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2 Wte Vpo Flux in Agoeoytem Method nd Model Review Víto Hugo Rmíez-Buile 1 nd Ei W. Hmen Ntionl Coffee Reeh Cente-Cenifé 2 Univeity of Pueto Rio 1 Colombi 2 USA 1. Intodution The wte vpo flux in goeoytem i the eond lget omponent in the hydologyl yle. Wte vpo flux o evpotnpition (ET) fom the vegettion to the tmophee i widely tudied vible thoughout the wold. ET i impotnt fo detemining the wte equiement fo the op, limti hteiztion, nd fo wte mngement. The etimtion of ET fom vegetted e i bi tool to ompute wte blne nd to etimte wte vilbility nd equiement. Duing the lt ixty ye evel method nd model to meue the wte flux in goeoytem hve been developed. The im of thi hpte i to povide litetue eview on the ubjet, nd povide n oveview of method nd model developed whih e widely ued to etimte nd/o meue ET in goeoytem. Evpotnpition ontitute n impotnt omponent of the wte fluxe of ou hydophee nd tmophee (Conoy et l., 2003), nd i widely tudied vible thoughout the wold, due to it pplibility in viou diipline, uh hydology, limtology, nd giultul iene. Peei et l., (1996) h epoted tht the etimtion of ET fom vegetted e i bi tool fo omputing wte blne nd to etimte wte vilbility nd equiement fo plnt. Meuement of ET i needed fo mny pplition in giultue, hydology nd meteoology (Suleimn & Cgo, 2004). ET i mjo omponent of the hydologi wte budget, but one of the let undetood (Wilon et l., 1992). ET pemit the etun of wte to the tmophee nd indue the fomtion of loud, pt of neve-ending yle. ET lo pemit the movement of wte nd nutient within the plnt; wte moving fom the oil into the oot hi, nd then to the plnt leve. ET i omplited poe beue it i the podut of the diffeent poee, uh evpotion of wte fom the oil, nd wte inteepted by the nopy, nd tnpition fom plnt leve. Phyiologil, oil nd limti vible e involved in thee poee. Symon in 1867 deibed evpotion...the mot depete t of the depete iene of meteoology (Monteith, 1997). The fit vpo flux meuement wee initited by Thonthwite nd Holzmn in 1930, but tht wok w inteupted by Wold W II (Monteith, 1997). In the lte 1940 Penmn (1948) publihed the ppe Ntul Evpotion fom open Wte, Be Soil nd G in whih he ombined themodynmi eqution fo

3 4 Evpotnpition the ufe het blne nd n eodynmi eqution fo vpo tnfe. The Penmn eqution i one of the mot widely ued eqution in the wold. The eqution w lte modified by Monteith (1965; 1981) nd i widely known the The Penmn-Monteith Model. It i lo neey to intodue eview of the wok of Bowen, who in 1926 publihed the eltionhip between the enible nd ltent het fluxe, whih i known the Bowen tio. Meuement of the wte vpou flux beme ommon ptie by men of the Bowen tio enegy blne method (Tnne, 1960). Allen et l. (1998) epted the fto tht ffet the ET into thee goup: ) Wethe pmete, uh dition, i tempetue, humidity nd wind peed. The evpotnpitionl powe of the tmophee i expeed by the efeene op evpotnpition (ET o ) the Penmn-Monteith (FAO-56), o uing diet meuement of pn evpotion dt (Dooenbo & Puit, 1977), o uing othe empiil eqution; b) Cop fto uh the op type, viety nd developmentl tge hould be onideed when eing the ET fom op gown in lge, well-mnged field. Diffeene in eitne to tnpition, op height, op oughne, efletion, gound ove nd op ooting hteiti eult in diffeent ET level in diffeent type of op unde identil envionmentl ondition. Cop ET unde tndd ondition (ET ) efe to exellent mngement nd envionmentl ondition, nd hieve full podution unde given limti ondition (eqution 2); nd ) Mngement nd envionmentl ondition (ET dj ). Fto uh op wte te, oil linity, poo lnd fetility, limited pplition of fetilize, the peene of hd o impemeble oil hoizon, the bene the ontol of diee nd pet nd poo oil mngement my limit the op development et., nd edue the ET, (ET dj eqution 3). One of the mot ommon nd fily elible tehnique fo etimting ET 0 i uing evpotion pn dt when djutment e mde fo the pn envionment (Gime et l. 2002) uing the pn evpotion nd the pn oeffiient (K p ). ET o K p. E p (1) Whee E p i the pn evpotion (mmdy -1 ), nd K p i the pn oeffiient, nd depend on lotion, o it i impotnt to know o lulte thi oeffiient befoe lulting the ET o. Allen et l., (1998) gve methodology to know o lulte Kp, nd i eentilly oetion fto tht depend on the peviling upwind feth ditne, vege dily wind peed, nd eltive humidity ondition oited with the iting of the evpotion pn (Dooenbo & Puitt 1977) 2. Cop wte flux uing ingle op oeffiient- The FAO ppoh The United Ntion Food nd Agiultul Ogniztion (FAO) i lo well knew the Two tep method, whih i vey ueful fo ingle op nd when efeene ondition e vilble (i.e., no op wte te). In thi e, op evpotnpition (ET ) n be etimted uing eqution 2 (Dooenbo & Puitt 1977; Allen t l., 1998): ET K. ET o (2) whee K i the oeffiient expeing the tio between the op nd efeene ET fo g ufe. The op oeffiient n be expeed ingle oeffiient, o it n be plit into two fto, one deibing the ffet of evpotion nd the othe the ffet of tnpition.

