R2 0.834194
SS MBE -0.61258
R2 0.806452
Tu. MBE 0.893226
R2 0.51871
XS MBE -2.44903
R2 0.48032
Ab. is Abtew, BGis Berengena-Gavilan, Ca is Caprio, CR is Castaneda-
Rao, Ch . is Christiansen, de is de Bruin, DP is Doorenbos-Pruitt, Ha. is
Hansen, Ir. is Irmak, JH is Jensen-Haise, JR is Jones-Ritchie, Ma. is
Makkink, MB is McGuinness-Bordne, MC is Modified Copais, MJHis
Modified Jensen-Haise, MPT is Modified Priestley-Taylor, MT is
Modified Turc, PT is Priestley-Taylor, St. is Stephens, SS is Stephens-
Stewart, Tu. is Turc, and XS is Xu-Singh
Fig. 1 The best (ES) and worst (KS) performance of the radiation
methods
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calibrated (constant coefficients in each model) based on
different weather conditions as well as parameters used
are not the same (in all models) for other models. Thus,
the coefficients of the radiation-based methods need to be
adjusted based on weather conditions of each province.
3.3 Increasing accuracy of the methods using
regression analysis
The best methods for each province (Table 3; Fig. 1) are
calibrated using regression analysis and similar to the
studies of Irmak et al. (2003) and Xu and Singh (2000).
Table5 shows the new formulas with the coefficients
calibrated for each province.
Figure2 compares the potential evapotranspiration
using the FPM with values estimated using the methods
calibrated (based on Table5) for each province.According to Figs. 1 and 2, precision of the methods
calibrated has been increased in all provinces. TheR2 values
are less than 0.98 for only six provinces (WA, EA, GO, NK,
AL, and QO). There are many researches that reported
increasing precision of radiation-based methods for esti-
mating the potential evapotranspiration after calibration
(Abbaspour1991; Martinez and Thepadia 2010; Thepadia
and Martinez2012; Xu et al. 2013; Zhai et al. 2010).
Table 5 Formula calibrated and their error for each province
Province The best method New Formula Symbol R2 MBE
CB Priestley-Taylor ETo 1:557T 0:228Tmin 1:307Tmax 0:118RH 0:0278n 10:152 Eq. 1 0.98 0.00EA Turc ETo 0:218T 0:0897Rs 0:892 Eq. 2 0.95 -0.01WA Stephens ETo 0:121T 0:117Rs 1:251 Eq. 3 0.97 -0.02AR Priestley-Taylor ETo 1:671T 0:817Tmin 0:809Tmax 0:102RH 0:016n 6:311 Eq. 4 1.00 0.01ES Berengena-Gavilan ETo 1
:
422T 0:
196Tmin 1:
497Tmax 0:
137RH 0:
0122n 16:
547 Eq. 5 0.99 -0.01
IL Abtew ETo 1:132T 0:862Tmax 0:161Rs 0:412 Eq. 6 0.98 0.08BU Stephens-Stewart ETo 0:158T 0:19Rs 3:771 Eq. 7 0.98 -0.03TE Abtew ETo 0:322T 0:158Tmax 0:187Rs 1:842 Eq. 8 0.99 -0.01AL Berengena-Gavilan ETo 7:275T 5:242Tmin 1:857Tmax 0:269RH 0:0106n 30:114 Eq. 9 0.97 0.02SK Abtew ETo 1:266T 0:847Tmax 0:0392Rs 5:741 Eq. 10 1.00 -0.03RK Berengena-Gavilan ETo 0:462T 1:103Tmin 0:514Tmax 0:14RH 0:007n 19:425 Eq. 11 0.99 -0.19NK Stephens ETo 0:187T 0:0984Rs 1:356 Eq. 12 0.96 -0.02KH Abtew ETo 1:418T 0:991Tmax 0:17Rs 1:591 Eq. 13 0.98 0.03ZA Stephens ETo 0:13T 0:114Rs 0:977 Eq. 14 0.97 -0.02SE Stephens-Stewart ETo 0:138T 0:153Rs 2:356 Eq. 15 0.99 -0.03SB Jones-Ritchie ETo
0:532Tmin
0:163Tmax
0:0197Rs
4:986 Eq. 16 1.00 0.03
FA Berengena-Gavilan ETo 0:67T 0:448Tmin 1:077Tmax 0:177RH 0:016n 18:701 Eq. 17 0.98 0.03QO Stephens ETo 0:154T 0:19Rs 2:987 Eq. 18 0.97 -0.04GH Stephens ETo 0:161T 0:122Rs 1:497 Eq. 19 0.98 -0.01KO Stephens ETo 0:158T 0:12Rs 1:358 Eq. 20 0.98 -0.01KE Abtew ETo 0:94T 0:587Tmax 0:00328Rs 4:611 Eq. 21 1.00 0.01KS Berengena-Gavilan ETo 4:086T 1:662Tmin 2:313Tmax 0:0041RH 0:0364n 0:926 Eq. 22 0.99 -0.15KB Stephens ETo 0:136T 0:139Rs 2:016 Eq. 23 0.98 -0.03GO Priestley-Taylor ETo 5:181T 2:562Tmin 2:455Tmax 0:261RH 0:0149n 20:204 Eq. 24 0.93 0.05GI Modified Priestley-Taylor ETo 2:078T 1:289Tmin 0:718Tmax 0:0845RH 0:00787n 4:459 Eq. 25 0.99 0.02LO Stephens ETo 0:164T 0:117Rs 1:853 Eq. 26 0.99 0.00MZ Modified Priestley-Taylor ETo 9:308T 4:547Tmin 4:672Tmax 0:234RH 0:00524n 19:347 Eq. 27 0.98 0.09
