This article was downloaded by: [UZH Hauptbibliothek / Zentralbibliothek Zürich] On: 01 August 2013, At: 01:17 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Archives of Agronomy and Soil Science Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gags20 Assessment of nine different equations for ET o estimation using lysimeter data in a semi-arid environment Fatemeh Razzaghi a & Ali Reza Sepaskhah a a Irrigation Department, Shiraz University, Shiraz, Islamic Republic of Iran Published online: 13 Aug 2009. To cite this article: Fatemeh Razzaghi & Ali Reza Sepaskhah (2010) Assessment of nine different equations for ET o estimation using lysimeter data in a semi-arid environment, Archives of Agronomy and Soil Science, 56:1, 1-12, DOI: 10.1080/03650340902829180 To link to this article: http://dx.doi.org/10.1080/03650340902829180 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms- and-conditions
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This article was downloaded by: [UZH Hauptbibliothek / Zentralbibliothek Zürich]On: 01 August 2013, At: 01:17Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Archives of Agronomy and Soil SciencePublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/gags20
Assessment of nine different equationsfor ETo estimation using lysimeter datain a semi-arid environmentFatemeh Razzaghi a & Ali Reza Sepaskhah aa Irrigation Department, Shiraz University, Shiraz, Islamic Republicof IranPublished online: 13 Aug 2009.
To cite this article: Fatemeh Razzaghi & Ali Reza Sepaskhah (2010) Assessment of nine differentequations for ETo estimation using lysimeter data in a semi-arid environment, Archives of Agronomyand Soil Science, 56:1, 1-12, DOI: 10.1080/03650340902829180
To link to this article: http://dx.doi.org/10.1080/03650340902829180
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Assessment of nine different equations for ETo estimation using lysimeter
data in a semi-arid environment
Fatemeh Razzaghi and Ali Reza Sepaskhah*
Irrigation Department, Shiraz University, Shiraz, Islamic Republic of Iran
(Received 3 November 2008; final version received 17 February 2009)
There are many equations for the estimation of reference crop evapotranspiration(ETo) by using climatic data measured in weather stations. Also, different types oflysimeter are used to measure ETo directly. However, lysimeters are not availablefor ETo measurement everywhere; therefore, an appropriate equation should beused for ETo estimation. Furthermore, there is a sharp fluctuation or noise in thedaily recorded weather data that should be smoothed for proper application. Inthis research, daily, smoothed daily, mean 10-day and mean monthly ETo wereestimated by Penman-FAO, Penman-Monteith, Hargreaves-Samani, Jensen-Haise, Turc, Priestley-Taylor, FAO-Blaney-Criddle, FAO-Radiation and PanEvaporation equations and the results of these equations compared with ETo datafrom a weighing type lysimeter. To indicate the most appropriate estimationequation, they are ranked according to statistical and error analysis. The resultsindicate that the FAO-Radiation and Hargreaves-Samani are the mostappropriate methods and the Priestley-Taylor method is the least appropriate.The Penman-Monteith ranked in third to fifth place according to the duration ofmean values. It is also concluded that smoothing weather data are preferred forestimation of daily ETo. Therefore, it is concluded that the FAO-Radiationmethod is the most suitable for estimation of ETo for irrigation planning andscheduling in regions where radiation and temperature data are available.However, the Hargreaves-Samani method is the most appropriate method whenonly temperature data are available.
Keywords: smoothed data; daily ETo; 10-day ETo; monthly ETo
Introduction
Accurate estimation of crop evapotranspiration (ETc) is essential for the planning,design and operation of irrigation systems. For determining ETc, reference cropevapotranspiration (ETo) should be estimated. ETo is defined as a rate ofevapotranspiration from an extensive surface of green grass cover in uniformheight, actively growing, completely shading and not short of water (Doorenbos andPruitt 1977). Accurate values of ETo are measured by different types of lysimeter(Jensen et al. 1990). However, the ETo measurement by lysimeter is not readilyaccessible in different irrigated areas; therefore, different methods of ETo estimationshould be considered in different regions to select an appropriate estimation method.Up to now about 50 empirical formulas are used for estimating ETo. The Food and
Agriculture Organization (FAO) recommended Penman-Montieth equations forestimating ETo (Allen et al. 1998). The Penman-Montieth method requires manyinput variables, which may not be readily available for all weather stations. On theother hand, Thornthwaite (1948) and Hargreaves and Samani (1985) equationsrequire only air temperature that is measured in all weather stations. TheThornthwaite (1948) method was adjusted based on measured ETo by lysimeter ina semi-arid region (Sepaskhah and Razzaghi 2009). Furthermore, other methods areused to estimate ETo especially for management of irrigation water and irrigationscheduling, such as Penman-FAO, Jensen-Haise, FAO-Blaney-Criddle, Turc,Priestley-Taylor, FAO-Radiation and Pan Evaporation.
