Daily Pan Evaporation Modelling With ANFIS and NNARX

Transcription

1 Iran Agrcultural Research, Vol. 3, No., Prnted n the Islamc Republc of Iran Shraz Unversty Daly Pan Evaporaton Modellng Wth ANFIS and NNARX J. PIRI and H. ANSARI Department of Water Engneerng, Sol and Water College, Unversty of Zabol, I.R. Iran Department of Water Engneerng, Ferdows Unversty of Mashhad, I.R. Iran Receved 5 September, Accepted 4 January 3, Avalable onlne June 6, 3 ABSTRACT- Evaporaton, as a major component of the hydrologc cycle, plays a key role n water resources development and management n ard and sem-ard clmatc regons. Although there are emprcal formulas avalable, ther performances are not all satsfactory due to the complcated nature of the evaporaton process and the data avalablty. Ths paper explores evaporaton estmaton methods based on nonlnear dynamc neural network model (NNARX ) and adaptve neuro-fuzzy nference system (ANFIS) technques. It has been found that NNARX and ANFIS technques have much better performances than the emprcal formulas (for the test data set, NNARX R =.95, ANFIS R =.94, Meyer R =.8 and Marcano R =.68). ANFIS and NNARX models are slghtly better albet the small dfference. Although NNARX and ANFIS technques seem to be powerful, ther data nput selecton process s qute complcated. More studes are needed to gan wder experence about ths data selecton tool and how t could be used n assessng the valdaton data. Keywords: ANFIS, Emprcal formulas, Evaporaton, NNARX INTRODUCTION Evaporaton has wde mplcatons amongst hydrologcal processes and plays a key role n water resources management n ard and semard clmatc regons. The most common and mportant factors affectng evaporaton are solar radaton, ar and sol temperature,relatve humdty, vapor pressure defct, atmospherc pressure, and wnd speed. In one of the earlest publshed papers, Dalton (7) ponted out that evaporaton was proportonal to the dfference between vapor pressure of the ar at the water surface and that of the overlyng ar, although apparently he never expressed ths relatonshp n mathematcal terms. () Later concluded that the vapor pressure defct was a much more senstve ndcator of the water vapor condtons of the atmosphere and underwent greater varatons for temperature changes than dd the relatve humdty. Evaporaton losses should be consdered n the desgn of varous water resources and rrgaton systems. In areas wth lttle ranfall, evaporaton losses can represent a sgnfcant part of the water budget for a lake or *Instructor and Assocate Professor, respectvely Correspondng Author

2 Pr and Ansar reservor, and may contrbute sgnfcantly to the lowerng of water surface elevaton (3).Therefore, accurate estmaton of evaporaton loss from the water body s of prmary mportance for montorng and allocatng water resources, at farm scales as well as at regonal scales. Owng to ts convenence and cost effectveness, an evaporaton pan s one of the most wdely used nstruments for the measurement of evaporaton, but ts performance s affected by nstrumental lmts and practcal ssues such as measurement errors and mantenance, whch can reduce the accuracy of evaporaton measurements. It s also dffcult to use the pan by telemetry technques, hence the human labor cost s hgh. Alternatvely, mathematc models could be used to estmate evaporaton from related weather varables. To date, many researchers have developed models for estmatng free water evaporaton all over the world (7). Mosner and Aulenbach (5) compared four emprcal methods of evaporaton estmaton, ncludng the Prestly Taylor, Penman, DeBrun Kejman, and Papa Daks equatons for Lake Semnole, southwestern Georga, and northwestern Florda, from Aprl to September. It has been found that the average monthly lake evaporaton estmates derved from the emprcal equatons were as much as 6% n error. Therefore, there s room for mprovement n the conventonal evaporaton models. In recent years, other methods have been explored by many researchers, such as the mass transfer methods (37, 7, ) and eddy correlaton technques (36, ). Despte the large amount of lterature publshed, most of the reported methods are too demandng for observed meteorologcal data and prone to errors f locally calbrated parameters are not avalable. In addton, evaporaton s an ncdental, nonlnear, complex, and unsteady process, so t s dffcult to derve an accurate formula to represent all the physcal processes nvolved. As a result, there s a new trend n usng data mnng technques such as fuzzy logc, artfcal neural networks (ANN), and ANFIS to estmate evaporaton. Ths followed a large number of studes n whch some hydrologcal processes were smulated by nonlnear models based on ANN, support vector machnes, fuzzy logcal system, polynomal functon, local lnear regresson, Bayesan networks, decson trees, etc. (7, 7, 7, 8). In evaporaton estmaton, some typcal studes reported so far use ANN n modelng daly sol evaporaton (8), daly evapotranspraton (9), daly pan evaporaton (3, 33, 8, 7), and hourly pan evaporaton (3). Usng temperature data alone, Sudheer et al. (3) found that a properly traned ANN model could reasonably estmate the evaporaton values at ther study area n a temperate regon. From these reports, t s clear that ANN models are superor to the conventonal regresson models, as ANN does not requre any predetermnaton of regresson forms. Ths advantage becomes more promsng when an engneerng problem s too complex to be represented by regresson equatons (3). In comparson wth a wder applcaton of ANN n other felds (such as flood forecastng,, 6, 35, 5, 4, ), the modelng experence of ANN n evaporaton estmaton s stll qute lmted and there s a need to study and report trals of ths technque n dfferent clmate regons so that some generalzaton of ths method could be acheved. MATERIALS AND METHODS Emprcal Methods of Estmatng Evaporaton Evaporaton pans are commonly used to estmate evaporaton from lakes and reservors. However, there are many problems wth them. Many factors can 5

