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1 Joural of Hydroscieces ad Eviromet Available olie at Estimatig the Hourly Referece Evapotraspiratio with Fuzzy Iferece Systems ad Limited Weather Data M. Naderiafar 1 *, H. Moradi, H. Asari 3 1. Assistat Professor of Irrigatio ad Draiage, Water Egieerig Departmet, Jiroft Uiversity, Ira. Ph.D Studet of Irrigatio ad Draiage, Water Egieerig Departmet, Ferdowsi Uiversity of Mashhad, Ira 3. Assistat Professor of Irrigatio ad Draiage, Water Egieerig Departmet, Ferdowsi Uiversity of Mashhad, Ira A R T I C L E I N F O A B S T R A C T Article history: Received: 10 July 016 Accepted: 5 Jauary 017 Keywords: Fuzzy Iferece System, Hourly Referece, Evapotraspiratio, Asce Model, Fao-56 Pema-Moteith Model. ISSN: Evapotraspiratio is the most importat part of the hydrological cycle, which plays a key role i water resource maagemet, crop yield simulatio, ad irrigatio schedulig. Therefore, developig a cost-effective ad precise model is essetial for estimatig hourly grass crop referece evapotraspiratio (o. I this study the potetial of the fuzzy iferece system (FIS is ivestigated as a simple techique for modelig hourly o obtaied usig the FAO-56 Pema-Moteith ad ASCE equatios. The, combiatios of efficiet hourly climatic data amely temperature, wid speed, relative humidity ad solar radiatio were used as iputs to the fuzzy model. Four fuzzy models were developed based o differet combiatios of iputs. Commo statistics such as Mea square error, average absolute relative error ad determiatio coefficiet ad two more statistics of Jacovides (t ad R/t are used as compariso criteria for evaluatio of the model performace. Here, Traiig ad testig fuzzy models were doe with Farima meteorological data a arid regio i the ortheast of Ira. The fuzzy model whose iputs are solar radiatio, air temperature, relative humidity ad wid speed, yield the highest correlatio ad compatibility to referece models of FAO-56 PM ad ASCE, based o commo statistics. Whereas, the fuzzy model whose iputs are solar radiatio, air temperature ad relative humidity, are selected as the best model based o combiatio of commo ad additioal statistics. The fuzzy model with two iputs amely solar radiatio ad relative humidity has acceptable results, too. The results show that solar radiatio is the most effective parameter o hourly referece evapotraspiratio ad temperature, relative humidity ad wid speed were other effective parameters, respectively. These results for traiig ad testig phase are alike. It was foud that the developed fuzzy models could be successfully employed i estimatig the hourly o with a limited weather data. 1. Itroductio Evapotraspiratio 1 is oe of the most importat compoets of the hydrological cycle. Therefore, its accurate estimatio is essetial for may studies, such as water hydrologic balace, desigig ad maagemet of irrigatio, plaig ad maagemet of water resources ad crop productio simulatio (Vaziri et al., 008. This subject is ecoutered with two facts: 1 The multiplicity of required parameters for calculatig evapotraspiratio ad, The lack of recordig some ifluetial parameters that make difficult its correct estimatio (Kuchakzadeh ad Bahmai, 005. Sice evapotraspiratio is complicated, developig a mathematical model cosiderig all effective climatic factors is hard. Also, the existece of ucertaity i efficiet parameters causes * Correspodig author s Naderia.mohamad@yahoo.com uavoidable errors. Moreover, most of these models require much data that preparig all of them is difficult, time-cosumig ad costly. Furthermore, ay developed mathematical model i a particular climate is just valid for that climate (Shayaezhad, 006. With due attetio to suitability of fuzzy techique to model high-ucertaity parameters ad oliear systems without ay complex equatio, the fuzzy model ca be a useful tool to cosider the ature of evapotraspiratio. Thus, we thik fuzzy model ca be a useful tool cosiderig the ature of evapotraspiratio. I cotrast to covetioal methods that eeds advaced ad complex math for desigig ad modelig a system, Fuzzy models use liguistic values ad coditios or kowledge of experts with simplifyig ad improvig the efficiecy (Ghasemezhad Moghadam et al. 1999; Kurehpaza Dezfuli, 006. Durig the past years, researchers were cotiuously seekig to model evapotraspiratio. So, i the last five decades, the most of studies have cocetrated o developig mathematical estimatio methods of evapotraspiratio ad improvig