Different equations for estimation of daily ETo were evaluated by using measuredETo by lysimeter and modifications were proposed for estimation of ETo for differentlocal conditions (Hargreaves and Allen 2003; Lecina et al. 2003; Dehghani-Sanij et al.2004; Pereira 2004). For precise irrigation planning and scheduling, it is necessary todetermine accurate ETo in different timescales such as daily, 10-day and monthlyperiods. A locally suitable equation should be used for accurate estimation of ETo withdifferent timescales. Furthermore, there is a sharp fluctuation or noise in the dailyrecorded data that should be smoothed for proper application. The accuracy of theHargreaves and Samani (1985) method was examined by measured ETo by lysimeter inthe Kooshkak study area (Fars province) (Sepaskhah and Razzaghi 2009); however,the accuracy of other methods remained to be investigated.
The objective of this research is to estimate daily, mean 10-day and meanmonthly ETo of the Penman-FAO, Penman-Monteith, Hargreaves-Samani, Jensen-Haise, Turc, Priestley-Taylor, FAO-Blaney-Criddle, FAO-Radiation and PanEvaporation equations and compare the result of these equations with measuredETo data by a weighing type lysimeter to determine their preference. In thiscomparison, the daily ETo was estimated by using daily original measured weatherdata and daily smoothed weather data from the weather station.
Materials and methods
Theory
Different equations for estimation of ETo are as follows:Penman-Monteith method (Allen et al. 1998):
ETo ¼0:408� D� Rn � Gð Þ þ g� 900
Tmþ273�U2 � es � eað ÞDþ g� 1þ 0:34�U2ð Þ ð1Þ
Penman-FAO method (Doorenbos and Pruitt 1977):
ETo ¼ C� ½0:408�W� Rn þ 1�Wð Þ � 0:27� fu � es � eað Þ� ð2Þ
Hargreaves-Samani method (Hargreaves and Samani 1985):
ETo ¼ aT � 0:013� Tm= Tm þ 15ð Þ½ � � Rs þ 50ð Þ ð8Þ
Pan Evaporation method (Jensen et al. 1990):
ETo ¼ KP � Epan ð9Þ
where: ETo is the reference crop evapotranspiration in mm d71; Rn is the netradiation in MJ m72 d71; G is the soil heat flux in MJ m72 d71 [due to negligiblevalue of G compared with Rn, it may be ignored (Allen et al. 1998)]; D is the slope ofthe saturation vapor pressure-temperature relationship in kPa 8C71; g is thepsychrometric constant in kPa 8C71; es is the saturated vapor pressure in kPa; ea isthe actual vapor pressure kPa; U2 is the daily wind speed at 2 m height in m s71; Tm
is the average daily temperature in 2 m height in 8C; W is the coefficient related ontemperature; fu is a function of wind speed; C is a correction coefficient; Tmax is themaximum daily temperature in 8C; Tmin is the minimum daily temperature in 8C; Ra
is the extraterrestrial radiation in MJ m72 d71; TD is the differences betweenmaximum and minimum air temperature in 8C; a1 is the empirical dimensionlesscoefficient (1.26); l is the latent heat in MJ kg71; p is the mean daily percentage oftotal annual daytime hours in different months (Doorenbos and Pruitt 1977); KP isthe coefficient of pan evaporation; and Epan is the evaporation from pan evaporationin mm d71. Allen et al. (1989) obtained the correction coefficient (C) in Equation (2)as a function of Ud (the wind speed during day in 2 m above ground in m s71); Un
(the wind speed during night in 2 m above ground in m s71); RHmax (the maximumdaily relative humidity in %) and Rs (the solar radiation in MJ m72 d71). The valueof a in Equation (4) is 70.3 mm d71 and the value of b is dependent on RHmean (thedaily average relative humidity in %) and Ud (Jensen et al. 1990). The values of CT,KT and Tx in Equation (5) are presented by Jensen et al. (1990). They depend on e1and e2 (the saturated vapor pressure in maximum and minimum temperature in kPa,respectively); Z (the high above mean sea level in m); S (the percent of the actualduration of sunshine to the maximum possible duration of sunshine) and TD. Thevalues of A and B in Equation (6) are dependent on RHmin (the minimum dailyrelative humidity in %); n (the actual duration of sunshine in h); N (the maximumpossible duration of sunshine in h) and Ud. The value of aT in Equation (8) dependson RHmean as presented by Jensen et al. (1990). The value of Kp in Equation (9)
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depends on U2; RHmean and F (the distance of green cover around pan evaporationin m) as presented by Cuenca (1989).