3 Daly Pan Evaporaton Modellng Wth ANFIS and ntroduce errors n pan evaporaton measurement, such as debrs n water, anmal actvty n and around the pan, pan sze, materals employed to construct the pan, exposure of the pan, strong wnds, and measurement of water depth n the pan (7). In practce, emprcal formulas have been derved to estmate evaporaton on the bass of feld measurements of evaporaton pans and reservor/lake water balances. Those formulas are lnked wth varous weather factors mpactng evaporaton. As the complexty of the emprcal methods ncreases, data requrements to drve the equatons often make the emprcal methods hard to apply for feld applcatons. A large number of emprcal methods for estmatng evaporaton based on dfferent meteorologcal nputs have been suggested durng the past decades (7). However, many of them are not applcable n ths study due to ther lmtatons n data avalablty. As a result, only two relevant emprcal methods are used n the case study (.e., they are compatble wth the avalable weather measurements), as lsted n Table. In ths table, for each formula, E=evaporaton rate (mm/day); es=saturaton vapor pressure (mllmeters of Hg); ea=actual vapor pressure (mllmeters of Hg); U=average wnd velocty (km/h) at a heght of m above the lake or surroundng land areas; and C for deep lake=.36, low lake=.5 Table. Evaporaton Formulas for Lakes and Reservors References Equaton Formula name Alzadeh, 4 E =.3U(es - ea) Marcano U Alzadeh, 4 E = ( + ) C ( e s ea ) Meyer 6 Adaptve Neural-based Fuzzy Inference System (ANFIS) and NNARX The adaptve neuro-fuzzy nference system s a new mproved tool and a data drven model lng approach for determnng the behavor of mprecsely defned complex dynamcal systems (7).An ANFIS ams at systematcally generatng unknown fuzzy rules from a gven nput output data set (5). Fg. represents a typcal ANFIS archtecture. Fg.. A typcal ANFIS archtecture (Jang 993) The fgure s based on: Layer : every node n ths layer s an adaptve node wth a node functon that may be a generalzed bell membershp functon (Equ.), a Gaussan membershp functon(equ. ), or any membershp functons 53