MA Stephens ETo 0:
119T 0:
143Rs 1:
69 Eq. 28 0.98 -0.01HO Stephens-Stewart ETo 0:162T 0:151Rs 3:118 Eq. 29 0.98 -0.05HA Stephens ETo 0:115T 0:132Rs 1:348 Eq. 30 0.98 -0.02YA Abtew ETo 1:343T 1:057Tmax 0:0719Rs 5:724 Eq. 31 1.00 0.00ETois the reference crop evapotranspiration (mm/day), Tis the average daily air temperature (C), u is the mean daily wind speed at 2 m (m/s),
RHis the average relative humidity (%), Rsis the solar radiation (MJ/m2/day),n is the actual duration of sunshine (h), Tminis the minimum air
temperature (C), and Tmax is the maximum air temperature (C)
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Therefore, calibration is a necessary tool for modification
of radiation-based methods to increase precision of estima-
tion and to adapt the best methods to weather conditions
(local conditions) of each province. In the methods cali-
brated (Fig. 2), the Abtew (for YA) estimated the potential
evapotranspiration better than the other methods.
Fig. 2 Comparison of evapotranspiration calculated using FAO Penman-Montieth (FPM) with the best method calibrated for each province
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3.4 Sensitive analysis for investigating variations
of the methods
The maps of annual average of weather parameters are
useful not only for the mentioned categories but also for
determining the best values of each parameter for which
the best precision of the radiation-based methods is
obtained (Table6).
Table6 has been obtained using sensitive analysis of
all weather parameters with respect to Fig. 3. According
to Table6, the precision of the new formulas is different
(e.g. 0.93 and 1.00 for the Priestley-Taylor-based modelin GO and AR, respectively). This underlines the impor-
tant role of selection of the best model for a specified
weather condition. Furthermore, we can see different
ranges in the new formulas (Table 6). Therefore, we can
use the mass transfer-based models for other regions (in
other countries) based on Table6 with respect to their
errors. The results are also useful for selecting the best
model when we must apply mass transfer-based models
based on available data.
3.5 Studying the obtained error index in 31 provinces
of Iran
Figure3 was plotted to compare the error of the provinces.
AlthoughR2 is more than 0.97 for 25 provinces, it is less
than 0.93 for GO and it is 0.95 and 0.97 for EA and WA,
respectively. This confirms that the categories are reliable
and these two categories need to receive more attention due
to specific weather conditions. Thus, we require other
temperature, mass transfer, and pan evaporation-based
models to estimate the reference crop evapotranspiration in
these provinces. For instance, values of solar radiation areless than 23.6 MJ m-2 day-1 for NK, GO, EA and WA,
hence the radiation-based methods may not be the best
method for these provinces. It is revealed that only if we
use the radiation-based methods for suitable (based on
Table6) and specific (based on Fig. 3) weather conditions,
the highest precision of estimating is obtained. Meanwhile,
precision of estimating is more than 0.97 for the categories
I, IV, and V (with the exception of AL and QO both 0.97).