Weighing lysimeter ETo
This study was conducted in the Kooshkak Agricultural Experiment Station, ShirazUniversity, located 60 km north of Shiraz with 528 340 E longitude, 308 70 N latitudeand 1650 m above mean sea level. Shiraz is located in the south of Iran. The long-term mean annual air temperature is about 15.38C. Two weighing type lysimetersinstalled in the station with 3.0 m diameter and 1.7 m depth. Lawn grass was plantedin lysimeters and the area around the lysimeter (40 6 40 m). The height of grass waskept as 0.12 m and irrigated frequently so that soil water content was kept at fieldcapacity. The amount of irrigation water was measured by volumetric method. Dailyreference evapotranspiration (ETo) in two lysimeters were determined according todifferences between weights of lysimeters in 24 h, the amount of irrigation orprecipitations and drainage water occurred in this period. The weighing increment oflysimeter is about 2.5 kg equal to 2.5 l of water. Therefore, with the area of lysimeter(7.07 m2) the resolution of measured daily ETo in lysimeter was equal to 0.28 mm.The texture of the soil in lysimeter is silty clay loam to clay loam that is arepresentative of the study area. The value of soil pH varied from 7.5–8.1, the soilCaCO3 content is 41.5–51.5%, soil clay, silt and sand contents are 35–39, 36–50 and12–28%, respectively, and the soil cation exchange capacity is 19.1–24.5 meq (100 gsoil)71 (Mahjoory 1975). Volumetric soil water contents at field capacity andpermanent wilting point at a depth of 0–30 cm were 0.39 cm3 cm73 and 0.213 cm3
cm73, respectively. These values at depth of 30–90 cm were 0.42 cm3 cm73 and0.282 cm3 cm73, respectively. Different layers of the original soil in the place oflysimeters were kept separately. After lysimeter installation, different soil layers werefilled in the lysimeter with a depth of 10 cm each, and were watered to settle downbefore the next layer was place in it. The filled lysimeter was watered for severalmonths for more settlement. The regional climate is classified as semi-arid (Malek1982). The weather data were recorded daily in a weather station located next to thelysimeters. Daily reference crop evapotranspiration (ETo) was measured in thelysimeters during 23 September 2005 to 22 September 2006.
Estimation of ETo
The methodology used here for computing daily original, daily smoothed, mean 10-day and mean monthly ETo is as follows: (i) computing ETo by the Penman-FAO,Penman-Monteith, Hargreaves-Samani, Jensen-Haise, Turc, Priestley-Taylor, FAO-Blaney-Criddle, FAO-Radiation and Pan Evaporation methods, and (ii) comparingthe results of these equations with ETo measured by weighing lysimeter during 2005–2006.
For computing ETo by the Penman-FAO, Penman-Monteith, Hargreaves-Samani,Jensen-Haise, Turc, Priestley-Taylor, FAO-Blaney-Criddle, FAO-Radiation and PanEvaporation methods, Equation (3) to Equation (9) are used, respectively.
Maximum and minimum temperature, maximum and minimum relativehumidity, wind velocity and sunshine hours were recorded daily in a weatherstation that was located in Kooshkak area next to the lysimeters. Due to usingmanual measured weather data for estimation of ETo, these data were controlled and
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the missed or incorrect data were determined. To do this, the linear relationshipbetween the manually measured weather data and those measured by logger datawere determined for Kooshkak area.