4 Pr and Ansar µ A( x ) = + µ A [ x c ] zb a x c ( x ) = exp a () () Where a, b and c are premse parameters.also x s the nput to node and A s the lngustc label (for example, low and hgh) assocated wth ths node functon. Premse parameters change the shape of the membershp functon. Layer : every node n ths layer s a fxed node labeled, representng the frng strength of each rule,and s calculated by the fuzzy AND connectve product of the ncomng sgnals by usng (Equ. 4). w = µ ( x ) ( x ) =, A µ B Every node n ths layer s a fxed node labeled N, representng the normalzed frng strength of each rule.the th node calculates the rato of the th rule s frng strength to the sum of two rule s frng strengths by usng (Equ. 4) = w w =, w + w (4) Layer 4: every node n ths layer s an adaptve node wth a node functon (Equ. 5), ndcatng the contrbuton of the th rule to wards the over all output. Wz = w(px+ qy + r) (5) Where p, q and r are consequent parameters. Layer 5: the sngle node n ths layer s a fxed node labeled P, ndcatng the over all output as the summaton of all ncomng sgnals calculated by (Equ. 6): Z = wz = wz w What should be realzed when nspectng the above layer ss prncpally three dfferent types of components that can be adapted as follows (4):. Premse parameters as nonlnear parameters that appear n the nput membershp functons.. Consequent parameters as lnear parameters that appear n the rules consequents (output weghts). 3. Rule structure that needs to be optmzed to acheve a better lngustc nterpretablty. In ths study, three Gaussan membershp functons were used to construct the ANFIS model. There are a wde varety of algorthms avalable for tranng a network and adjustng ts weghts. In ths study, an adaptve technque called momentum Levenberg Marquardt based on the generalsed delta rule was adopted (5). In ths scheme, the adaptve learnng rates were used for ncreasng the convergence velocty throughout all ANFIS smulatons. The ANN s an evolvng technque and new progress stll beng made wth tme. In recent years, a combnaton of ANN and ARX (Autoregressve Extra Input) has ganed some popularty n the control feld. Tradtonally, The ARX model has been wdely used n control theory for modellng varous control processes (). Its smple structure s bascally lnear and can be descrbed as 54 (3) (6)

5 Daly Pan Evaporaton Modellng Wth ANFIS and A(q)y(t)= B(q) u(t-n k )+e(t) (7) Where y(t) s the output(evaporaton) u(t) s a vector wth all the nputs, such as wnd, temperature, relatve humdty and vapour pressure defct e(t) s the whte nose, A(q) and B(q) are the polynomals n terms of tme shft operator, of the n a and n b orders respectvely and n k s the tme delay. Ths model s structure s shown n Fgure (a). The ntegrated model of NNARX s a combnaton of the ANN and ARX. Such a model has recently been explored and studed by researchers n other felds wth some successful results (6). The estmated value of y(t) shown by y ( t θ ) s expressed below: y( t θ) = f ( u( t nk),..., u( t nb nk + ), (8) y( t ),..., y( t na)) Where f (.) s the nonlnear mappng by ANN, and θ = model parameters. Ths structure s almost the same as the structure n Fgure (a) but nstead of usng a smple summaton block, a neural network structure s replaced as shown n Fgure 3(b). x(t x(t x(ty(t-) y ( t / θ ) x(ty(t-) Neural Network y ( t / θ ) y(t- y(t- Fg.. (a) The ARX block and (b) The NNARX model block Study Area and Data The study area s the Sstan plan located n the Southeast of Iran, one of the drest regons of Iran and famous for ts " day wnd" (bād-e sad-o-bst-roz), a hghly persstent dust storm n the summer whch blows from north to south wth veloctes of nearly knots. Hrmand Rver, orgnated from Afghanstan, s bfurcated nto two branches when t reaches the Iranan border, namely Paran and Sstan. Sstan s the only water supply known n Sstan and Baluchstan provnce. It s the man stream of Hrmand Rver, whch flows through Sstan plan and dscharges nto the natural swamp of Hamun-e-Hrmand (Fgure 3). As can be seen n the fgure, Sstan plan s essentally an nland delta wth ts major watercourses leadng to a seres of lakes. The Sstan delta has a very hot and dry clmate. In summer, the temperature exceeds 5 o C. Ranfall s about 6 mm/year and occurs only n autumn and wnter. Open water evaporaton s very hgh and s estmated to be 3 mm/year. Strong wnds n the regon are qute unque and are an mportant contrbutng factor for the hgh evaporaton. The Chahnme reservors are a seres of natural depressons used 55