Therefore, according to the important role of irrigation and
Fig. 3 The values of error index of the best calibrated method for each province
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drainage (Mahdizadeh Khasraghi et al. 2014; Valipour
2012e, f, g, h, i, j; Valipour 2012j, 2013d; Valipour and
Montazar2012a,b, c), environmental (Valipour2013g,h;
Valipour et al. 2012c, Valipour 2012d, 2013e, 2012d,
2013a,2012a, Valipour et al. 2013b), and water resources
management (Banihabib et al. 2012; Valipour 2012c;
Valipour2012c,d; Valipour2013e; Valipour et al.2013b;
Valipour 2013f; Valipour et al. 2012a; Valipour 2012b,Valipour et al. 2013c), selecting an appropriate evapo-
transpiration equation has a highlighted effect to achieve
sustainable agriculture (Valipour 2013a, b, c; Valipour
2014a,b,c,d,e,f,g,h,i,j,t, u,v,w,x,y; Valipour et al.
2013a, Valipour et al. 2014) in various climates.
4 Conclusions
In the present study, 22 radiation-based methods were used
to estimate the potential evapotranspiration in 31 provinces
of Iran.
The precision of estimation by radiation-based methods
is very sensitive to variations of the parameters used in
each method. Thus, the coefficients of the radiation-based
methods need to be adjusted based on weather conditions
of each province.
Only if the radiation-based methods are used for suitable
and specific weather conditions (based on weather condi-
tions and the categories), the highest precision of estima-
tion is obtained.
According to the results, calibration is a tool required
to modify radiation-based methods to increase the pre-
cision of estimation and to adapt the best methods to
weather conditions (local conditions) of each province.
In the methods calibrated, the Abtew estimates the
potential evapotranspiration for YA better than the other
methods.
Precision of the methods calibrated has been increased
in all provinces. The R2 values are less than 0.98 for only
six provinces (WA, EA, GO, NK, AL, and QO).
In the methods calibrated, the Abtew (for YA) estimated
the potential evapotranspiration better than the other
methods.
The results are also usable for other countries with
similar values of weather parameters.
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Valipour M (2014r) Comparative evaluation of radiation-based
methods for estimation of potential evapotranspiration.
J Hydrol Eng. doi:10.1061/(ASCE)HE.1943-5584.0001066
Valipour M (2014s) Investigation of Valiantzas evapotranspiration
equation in Iran. Theor Appl Climatol. doi:10.1007/s00704-014-
1240-x
Valipour M (2014t) Handbook of water engineering problems. Fostercity, CA: OMICS Group eBooks. http://www.esciencecentral.
org/ebooks/handbook-of-water-engineering-problems/pdf/hand
book-of-water-engineering-problems.pdf
Valipour M (2014u) Handbook of irrigation engineering problems.
Foster city, CA: OMICS Group eBooks. http://www.escience
central.org/ebooks/handbook-of-irrigation-engineering-problems/
pdf/handbook-of-irrigation-engineering-problems.pdf
Valipour M (2014v) Handbook of hydraulic engineering problems.
Foster city, CA: OMICS Group eBooks. http://www.escience
central.org/ebooks/handbook-of-hydraulic-engineering-problems/
pdf/handbook-of-hydraulic-engineering-problems.pdf
M. Valipour
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7/23/2019 Evaluation of radiation methods to study potential evapotranspiration of 31 provinces
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Valipour M (2014w) Handbook of hydrologic engineering problems.
Foster city, CA: OMICS Group eBooks. http://www.escience
central.org/ebooks/handbook-of-hydrologic-engineering-problems/
pdf/handbook-of-hydrologic-engineering-problems.pdf
Valipour M (2014x) Handbook of environmental engineering prob-
lems. Foster city, CA: OMICS Group eBooks. http://www.
esciencecentral.org/ebooks/handbook-of-environmental-engineer
ing-problems/pdf/handbook-of-environmental-engineering-pro
blems.pdf
Valipour M (2014y) Handbook of drainage engineering problems.
