Evaluation of radiation methods to study potential evapotranspiration of 31 provinces

7/23/2019 Evaluation of radiation methods to study potential evapotranspiration of 31 provinces

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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]

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Meteorol Atmos Phys

DOI 10.1007/s00703-014-0351-3


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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

M. Valipour

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Table 1 continued


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

Evaluation of radiation methods to study potential

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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


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

M. Valipour

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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

M. Valipour

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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)

M. Valipour

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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

M. Valipour

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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 (2014v) Handbook of hydraulic engineering problems.


central.org/ebooks/handbook-of-hydraulic-engineering-problems/

pdf/handbook-of-hydraulic-engineering-problems.pdf

M. Valipour

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http://www.theijes.com/papers/v1-i1/H011037043.pdfhttp://www.theijes.com/papers/v1-i1/H011037043.pdfhttp://omicsgroup.org/journals/necessity-of-irrigated-and-rainfed-agriculture-in-the-world-2168-9768.S9-e001.php?aid=12800http://omicsgroup.org/journals/necessity-of-irrigated-and-rainfed-agriculture-in-the-world-2168-9768.S9-e001.php?aid=12800http://omicsgroup.org/journals/necessity-of-irrigated-and-rainfed-agriculture-in-the-world-2168-9768.S9-e001.php?aid=12800http://dx.doi.org/10.4172/2168-9768.1000e114http://dx.doi.org/10.4172/2168-9768.1000e114http://dx.doi.org/10.4172/2168-9881.S10-e001http://ejournal.sedinst.com/index.php/agser/article/view/247http://ejournal.sedinst.com/index.php/agser/article/view/247http://ejournal.sedinst.com/index.php/agser/article/view/244http://dx.doi.org/10.1007/s13201-014-0199-1http://dx.doi.org/10.1080/03650340.2014.961433http://dx.doi.org/10.1080/03650340.2014.925107http://dx.doi.org/10.1080/03650340.2014.925107http://dx.doi.org/10.1002/met.1465http://dx.doi.org/10.1080/03650340.2014.941823http://dx.doi.org/10.1080/03650340.2014.941823http://dx.doi.org/10.1007/s13201-014-0234-2http://dx.doi.org/10.1007/s13201-014-0234-2http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001066http://dx.doi.org/10.1007/s00704-014-1240-xhttp://dx.doi.org/10.1007/s00704-014-1240-xhttp://www.esciencecentral.org/ebooks/handbook-of-water-engineering-problems/pdf/handbook-of-water-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-water-engineering-problems/pdf/handbook-of-water-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-water-engineering-problems/pdf/handbook-of-water-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-irrigation-engineering-problems/pdf/handbook-of-irrigation-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-irrigation-engineering-problems/pdf/handbook-of-irrigation-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-irrigation-engineering-problems/pdf/handbook-of-irrigation-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-hydraulic-engineering-problems/pdf/handbook-of-hydraulic-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-hydraulic-engineering-problems/pdf/handbook-of-hydraulic-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-hydraulic-engineering-problems/pdf/handbook-of-hydraulic-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-hydraulic-engineering-problems/pdf/handbook-of-hydraulic-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-hydraulic-engineering-problems/pdf/handbook-of-hydraulic-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-hydraulic-engineering-problems/pdf/handbook-of-hydraulic-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-irrigation-engineering-problems/pdf/handbook-of-irrigation-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-irrigation-engineering-problems/pdf/handbook-of-irrigation-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-irrigation-engineering-problems/pdf/handbook-of-irrigation-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-water-engineering-problems/pdf/handbook-of-water-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-water-engineering-problems/pdf/handbook-of-water-engineering-problems.pdfhttp://www.esciencecentral.org/ebooks/handbook-of-water-engineering-problems/pdf/handbook-of-water-engineering-problems.pdfhttp://dx.doi.org/10.1007/s00704-014-1240-xhttp://dx.doi.org/10.1007/s00704-014-1240-xhttp://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001066http://dx.doi.org/10.1007/s13201-014-0234-2http://dx.doi.org/10.1007/s13201-014-0234-2http://dx.doi.org/10.1080/03650340.2014.941823http://dx.doi.org/10.1080/03650340.2014.941823http://dx.doi.org/10.1002/met.1465http://dx.doi.org/10.1080/03650340.2014.925107http://dx.doi.org/10.1080/03650340.2014.925107http://dx.doi.org/10.1080/03650340.2014.961433http://dx.doi.org/10.1007/s13201-014-0199-1http://ejournal.sedinst.com/index.php/agser/article/view/244http://ejournal.sedinst.com/index.php/agser/article/view/247http://ejournal.sedinst.com/index.php/agser/article/view/247http://dx.doi.org/10.4172/2168-9881.S10-e001http://dx.doi.org/10.4172/2168-9768.1000e114http://dx.doi.org/10.4172/2168-9768.1000e114http://omicsgroup.org/journals/necessity-of-irrigated-and-rainfed-agriculture-in-the-world-2168-9768.S9-e001.php?aid=12800http://omicsgroup.org/journals/necessity-of-irrigated-and-rainfed-agriculture-in-the-world-2168-9768.S9-e001.php?aid=12800http://omicsgroup.org/journals/necessity-of-irrigated-and-rainfed-agriculture-in-the-world-2168-9768.S9-e001.php?aid=12800http://www.theijes.com/papers/v1-i1/H011037043.pdfhttp://www.theijes.com/papers/v1-i1/H011037043.pdf


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Valipour M (2014w) Handbook of hydrologic engineering problems.


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.


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


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