6 Pr and Ansar Fg. 3. The Sstan plan and locaton of the Chahnme reservors Prmarly to store water for rrgaton. However, they also play an mportant part n attenuatng floods. Durng perods of hgh flows, water s dverted to these reservors va an ntake and canal whch has a capacty of up to m 3 /s. The daly weather varables of an automated weather staton, Chahnme Staton of Zabol (lattude W, longtude N) operated by the IR Sstan and Balochstan Regonal Water (IR SBRW) were used n ths study. The measured daly meteorologcal data for the Chahnme staton were obtaned from the IR SBRW ( The data sample conssted of eleven years (5 9) of daly records of ar temperature (T), wnd speed (W), sunshne hours (SR), relatve humdty (RH) and pan evaporaton (E). For the staton of nterest, the frst deta of day nne years (983 4) were used for tranng modes and the remanng data were used for testng. The daly statstcal parameters of the weather data are gven n Table. In the table, the Xmean, Sx, Cv, Csx, Xmax and Xmn denote the mean, standard devaton, coeffcent of varaton, skewedness, maxmum and mnmum of the weather factors, respectvely. Table. Correlaton matrx for nput-output varables of ANFIS and NNARX models Staton Chahnmeh Data set Unt X mean Sx Cv (Sx/X mean ) Csx X mn X max Correlaton wth ET T C RH % Wnd m/s Sun shne hours ET mm/ day The last column n Table represents the correlaton vector between the potental nput varables for the models (T, SR, W, and RH) and the output varable 56

7 Daly Pan Evaporaton Modellng Wth ANFIS and (E). In the table, the bold characters hghlght the sgnfcant factors that affect evaporaton. Evaporaton losses n the Chahnme staton are moderately hgh due to hgh temperature and long sunshne hours that show sgnfcantly hgh varatons. The data were analyzed wth the Mntab program. A smlarty matrx was constructed usng Jaccard s coeffcent of smlarty and a dendrogram was obtaned as shown n Fgure 4. The dendrogram analyss revealed a strong lnk between evaporaton and the two nput varables of wnd speed and ar temperature. The other two weather factors (sunshne hours and relatve humdty) played useful but less mportant roles n the evaporaton process. It s concluded that for the ANFIS and NNARX models, all four varables (ar temperature, wnd speed, sunshne hours, and relatve humdty) should be consdered as potental nputs. Fg. 4. The rdendrogram of weather varables of nterest RESULTS Among the four meteorologcal varables consdered, t s clear that some would play more mportant roles than others and t s mportant that only the sgnfcant ones are used as nputs for the fnal model. In ths study, varous combnatons of these varables were examned to evaluate the mpact of each varable. Root mean square error (RMSE), ndex of operaton (d), mean absolute error (MAE), mean square error (MSE), mean absolute relatve error (MARE) and determnaton coeffcent (R) were all used as evaluaton crtera. The RMSE represents the devaton between smulated values and observed values. The parameter d shows the operaton of the model whch vares between zero and one (best values for d are closer to one). The lower MAE values ndcate more accurate estmatons. MSE and MARE provde dfferent types of nformaton about the predctve capabltes of the model. The MSE measures the goodness-of-ft relevant to hgh evaporaton values whereas the MARE yelds a more balanced estmaton of the goodness-of-ft at moderate evaporaton (5). R measures the degree to whch two varables are lnearly related. A lst of the performance measures are depcted n Table 3. Where O and P are the observed and predcted evaporaton at tme, respectvely; ō s the mean of the observed evaporaton; and N s the number of data ponts. 57

8 Pr and Ansar Table 3. Lst of the performance crtera Performance Crtera Root mean square error (RMSE) Index of operaton (d) Mean absolute error (MAE) Mean square error (MSE) Expresson RMSE = d ( n = n = = = n p = MAE ( p o ) N ( p o ) ( p + o ) p o n = = MSE = N N, p o N = o o = o o ( o p) ) The combnatory archtectures of the ANFS models for the Chahnme staton are gven n Table 4. Ths table ndcates the number of nput varable as well as ther correspondng performance crtera of RMSE, d, MAE, MSE, MARE, and R. It was concluded that the best nput combnaton should nclude all the varables ther order of mportance beng T, SR, W and RH. Table 4. A summary of statstc analyss for the ANFIS model (testng perod) Input varables RMSE d MAE (mm/day) MSE(mm /day ) R T (%) T, W T, W, SR T, W, SR and Varous nput combnatons for NNARX model were also tested and the results are dsplayed n Table 5. It s clear that the performance of NNARX s better than ANFS and the nput weather factors should nclude all four varables. Accordng to Table 6, the results of emprcal equatons to smulate evaporaton and The artfcal ntellgence( ANFIS and NNARX), smulaton models can be concluded that evaporaton results are more acceptable. Table 5. A summary of statstc analyss for the NNARX model (testng perod) Input varables RMSE d MAE (mm/day) MSE(mm /day ) R T T, W T, W, SR T, W, SR and The evaporaton smulatons usng the fnal ANFIS and NNARX models are showed n Fgure 5 and Fgure 6. As shown n the fgures (and also through Table 4 & 5), the NNARX estmates are closer to the correspondng observed evaporatons than the ANFIS model. 58