2 the performace of available methods. Also, may researches have coducted fuzzy systems i may egieerig fields like drought moitorig, reservoir maagemet, deposits estimatio, weather predictio, ad river flow ad ruoff predictio. However, some studies focused o modelig daily referece crop evapotraspiratio (Aytek, 009; Hashemiajafi et al., 007; Doğa, 009; Jia Big et al., 004; Kisi ad Öztürk, 007; Kisi, 010; Odhiambo et al., 001; Shayaezhad, 007, but modelig hourly referece evapotraspiratio with fuzzy iferece system has t bee performed, yet. The metioed studies shows that fuzzy model ca apply differet iput data for daily estimatio ad fially, ad their comparisos to other methods are represetig its capabilities for estimatig daily referece evapotraspiratio. Some researchers used artificial eural etworks to estimate evapotraspiratio ad itroduced them as a useful tool for estimatig these parameters besides fuzzy model. It is ecessary to metio whe wid speed, temperature of dew poit or cloudiess level durig day vary, it is better to output be hourly. As value of eergy to evaporate varies durig a day, the its effects caot be geeralized by simply averagig hourly values to daily (Alle et al., This causes large errors i calculatio of daily evapotraspiratio. Cosiderig the results of the previous studies about fuzzy logic potetiality, this study aims at usig fuzzy iferece system to estimate hourly referece evapotraspiratio. Additioally, the absece of meteorological data ad costly recordig hourly data, made us suggest a model with miimum iputs. Clearly, if it is possible to provide such a model, it could be as the expected model with high accuracy because of reduced measurig error usig fewer data.. Method ad materials.1. The Study area The study area, Farima Couty, is located i the Khorasa Razavi state, Ira. The climate of study area is similar to the climate of Khorasa Razavi state based o climatically aggregatios. Based o average aual temperature of 1.4 C ad aual average raifall of 150 mm, study area is classified as arid ad semi-arid climate. The study area is over 413 km which cosists of.5 percet of Khorasa Razavi provice area. The study couty is located i latitude 35 4 orth ad logitude east, ad its height is 1411m above sea level. Hourly values of iputs were gathered ad evaluated for calculatig hourly referece evapotraspiratio. The olie private weather statio has the ability to collect simultaeously the primary parameters such as temperature, relative humidity, wid speed ad directio, radiatio rate, soil moisture i differet layers ad soil temperature. Soil moisture depletio rate of root zoe gathered from soil sesors i every 10 miutes. Also, evapotraspiratio ad plat's water requiremet calculatio usig Pema-Motith formula does at the same time. Statio data iforms farm maager via SMS every three hours after receivig ad logical aalyzig data ad save them o server computer. Recorded data i surveyed statio was used for traiig ad testig models durig 008 ad 009. Discardig faraway ad lost poits, the umber of remaiig data i the statistical period was 6000, that 70 percet of data (400 data used for traiig ad 30 percet (1800 for testig... Hourly referece evapotraspiratio models Pema-Motith-FAO ad the America Society of Civil Egieers (ASCE methods were used to calculate hourly referece evapotraspiratio. Four fuzzy models were used to combie differet iput parameters i this study (table 1. Model I Model II Model III Model IV Model No. Table 1. Fuzzy models ad iputs Iputs Temperature(T Solar Radiatio(Rs Wid Speed(U Temperature(T Solar Radiatio(Rs Solar Radiatio(Rs Temperature(T Pema-Motith-FAO 56 (FAO-56 PM model: Geeral equatio for calculatig referece evapotraspiratio i hourly time step is as follows (Alle et al., 1998: o 37U T 73 ( U ( R G ( es ea Where, o is hourly referece evapotraspiratio (mm, Δ is the slope of saturated vapor pressure curve i air temperature (kpa C -1, R is the et radiatio i grass surface (MJ/m /h, ad G is desity of heat flux of soil (MJ/m /h determied as: (1 If R> 0, or daytime G = 0.1 R If 0 R or ighttime G = 0.5 R Where, T is the mea air temperature (hourly at m height from the groud ( C, U is hourly mea wid speed (ms -1 at.0 m height, e s is mea saturated vapor pressure at m height (kpa, e a is mea vapor pressure of air i 1.5- m height (kpa, ad γ is psychometric costat (kpa o C -1. The istructios provided i the FAO paper No. 56 ca be used for calculatig compoets of the FAO Pema-Motith.