Daily weather data fluctuate on consecutive days and show noise. By using fiveconsecutive data with specific weights (i.e., 1, 2, 3, 2, and 1) they are smoothed byusing the following equation:
Sj ¼xj�2 þ 2xj�1 þ 3xj þ 2xjþ1 þ xjþ2
9ð10Þ
j ¼ 3 to n 7 2
where n is the total number of data; Sj is the value of smoothed data on jth day, x isthe value of original data, and j is the number of day. This procedure is somewhatsimilar to calculate a weighted average for a 5-day ETo as used by Hargreaves andAllen (2003).
The value of daily ETo was estimated by original and smoothed data in differentmethods and the results were compared with the original and smoothed data ofmeasured daily ETo by lysimeter. Furthermore, the mean 10-day and mean monthlyweather data were used to estimate the corresponding ETo. The results were alsocompared with mean 10-day and mean monthly measured ETo by lysimeter.
Statistical analysis
The estimation accuracy of daily, smoothed daily, mean 10-day and mean monthlyETo was determined by mean absolute error (MAE), normalized root mean squareerror (NRMSE) and index of agreement (d) by using the following equations(Willmott et al. 1985):
where Oi is the measured ETo by lysimeter in mm d71; Pi is the predicted ETo in mmd71; O is the average measured ETo by lysimeter in mm d71 and n is the totalnumber of data.
Results and discussion
The estimated value of daily, smoothed daily, mean 10-day and mean monthly ETo
by different methods are compared with corresponding measured value by lysimeter
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and a linear regression equation was obtained between the estimated and measuredvalues as follows:
Y ¼ pX þ q ð14Þ
where Y is the ETo estimated by different methods; X is the measured ETo bylysimeter and p and q are the regression coefficients. When the intercept for linearrelationship using daily, smoothed daily, mean 10-day and mean monthly data is notstatistically significant, at 5% level of probability the linear relationship is presentedas follows:
Y ¼ pX ð15Þ
Daily ETo
Coefficients of determination, R2 and the results of statistical analysis are shown inTable 1 for the linear relationship between estimated daily ETo with differentmethods and daily measured ETo by lysimeter. For selecting the most appropriateequation, the estimation methods are ranked according to a holistic approach basedon the values of slope, intercept, R2, MAE, NRMSE and d such that the values of p,R2 and d closer to 1.0; and q, MAE, and NRMSE closer to 0.0 are preferred. Resultsindicate that the FAO-Radiation method is the most appropriate and the Priestley-Taylor is the least appropriate method. In the FAO-Radiation method, the slope oflinear equation is 0.83 which is the most closest slope to 1.0, the R2 is 0.92 which ishigh and near to 1.0 and the values of NRMSE and MAE are low (0.14, 0.63,respectively). The Hargreaves-Samani method showed a slope similar to that of theFAO-Radiation method, the value of intercept and the R2 are less than thoseobtained for the FAO-Radiation method but the value of NRMSE is higher and thevalue of d is lower than those of FAO-radiation. So it is ranked in second place. Theslope of linear relationship between daily ETo estimated by the Penman-Monteithmethod and daily ETo measured by lysimeter is 0.65, which is lower than 1.0 and the
Table 1. Ranking the linear relationship between estimated daily ETo by different methodsand measured daily ETo by lysimeter in 2005–2006.
MAE, mean absolute error; NRMSE, normalized root mean square error; d, index of agreement.
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value of NRMSE is higher than those for the FAO-Radiation and Hargreaves-Samani method. Therefore, it is ranked in third place. The slopes of linear equationfor the Jensen-Haise and Priestley-Taylor methods are much different from 1.0, thevalue of NRMSE is high and the value of d is low. So the accuracy of these equationsis the lowest.
Smoothed daily ETo
In ranking the different ETo estimation methods by using smoothed daily data, theFAO-Radiation and Priestley-Taylor methods are the most appropriate and leastappropriate methods, respectively (Table 2). The slope of linear relationship betweensmoothed daily ETo estimated by the Hargreaves-Samani and FAO-Blaney-Criddlemethods and smoothed daily ETo measured by lysimeter is the same as that obtainedfor the FAO-Radiation, but the value of R2 and d for the Hargreaves-Samanimethod is lower and the MAE and NRMSE are higher than those for the FAO-Radiation method; therefore, they are ranked in second and third places,respectively. The slope of linear relationship between the Penman-Monteith andPenman-FAO methods and measured ETo by lysimeter are much less than 1.0, theintercept is equal to 0, R2 is high and near to 1.0 but the value of MAE and NRMSEare higher and the value of d is lower than those of methods ranked from 1–3. Theslope of linear equation for the Priestley-Taylor method is the lowest and the valueof error terms are the highest. The other equations were ranked higher than thePriestley-Taylor and lower than the Penman-Monteith methods. Comparison of theresults in Tables 1 and 2 showed that smoothing the data decreased the fluctuation ofmeasured daily weather data and ETo of lysimeter and consequently resulted in thevalue of slope of the linear relationship closer to 1.0 and lower error.