9 Daly Pan Evaporaton Modellng Wth ANFIS and Table 6. A summary of statstc analyss for the estmated values of evaporaton for the testng data set of Marcano and Meyer Formula RMSE d MAE (mm/day) MSE(mm /day ) R Marcano Meyer The evaporaton smulatons usng the fnal emprcal equatons (Marcano and Meyer ) are shown n Fgures 7 and 8. The Meyer estmates are closer to the correspondng observed evaporatons than the Marcano equaton. Evaporaton, mm A Observed ANFS Model, mm 4 35 M =.9437O R = Elapsed tme, day Observed, mm Fg. 5. Comparson of the observed and estmated evaporaton for the testng data wth the ANFIS model Evaporaton, mm Observed NN-ARX Model, mm 4 M = R = Elapsed tme, day Observed, mm Fg. 6. Comparson of the observed and estmated evaporaton for the testng data wth the NNARX model E v a p o ra t o n, m m 4 35 Observed 3 Marcano Elapsed tme, day m o d e l, m m /d a y 6 M =.475O 5 R = Observed,mm/day Fg. 7. Comparson of the observed and estmated evaporaton for the testng data wth the Marcano model 59

10 Pr and Ansar Evaporaton, mm Observed Meyer 6 M =.554O Model,mm /day R = Elapsed tme, day Observed,mm/day Fg. 8. Comparson of the observed and estmated evaporaton for the testng data wth the Meyer model DISCUSSION AND CONCLUSION Overall, the objectves of ths study were to evaluate the ANN model for evaporaton estmaton under a hot and dry clmate, to mprove the ANN model by ncorporatng ARX component, and to nvestgate the sutable nput data for the ANFIS model n comparson wth those from prevously publshed works. It s qute clear that all the planned objectves have been acheved resultng n some nterestng fndngs about weather varable selectons. Ths paper s the frst attempt n applyng ths model n a Mddle Eastern regon. It s confrmed that ANFIS works well for a hot and dry place such as Iran. The mproved performance by ntegratng ANN and ARX s not only novel (the frst applcaton of such a model n evaporaton research feld) but s also qute mnd broadenng snce t ndcates that there s stll room for mprovng the exstng ANN model despte ts beng a unversal nonlnear regresson tool. Another nterestng fndng n ths study s the unque combnaton of the contrbutng varables. It has been demonstrated that the mportant weather factors to be ncluded n the model nput are: ar temperature, sunshne hours, wnd speed and relatve humdty. Ths result s dfferent to all others reported n the lterature. In the USA, Han and Felker (7), used three weather nput varables to estmate evaporaton from the sol, relatve ar humdty, ar temperature, wnd speed. Kumar et al. (9) selected sx nput varables, mnmum and maxmum temperature, mnmum and maxmum relatve humdty, wnd speed, and solar radaton. In Inda wth ts hot and humd clmate, Sudheer et al. (3) found that ther model worked best wth sx nputs: mnmum and maxmum temperature, mnmum and maxmum relatve humdty, and wnd speed (although the mprovement of usng mnmum and maxmum temperature over the mean temperature was qute small). In Turkey, there were mxed results from the publshed papers. Terz and Kesk (34) nvestgated the evaporaton at Lake Egrdr and found that mportant weather factors were (n order of ther mportance): ar temperature, solar radaton and ar pressure. It s surprsng to note that they found the nfluences of relatve humdty and wnd were neglgble but the ar pressure was ncluded. One year later, the authors reported that only two weather nput varables (ar temperature and solar radaton) were good enough and ar pressure was dsmssed. Another paper by the authors(33) reported three contrbutng weather factors to be consdered n ther model: solar radaton, ar temperature, and relatve humdty (wnd and ar pressure were gnored). The caprcous choce of the weather varables may ndcate that ther model nput selecton schemes were not very stable. Tan et al. (3) found the mportant varables were: sola radaton, relatve humdty, ar temperature and surface wnd speed. 6