3 America Society of Civil Egieers (ASCE model: Stadard equatio suggested by the America Society of Civil Egieers (ASCE i order to calculate hourly referece evapotraspiratio of grass is as follows (Syder ad Pruitt, 199: o 37U T 73 (1 CU ( R G ( es ea d ( researchers suggestios especially FAO-56, we used 8, 9, 6 ad 7 rages for temperature, relative humidity, solar radiatio ad wid, respectively. The model output with 10 levels was cosidered proportioal to iput variatio i traiig (figure 1-5. Membership fuctio variables ad the degree of overlappig fuzzy fuctios determied to physical characteristics of the metioed subject ad expert opiios (Coa ad Kadel, Cosiderig the extesive use of triagular ad trapezoidal membership fuctios i practical problems ad the ivestigatios results, this fuctios also used to fuzzificatio of variables, i this study. Where, C d is costat from time steps of plat resistace (rs ad the aerodyamic resistace (ra which varies with the referece plat ad time period of day or ight. For hourly time period, C d is 0.4 ad 0.96 ad rs is 50 (sm -1 ad 00 (sm -1 durig day ad ight, respectively. Other parts of the equatio ad their uits are the same as FAO- 56 Pema-Moteith equatio..3. Fuzzy models Each Fuzzy model icludes three parts of iputs, fuzzy rules as iferece egie, ad outputs. Fuzzy models use differet methods to describe iputs ad outputs ad how to combie rules to get results. I fuzzy models, the iputs ad outputs are fuzzified variables, usually relates with fuzzy rules (IF_THEN. Sice i most applicatios, iputs ad outputs i a fuzzy system are atural umbers, we have to create itermediaries betwee fuzzy iferece egie ad eviromet. These itermediaries allow crisp umbers to become fuzzy umbers ad coversely. Oe of the most importat parts of each fuzzy model is fuzzy iferece system. Fuzzy iferece system is a o-liear model based o IF_THEN rules that with respective rules relates iput ad output variables of a real system together (Kerre, 199. Some idices of selectig iferece egie are ituitive meaig, computatioal efficiecy ad special features. Defiitio of fuzzy rules ad combiatio of fuctios metioed like: Figure 1. Membership fuctios of wid speed Figure. Membership fuctios of air temperature If ( x isa 1 1, m Ad ( xisa, m Ad ( xkisak, m The yisb j, m (3 I other words, a fuzzy rule expresses the relatioship k iput variables x 1, x... x k, ad output y. Where x k (iput ad y(output are defied fuzzy sets ad A k,m ad B j,m (j=1, k are liguistic variables (Asari et al., 010. I order to develop a fuzzy model, at first iput parameter were determied ad fuzzified (with fidig out membership fuctios, the by describig iferece rules to estimate evapotraspiratio, fuzzy outputs were coected to fuzzy iputs ad defuzzificatio of fuzzy outputs accomplished. Producig fuzzy iput ad output parameters were ivestigated accordig to the rage of available data ad proper umber of levels was cosidered for them. So, i this research based o Figure 3. Membership fuctios of relative humidity 3

4 Output value of ceter of gravity is estimated with followig equatio: Y y ( y dy ( y dy Where, y is fuzzy output value, µ (y is output membership of y, ad Y is the real value of output idex. (4 Figure 4. Membership fuctios of solar radiatio Figure 5. Membership fuctios hourly referece evapotraspiratio As referred i fuzzy rule s defiitio-oe of the most importat steps of developig a fuzzy model-we cosidered differet rules, membership fuctios, ad various degree of overlappig i traiig. It is otable; rules with differet weights for each set of iput variables were metioed. These weights were calculated by the ratio of observed output of basic model i a give level to predict output i the same level. To complete modelig, Mamdai method for fuzzy iferece, miimum method for implicatio, ad maximum method for aggregatio were used (Coa ad Kadel, 1989, Bardossy et al., 1990; Lee, As fial iferece leads to a fuzzy result, achievig to a real ad crisp umber is satisfied with may defuzzificatio methods suggested by researchers. The most commo methods preseted i figure 6 are cetroid of area (ceter of gravity, bisector of area (crossig