Mean 10-day ETo
According to the results in Table 3, the FAO-Radiation method is the mostappropriate to estimate the mean 10-day ETo, although the slope of linearrelationship for the Hargreaves-Samani equation is somewhat higher than that for
Table 2. Ranking the linear relationship between estimated smoothed daily ETo by differentmethods and measured smoothed daily ETo by lysimeter in 2005–2006.
MAE, mean absolute error; NRMSE, normalized root mean square error; d, index of agreement.
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the FAO-Radiation equation, but the values of MAE and NRMSE for theHargreaves-Samani equation are higher than those for the FAO-Radiation equation.Although the FAO-Blaney-Criddle method ranked in third place, it overestimatedthe 10-day ETo. Other methods ranked lower than third place and, with theexception of the Jensen-Haise method, underestimated the 10-day ETo. Again, thePriestley-Taylor method was ranked in last place.
Mean monthly ETo
According to Table 4, the values of MAE and NRMSE for the FAO-Radiation andHargreaves-Samani methods are the least and the values of coefficient of linearrelationship, R2 and d are the highest. Therefore, the accuracies of these equations toestimate the mean monthly ETo are high. Also, the values of MAE and NRMSE forthe FAO-Radiation and Hargreaves-Samani methods for mean monthly data areless than those for mean 10-day data (Table 3), smoothed daily (Table 2) and daily
Table 3. Ranking the linear relationship between estimated mean 10-day ETo by differentmethods and measured mean 10-day ETo by lysimeter in 2005–2006.
MAE, mean absolute error; NRMSE, normalized root mean square error; d, index of agreement.
Table 4. Ranking the linear relationship between estimated mean monthly ETo by differentmethods and measured mean monthly ETo by lysimeter in 2005–2006.
MAE, mean absolute error; NRMSE, normalized root mean square error; d, index of agreement.
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data (Table 1). The accuracy of the Priestley-Taylor method is lowest according tothe slope, intercept and the statistical parameters. Other methods ranked lower thansecond places and, with the exception of the FAO-Blaney-Criddle and Jensen-Haisemethods, underestimated the mean monthly ETo.
Final episode
According to the results of Tables 1–4, the FAO-Radiation and Hargreaves-Samanimethods are the most appropriate; however, the Hargreaves-Samani method can beimproved by modifying its coefficients. The relationships between estimated ETo byFAO-Radiation method and measured ETo by lysimeter are shown in Figure 1. Theslope of linear relationship is close to 1.0, the intercept is low and R2 is high.Therefore, the accuracy of this method is high. According to the value of b inEquation (4) that is obtained from an equation presented by Jensen et al. (1990),wind velocity is not very effective in ETo estimation by the FAO-Radiation method.On the other hand, the daily value and variation of wind velocity in the Kooshkakregion is low. Therefore, the FAO-Radiation method resulted in appropriateestimation of ETo.
The relationship between estimated ETo by the Hargreaves-Samani method andmeasured ETo by lysimeter are shown in Figure 2. This method also showed anappropriate result after the FAO-Radiation method. According to Equation (3) onlyTmax and Tmin are required for ETo estimation by this method which are measured inall types of weather stations. Therefore, the Hargreaves-Samani method can be usedwith an acceptable level of error. This is in accordance with that reported bySepaskhah and Razzaghi (2009). According to Sepaskhah and Razzaghi (2009) it isshown that the Hargreaves-Samani method is modified to estimate ETo with higheraccuracy. Hargreaves and Allen (2003) compared daily ETo estimated by Hargreavesand Samani (1985) with daily ETo measured by weighing lysimeter in KimberlyIdaho. Predicted values of daily ETo by the Hargreaves and Samani (1985) methodwas 0.97 times the measured daily ETo by lysimeter after adjustment of lysimeterdata.