11 Daly Pan Evaporaton Modellng Wth ANFIS and The results n the testng of NNARX and ANFIS are lsted n Table 4, 5, 6 along wth the emprcal methods. It s observed that NNARX and ANFIS have much better performances than the emprcal equatons. The best result for the emprcal formula Marcano s R =.68 and for Meyer t s R=.8 for the test data set. In contrast, the R s.95 for NNARX and.94 for ANFIS both sgnfcantly better than all the three emprcal formulas. Between NNARX and ANFIS, NNARX has a slghtly better performance, whch ndcates that the fuzzy approach has not helped mprove the evaporaton modelng results. Fgs. 5 and 6 llustrate the scatter plots for all the models (snce no tranng s needed for the emprcal models, only the estmaton results on the testng data are presented n Fg. 6).Ths phenomenon could also occur n other clmate regons and we hope ths paper wll nspre more researchers to explore ths n ther future evaporaton studes. REFERENCES. Anderson, D.B Relatve Humdty or Vapour Pressure Defct, Ecology, 7(): Blanken, P.D., W.R. Rouse, A.D. Culf, C. Spence, L.D. Boudreau, J.N. Jasper, B. Kochtubajda, W.M. Scertzer, P. Marsh and D. Verseghy.. Eddy covarance measurements of evaporaton from Great Slave Lake, Northwest Terrtores, Canada. Water Resources Research 36 (4), Blodgett, T.A., J.D., Lenters and B.L. Isacks Constrants on the orgn of paleolake expansons n the Central Andes, Earth Interactons. 4. Clar, T. A., and J. M. Ehrman Usng neural networks to assess the nfluence of changng seasonal clmates n modfyng dscharge, dssolved organc carbon, and ntrogen export n eastern Canadan rvers. Water Resour. Res. 34(3): Elshorbagy, A., S. P., Smonovc and U. S. Panu.. Performance evaluaton of artfcal neural networks for runoff predcton. J. Hydrologc. Eng. 5(4): Fernando, D. A. and A. W. Jayawardena Runoff forecastng usng RBF network wth OLS algorthm. J. Hydrologc. Eng. 3(3), Han, D., T. Kwong and S. L. 7. Uncertantes n real-tme flood forecastng wth neural networks, D. Han, T. Kwong, and S. L, Hydrologc. Processes, DOI:./hyp.684,, Han, H. and P. Felker Estmaton of daly sol water evaporaton usng an artfcal neural network, J Ard Envron. 37: Hostetler, S.W. and P.J., Bartlen. 99. Smulaton of lake evaporaton wth applcaton to modelng lake level varatons of Harney Malheur Lake, Oregon. Water Resour. Res. 6 (): Hsu, K., H.V., Gupta and S., Sorooshan Artfcal neural network modelng of the ranfall-runoff process. Water Resour. Res., 3(), Ikebuch, S., M., Sek and A., Ohtoh Evaporaton from lake Bwa. Journal of Hydrology, Lard, N.F., Krstovch, D.A.R.,. Varatons of 6