bisectors, mea of maximum (mom, smallest of maximums (som ad largest of maximums (lom. The ceter of gravity method was applied for defuzzificatio because it is a comprehesive method suggested i may studies ad yielded good results here..4. Model s performace criteria Statistical differece measuremets are all arise from the fudametal quality of outputs (P i - O i, although each measuremet is scaled i a differet way to describe particular features of its magitude. The MBE ad RMSE statistics estimate the average error, but oe of them provide iformatio about, 1 the relative size of the average differece or the ature of the differeces comprisig MBE or RMSE. Relative differece statistics such as RMSE/Ō occasioally appear i the literature, but the geeral utility of such idices is questioable because they are ubouded. Therefore, Statistical tests proposed by Jacovides (1998 cotribute to evaluate models precisio ad comparig the results of fuzzy models to Pema-Motith-FAO ad ASCE models. Accordig to his recommedatio besides two criteria geerally used to compare evapotraspiratio models, a third criterio called t statistic should be used which is a combiatio of the two metioed criteria. RMSE t MBE ( model obs ( model obs ( 1(MBE (RMSE MBE Where, t is Jacovides criterio ad is the umber of observatios. The less t, the more accuracy the model is. Sometimes it might be followed the results of a model show high R but acceptable value of RMSE, MBE ad t; it makes it difficult to select the best model. Thus, i this study as well as the criteria itroduced by Jacovides, ew combied criterio which is the ratio of R /t (Sabziparvar et al., 008, was also used; its higher value idicate higher compatibility of the model to reality. (5 (6 (7 3. Results ad Discussio As stated before, values of hourly evapotraspiratio calculated by FAO-56 Pema-Moteith methods as outputs ad differet combiatios of effective parameters i pema equatio (table as iputs were cosidered to develop fuzzy models. Figure 6. Defuzzificatio methods 4

5 Table. Statistic tests of differet meteorological parameters affectig evapotraspiratio Data set x Mea x mi x max S x Correlatio whit O Solar radiatio (w/m (Rs Temperature ( C (T Wid Speed (m/s (U Relative Humidity (% (RH Evapotraspiratio (o(mm/hr Accordig to table, solar radiatio ad wid speed have the highest ad lowest correlatio coefficiet with hourly referece evapotraspiratio, respectively. After data aalyzig, differet combiatios of suitable iputs were selected for fuzzy models. The, output of fuzzy models with ASCE ad both of them were compared with FAO-56 Pema-Moteith as a referece model i traiig ad testig. As we expected, comparig the outputs of FAO-56 PM ad ASCE models i the traiig ad testig preset high correlatio ad low MBE ad RMSE (table 3, because theoretical basis of ASCE ad FAO-56 PM equatios are the same. Meawhile, the value of statistics i both of traiig ad testig are approximately alike. Table 3. Statistic tests to compare FAO-56 PM ad ASCE outputs Phase R RMSE MBE t R /t Traiig Testig Fuzzy models vs. FAO-56 PM model The results of fuzzy models show proper correlatio with FAO-56 PM ad ASCE i traiig step. Matchig the results of fuzzy models to FAO-56 PM poits out fuzzy models I (whose iputs are T, RH, U ad R s ad IV (whose iputs are T ad RH has the highest ad lowest correlatios, respectively (table 4. Besides, Mea Biased Error was about to mm/hour. These small values represet high accuracy of developed fuzzy models. Sice the MBE values are egative, clearly the estimated values of fuzzy models are more tha FAO-56 PM model. Fuzzy Model Table 4. Statistic tests to compare fuzzy models with FAO-56 PM model outputs Traiig Testig R RMSE MBE t R /t R RMSE MBE t R /t Model I (T, U, Rh, Rs Model II (T, Rh, Rs Model III (Rh, Rs Model IV (T, Rh Also, the Fuzzy models RMSE i traiig are calculated betwee 0.31 to 0.18 mm/hour with the lowest value for Model I. Cosiderig R, RMSE ad MBE statistics poit out, selectig proper model is ot simple; because there is t a sigificat differece amog models I to III. Moreover, t ad R /t values do ot justify the results of geeral statistics. Therefore, it is