In general, smoothing daily weather data resulted in a closer slope to 1.0 andsmaller intercept for the FAO-Radiation and Hargreaves-Samani methods thanthose for original weather data (Tables 1 and 2), therefore, smoothing weather dataare preferred for estimation of daily ETo.
The estimated ETo by the Hargreaves-Samani method is more appropriate thanthose obtained by the Penman-Montheith method, but the FAO-Radiation methodshowed the best results. Hargreaves and Allen (2003) showed that the slope of linearrelationships between ETo estimated by the Hargreaves-Samani and Penman-Monteith methods and measured ETo by lysimeter are close to 1.0. However, in ourstudy the slope of linear relationship between ETo estimated by the Hargreaves-Samani method and measured ETo by lysimeter is closer to 1.0 than the slope oflinear relationships between ETo estimated by the Penman-Monteith method andmeasured ETo by lysimeter. This indicates that the Penman-Monteith method shouldbe modified for the study region by using the lysimeter data. However, Lecina et al.(2003) showed that no differences occurred between daily ETo estimated by fixedinvariable crop resistance parameter (rc) in the Penman-Monteith method and dailyETo measured by weighing lysimeter in Spain. This discrepancy may be related to thedifference in study region due to advection.
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Monthly ETo estimated by Blaney-Criddle is higher than monthly measured ETo
during study period, but the Hargreaves-Samani and Penman-Monteith methodsunderestimated monthly ETo and the Penman-FAO method underestimatedmonthly ETo during April to September and overestimated monthly ETo duringJanuary to March and October to December. These results are similar to thosereported by Dehghani-Sanij et al. (2004) obtained in April and June.
Furthermore, the accuracy of estimated daily, mean 10-day and mean monthlyETo by the Priestley-Taylor method is low, that is, in contrast to the result of Periera(2004) that used 1.26 for the coefficient a for the Priestley-Taylor method. Pereira(2004) compared daily ETo estimated with the Priestley and Taylor (1972) methodwith daily ETo measured by weighing lysimeter under climatic condition, rangingfrom humid tropical to semi-arid. The results showed that for the tropical climate ofPiracicaba, the value of coefficient for the Priestley-Taylor method, a is 1.20 and for
Figure 1. Relationship between estimated ETo by the FAO-Radiation method and measuredETo by lysimeter in 2005–2006. (a) Daily; (b) smoothed daily; (c) mean 10-day and (d) meanmonthly data.
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the semi-arid climate of Davis it resulted in a ¼ 1.27. The original Priestley-Taylorfixed average a ¼ 1.26 worked well for Davis in the absence of heat advection. ForPiracicaba there was a slight over-prediction of 5%. These indicate that the value ofa for Priestley and Taylor (1972) method should be modified in the study region dueto advection.
Conclusion
It is concluded that the FAO-Radiation and Priestley-Taylor methods are the mostappropriate and least appropriate methods, respectively. Hargreaves-Samani isacceptable in predicting daily, smoothed daily, mean 10-day and mean monthly ETo.However, for more accurate estimation the modified Hargreaves-Samani method(Sepaskhah and Razzaghi 2009) should be used. Furthermore, the accuracy of thePenman-Monteith method for estimation of ETo is ranked in a third to fifth placeaccording to the duration of mean value (i.e. daily to monthly). Therefore, its
Figure 2. Relationship between estimated ETo by the Hargreaves-Samani method andmeasured ETo by lysimeter in 2005–2006. (a) Daily; (b) smoothed daily; (c) mean 10-day and(d) mean monthly data.
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1 A
ugus
t 201
3
accuracy is not acceptable and it should be modified for the study region.Furthermore, it is concluded that smoothing weather data are preferred forestimation of daily ETo. In general, it is concluded that with no modification ofdifferent equations for ET estimation, the FAO-Radiation method is the mostsuitable for estimation of ETo for irrigation planning and scheduling in regionswhere radiation and temperature data are available. However, the Hargreaves-Samani method is the most appropriate method when only temperature data areavailable. Furthermore, modification of different equations for ETo estimation isrecommended for the study region.
Acknowledgements
This research was supported in part by Grant no. 86-GR-AGR 42 of Shiraz UniversityResearch Council and Center of Excellence on Farm Water Management.
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