12 Pr and Ansar sensble and latent heat fluxes from a great lakes buoy and assocated synoptc weather patterns. J. Hydrometeorol 3 (): 3.. Imre, C. E., S., Durucan and A., Korre.. Rver flow predcton usng neural networks: Generalzaton beyond the calbraton range. J. Hydrologc. Eng. 33(3-4): Terz, Ö., Erol Keskn, M., and Dlek Taylan, E. 6. Estmatng Evaporaton Usng ANFIS. J. Irrg. Dran Eng., 3(5), Jang J-SR. ANFIS: adaptve-network-based fuzzy nference system. IEEE Trans. 5. Karunanth, N., W.J. Grenney, D. Whtley and K. Bovee Neural networks for rver flow predcton. J Computng n Cvl Eng. 8():. 6. Keshavarz, E. and M. Roopae. 6. "Intellgent Structures n Economcal Forecastng", Proceedngs of nternatonal conference on advanced technologes n telecommuncatons and control engneerng (ATTCE), Malaysa, August. 7. Keskn, M.E. and O. Terz. 6. Artfcal Neural Network Models of Daly Pan Evaporaton, J Hydrologc. Eng. ASCE, 65-7 DOI:.6/(ASCE)84-699(6):(65) 8. Ks, O. 6. Daly pan evaporaton modelng usng a neuro-fuzzy computng technque, J. Hydrol. 39( ), DOI:.6 /j. jhydrol Kumar, M., N.S., Raghuwansh, R., Sngh, W.W., Wallender and W.O., Prutt.. Estmatng evapotranspraton usng artfcal neural network, J. Irrg. Dran. Eng. 8(4): Lard, N.F. and D.A.R. Krstovch.. Varatons of sensble and latent heat fluxes from a great lakes buoy and assocated synoptc weather patterns. J Hydrometeorol. 3 (): 3. Long, S.Y., S. T., Khu and W.T., Chan.. Dervaton of pareto front wth genetc algorthm and neural network. J. Hydrologc. Eng.. 6(): Ljung, L System Identfcaton. Theory for the user. Prentce Hall PTR 3. McCuen, R.H Hydrologc Analyss And Desgn, Prentce Hall, Englewood Clffs, New Jersey. 4. McCulloch, W.S. and W. Ptts A logcal calculus of the deas mmanent n nervous actvty, Bull. Math. Bophyscs 5: Moghaddamna, A., M. Ghafar Gousheh, J. Pr, s. Amn and D. Han. 9. Evaporaton estmaton usng artfcal neural networks and adaptve nero-fuzzy nference system technques. J Adv. water Resour.3 : Mosner, M.S. and B.T. Aulenbach. 3. Comparson of methods used to estmate lake evaporaton for a water budget of lake Semnole, southwestern Georga and northwestern Florda, Proceedngs of the 3 Georga Water Resources Conference, held Aprl 3 4, 3, at the Unversty of Georga. 7. Pr, J., S. Amn, A. Moghaddamna, D. Han and D. Remesun. 9. Daly pan evaporaton modellng s hot and dry clmate. J. Hydrologc, Eng., : Rumelhart, D. E., G. E. Hnton and R. J. Wllams Learnng nternal representatons by back propagaton. In D. E. Rumelhart, J. L. McClelland, and 6

13 Daly Pan Evaporaton Modellng Wth ANFIS and PDP Research Group (Eds.), (Vol. ) (pp ). Parallel Dstrbuted Processng, Cambrdge, MA: MIT Press. 9. Smth, M Neural networks for statstcal modelng, Van Nostrand Renhold.5 Ffth Avenue, New York, NY Sudheer, K.P., A.K., Gosan, D.M., Rangan and S.M., Saheb.. Modellng evaporaton usng an artfcal neural network algorthm, Hydrol. Process. 6, Jang, J. S. R Adaptve-network-based fuzzy nference system. Syst Man Cybern;3(3): Tan,.S.B.K, E.B. Shuy and L.H.C. Chua. 7. Modellng hourly and daly openwater evaporaton rates n areas wth an equatoral clmate. Hydrologc. processes. : DOI:./hyp Terz, O and Keskn, M.E. and Taylan, E.D. 6. Estmatng Evaporaton usng ANFIS, J Irr. Dran. Eng. ASCE, : Terz, O and M.E. Keskn. 5. Modellng of Daly Pan Evaporaton, J App Sc 5(): Tokar, A.S. and P.A., Johnson Ranfall-runoff modelng usng artfcal neural networks, J. Hydrologc. Eng. 4(3): Wnter, T.C. 98. Uncertantes n estmatng the water balance of lakes, Water Resour. Bull. 7 (): Yu, Y.S. and H.V., Knapp, 985. Weekly, monthly, and annual evaporatons for Elk Cty Lake, J Hydrol. 8:

14 Pr and Ansar NN_ARX ANFIS * -... NN-ARX ANFIS.. ( ARX ) ANFIS NNARX ANFIS R=.95 NNARX ) NNARX ANFIS.(R=.68 Marcano R =.8 R =.94 ANFIS NNARX... ANFIS NNARX : * 64