better to use t ad R /t as additioal statistics. Jacovides statistic (t shows that Miimum ad maximum values equal to 6.8 ad 59.6 for Fuzzy models IV ad I, respectively but R /t is ot maximum for model IV. However, this statistic is almost the same for model II with three variables (temperature, relative humidity, ad solar radiatio ad model III with two variables (relative humidity, solar radiatio. Simultaeous evaluatios of all statistics show that Estimatig O with fuzzy model II (temperature, relative humidity ad solar radiatio yields the best result i traiig. But it is otable that there is t much differece betwee models II ad III. Matchig outputs of fuzzy models ad FAO-56 PM model i the testig revealed the results are almost similar to what eared i traiig (table 4. Based o geeral statistics (R, MBE ad MRSE the best results are for fuzzy model II. Figure 7 marks results of the fuzzy model with three iputs agaist FAO-56 PM i testig. The liear relatioship is determied as O (Fuzzy = O (FAO-56 PM (R =0.97. The slope of the lie is close to 1 ad its itercept is zero. This result shows a good aligmet alog the 1:1 lie ad demostrates that simulated values by Fuzzy model are close to those foud by FAO-56 PM model. 5

6 Figure 7. Hourly referece evapotraspiratio obtaied from three-parameter fuzzy model compared with FAO-56 PM model i testig 3.. Fuzzy models vs. ASCE model The performace of the FIS models is compared with ASCE model for traiig ad testig. The results show that fuzzy model I (R s, T, RH, ad U has the highest ad fuzzy model IV (T ad RH has the lowest correlatio amog fuzzy models i traiig. Also, preseted fuzzy models have low RMSEs; their values are to mm /hr. Cosiderig MBE chages to mm/hr, i coclusio fuzzy models estimates hourly evapotraspiratio values slightly more tha ASCE model. Accordig to above statistics, model IV has the highest accuracy i traiig. But, this result is ot justified with t ad R /t statistics. Based o these two statistics, fuzzy model II (R s, T ad RH is the best (table 5. These results have bee justified i testig however the statistics values are fairly differet. But o the whole, results affirmed that model II is the best i both of traiig ad testig phases ad results preseted i table 5 approve it, too. Table 5. Statistic tests to compare fuzzy models with combied ASCE model outputs Fuzzy Model Traiig Testig R RMSE MBE t R /t R RMSE MBE t R /t Model I (T, U, Rh, Rs Model II (T, Rh, Rs Model III (Rh, Rs Model IV (T, Rh Coclusio This paper suggests simple fuzzy models for estimatig hourly referece evapotraspiratio with limited weather data. The ability of fuzzy iferece system (FIS has bee ivestigated as a simple techique. The FIS models performace is compared with o obtaied with the FAO-56 Pema-Moteith ad ASCE equatios. The FAO-56 PM equatio is recommeded as the stadard for computig referece evapotraspiratio, but usig these equatios is limited due to data availability i areas where meteorological iformatio is scarce. At first, the commo climatic variables amely solar radiatio, temperature, ad relative humidity ad wid speed have bee selected as iputs for FIS models. Also, the correlatio betwee these climatic data with values of the hourly o estimated with FAO-56 PM equatio were cosidered. The results showed that solar radiatio (R s was foud to be more effective i o estimatio tha the other three parameters. Other effective parameters were determied as air temperature, relative humidity ad wid speed, respectively. The basic cause is possibly that solar radiatio acts as a eergy resource. As short-term chages of meteorological parameters ifluece each other, therefore the estimatio of hourly o ca be carried out with selectig more efficiet parameters ad removig some of them. Four fuzzy models were developed based o differet combiatios of these iputs. Accordig to the results obtaied, FIS models appear to be a useful tool ad these models have high compliace ad eough ability for predictig the hourly referece o. The fuzzy models whose iputs are the solar radiatio, temperature, ad relative humidity have the best performace criteria amog the iput combiatios tried i the study. Moreover, fuzzy models whose iputs are the solar radiatio, temperature, relative humidity ad wid speed, ad fuzzy models whose iputs are the solar radiatio ad relative humidity have high correlatios ad low RMSEs, too. The fuzzy models whose iputs are temperature ad relative humidity have the lowest precisio. Based o the compariso results, fuzzy models ca be developed based o data availability or data precisio i ay regio. But, iitially the fuzzy models which are supposed to use, must be evaluated ad validated, agai. 6