Foster city, CA: OMICS Group eBooks. http://www.escience
central.org/ebooks/handbook-of-drainage-engineering-problems/
pdf/handbook-of-drainage-engineering-problems.pdf
Valipour M, Eslamian S (2014) Analysis of potential evapotranspi-
ration using 11 modified temperature-based models. Int J Hydrol
Sci Technol, Accepted
Valipour M, Montazar AA (2012a) Optimize of all effective
infiltration parameters in furrow irrigation using Visual Basic
and Genetic Algorithm Programming. Aust J Basic Appl Sci
6(6):132137
Valipour M, Montazar AA (2012b) Sensitive analysis of optimized
infiltration parameters in SWDC model. Adv Environ Biol
6(9):25742581
Valipour M, Montazar AA (2012c) An Evaluation of SWDC and
WinSRFR Models to optimize of infiltration parameters in
furrow irrigation. Am J Sci Res 69:128142
Valipour M, Banihabib ME, Behbahani SMR (2012a) Monthly inflow
forecasting using autoregressive artificial neural network. J Appl
Sci 12(20):21392147
Valipour M, Banihabib ME, Behbahani SMR (2012b) Parameters
estimate of autoregressive moving average and autoregressive
integrated moving average models and compare their ability for
inflow forecasting. J Math Stat 8(3):330338
Valipour M, Mousavi SM, Valipour R, Rezaei E (2012c) Air, water,
and soil pollution study in industrial units using environmental
flow diagram. J Basic Appl Sci Res 2(12):1236512372
Valipour M, Mousavi SM, Valipour R, Rezaei E (2012d) SHCP: Soil
Heat Calculator Program. IOSR J Appl Phys (IOSR-JAP)
2(3):4450
Valipour M, Mousavi SM, Valipour R, Rezaei E (2013a) A new
approach for environmental crises and its solutions by computer
modeling. In: The First International Conference on Environ-
mental Crises and its Solutions, Kish Island, Iran
Valipour M, Mousavi SM, Valipour R, Rezaei E (2013b) Deal with
environmental challenges in civil and energy engineering
projects using a new technology. J Civil Environ Eng 3(1):127.
doi:10.4172/2165-784X.1000127
Valipour M, Banihabib ME, Behbahani SMR (2013c) Comparison of
the ARMA, ARIMA, and the autoregressive artificial neural
network models in forecasting the monthly inflow of Dez dam
reservoir. J Hydrol 476:433441
Valipour M, Ziatabar Ahmadi M, Raeini-Sarjaz M, Gholami
Sefidkouhi MA, Shahnazari A, Fazlola R, Darzi-Naftchali A
(2014) Agricultural water management in the world during past
half century. Arch Agron Soil Sci. doi:10.1080/03650340.2014.
944903
Xu CY, Singh VP (2000) Evaluation and generalization of radiation-
based methods for calculating evaporation. Hydrol Process
14:339349
Xu CY, Singh VP (2002) Cross comparison of empirical equations for
calculating potential evapotranspiration with data from Switzer-
land. Water Resour Manage 16:197219
Xu CY, Gong L, Jiang T, Chen D, Singh VP (2006) Analysis of
spatial distribution and temporal trend of reference evapotrans-
piration in Changjiang (Yangtze River) catchment. J Hydrol
327:8193
Xu CY, Singh VP, Chen YD, Chen D (2008) Evaporation and
evapotranspiration. In: Singh VP (ed) Hydrology and hydraulics,
1st edn. Water Resources Pubns, USA, pp 229276
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. Arch Agron Soil Sci
59:845858
Ye J, Guo A, Sun G (2009) Statistical analysis of reference
evapotranspiration on the Tibetan Plateau. J Irrig Drain Eng
135:134140
Ye X, Li X, Liu J, Xu CY, Zhang Q (2014) Variation of reference
evapotranspiration and its contributing climatic factors in the
Poyang Lake catchment. Hydrol Process, China. doi:10.1002/
hyp.10117
Yoder RE, Odhiambo LO, Wright WC (2005) Evaluation of methods
for estimating daily reference crop evapotranspiration at a site in
the humid southeast US. Appl Eng Agr 21:197202
Zhai L, Feng Q, Li Q, Xu C (2010) Comparison and modification of
equations for calculating evapotranspiration (ET) with data from
Gansu Province, Northwest China. Irrig Drain 59:477490
Evaluation of radiation methods to study potential
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