7 M. Naderiafar et al / Joural of Hydroscieces ad Eviromet 1 (1 : Referece 1. Alle, R.G., Pereira, L.S., Raes, D., Smith, M., Crop evapotraspiratio guidelies for computig crop water requiremets. Uited Natios Food ad Agriculture Orgaizatio, Irrigatio ad Draiage Paper 56, Rome, Italy, 300 pp.. Asari, H., Davari, K., Saaieezhad, S.H., 010. Drought moitorig usig a ew idex of stadard raifall evapotraspiratio developed based o fuzzy logic. Iraia J. Soil ad Water, 4 (1, Aytek, A., 009. Co-active Nero-fuzzy iferece system for evapotraspiratio modelig, Soft Comput, 13 ( Bardossy, A., Bogardi, I., Duckstei, L., Fuzzy regressio i hydrology. Water Resour. Res, 6 (7, Coa, Z., Kadel, A., Applicability of some fuzzy implicatio operators. Fuzzy Sets ad Systems 31 (, Doğa, E., 009. Referece evapotraspiratio estimatio usig adaptive Nero-fuzzy iferece system. Irrig ad Drai, 58 (5, Ghasemezhad Moghadam, N., Baghaieia, F., Bafadeh Zedeh, A., Fuzzy logic i simple laguage. Iraia Magazie of Quality Cotrol, 4, Hashemiajafi, F., Palagi, G.A., Azbarmi., R., 007. Estimatio of referece evapotraspiratio usig adaptive Nero-fuzzy iferece system. The 9th semiar of irrigatio ad reductio of evaporatio, Kerma, Ira. 9. Jacovides, C.P., Reply to commet o Statistical procedures for the evaluatio of evapotraspiratio computig models, Agr. Water Maage, 37 (1, Jia Big C., Zuo, L., Tig Wu., L., Di. X., 004. Predictio of daily referece evapotraspiratio usig adaptive eurofuzzy iferece system, Trasactio of the Chiese Society of Agricultural Egieerig, 0 (4, Kerre, E., 199. A comparative study of the behavior of some popular fuzzy implicatio operators o the geeralized modus poes. L. Zadeh, J. Kacprzyk, Editors, Fuzzy Logic for the Maagemet of Ucertaity, Wiley, New York, pp Kisi, Ö., Öztürk, Ö., 007. Adaptive Nero-fuzzy computig techique for Evapotraspiratio Estimatio, J. Irrig. Drai Eg, 133 (4, Kisi, Ö., 010. Fuzzy geetic approach for modelig referece evapotraspiratio, J. Irrig. Drai Eg, 136 (3, Kuchakzadeh, M., Bahmai, A., 005. Evaluatio of artificial eural etworks Performace i reducig the required parameters for estimatig referece evapotraspiratio, Iraia J. Agric. Sci, 11, Kurehpaza Dezfuli, A., 006. Theory priciples of fuzzy sets ad its applicatios i water problems modelig, Jahad daeshgahi press of Saati Amir Kabir Uiversity, Tehra, Ira, 61 pp. 16. Lee, C.C., Fuzzy logic i cotrol systems: fuzzy logic i cotroller, part II. IEEE Trasactio o Systems, Ma ad Cyberetics, 0 (, Odhiambo, L.O., Yoder, R.E., Yoder, D.C., 001. Estimatio of referece crop evapotraspiratio usig fuzzy state models. Tras of the ASAE, 44 (3, Sabziparvar, A.A., Tafazoli, F., Zareayae, H., Baezhad, H., Mosavibayegi., M., Mohseimovahed, A., Meryaji., N., 008. Compariso of several models to estimate referece evapotraspiratio i cold ad semi-arid climates i order to optimize usage of radiatio models, Iraia J. Soil ad Water, (, Shayaezhad, M., 006. Compariso of accuracy i artificial eural etworks ad Pema-Motith i the calculatio of potetial evapotraspiratio. The th coferece o Maagemet of Irrigatio ad Draiage Networks, Ahvaz, Ira. 0. Shayaezhad, M., 007. Determiatio of potetial evapotraspiratio usig fuzzy regressio, Iraia J. Water Resour. Res, 3, Syder, R.L., Pruitt, W.O., 199. Evapotraspiratio data maagemet i Califoria. Irrigatio ad Draiage Sessio Proceedigs Water Forum 199, ASCE. August -6, Baltimore, MD., pp Vaziri, Z.H., Salamat, A., Etesari, M.R., Maschi, M., Heydari, N., Dehghai Saich, H., 008. Crop evapotraspiratio guidelies for computig crop water requiremets. Natioal Committee of Irrigatio ad Draiage Press, Tehra, Ira, 36 pp. 7