4 Wte Vpo Flux in Agoeoytem Method nd Model Review 5 A oil evpotion my flutute dily, eult of infll nd/o iigtion, the ingle op oeffiient expee only the time-vege (multi-dy) effet of op ET, nd h been onideed within fou ditint tge of gowth (ee. FAO,56. Allen et l., 1998). When te ondition exit, the effet n be ounted fo by op wte te oeffiient (K ) follow: ET dj. K. K. ET o (3) 2.1 Cop oeffiient Although numbe of ET etimtion tehnique e vilble, the op oeffiient (K ) ppoh h emeged the mot widely ued method fo iigtion heduling (Hunke et l., 2002). A ET i not only funtion of the limti fto, the op oeffiient n inlude ondition elted to the op development (K ), nd non-tndd ondition (K ). The K i the pplition of two onept: ) op tnpition epeented by the bl op oeffiient (K b ), nd b) the oil evpotion K e (Allen et l., 1998) follow: K K b + K e (4) K i n empiil tio between ET nd ET o ove g o lflf, bed on hitoi meuement. A K uve i ontuted fo n entie op gowing eon, nd whih ttempt to elte the dily wte ue te of the peifi op to tht of the efeene op (Hunke et l., 2002). The FAO ppe # 56 (Allen et l., 1998) povided detiled intution fo lulting thee oeffiient. Fo limited oil wte ondition, the ftionl edution of K by K depend on the op, oil wte ontent, nd mgnitude of the tmophei evpotive demnd (Dooenbo &Puitt, 1977). The vlue fo K equl K b fo ondition whee, fit, the oil ufe lye i dy (i.e., when K e 0) nd, eond the oil wte within the oot zone i dequte to utin the full tnpition (non-teed ondition, i.e., K 1). When the vilble oil wte of the oot zone beome low enough to limit potentil ET, the vlue of the K oeffiient i le thn 1 (Allen et l., 1998; Hunke, 1999, Hunke et l., 2002). The oil evpotion oeffiient ount fo the evpotion omponent of ET when the oil ufe i wet, following iigtion o infll (Allen et l., 1998; Hunke et l. 2002). When the vilble oil wte of the oot zone beome low enough, op wte te n ou nd edue ET. In the FAO-56 poedue, the effet of wte te e ounted fo by multiplying K b (o K ) by the wte te oeffiient (K ). K. K (K b. K + K e ) ET /ET o (5) Whee K < 1 when the vilble oil wte i inuffiient fo the full ET nd K 1 when thee i no oil wte limittion on ET. Thu, to detemine K, the vilble oil wte within the op zone fo eh dy need to be meued o lulted uing oil wte blne ppoh (Hunke et l., 2002). The etimtion of K e uing the FAO-56 method, equie the ue of the oil field pity (FC), the pemnent wilting point (PWP), totl evpoble wte (TEW), the ftion of the oil ufe wetted (f w ) duing eh iigtion o in, nd the dily ftion of the oil ufe hded by vegettion (f ), o onveely the unhded ftion (1-f ). Hunke et l., (2002) epoted n exponentil eltion between 1-f nd height of the Alflf op.

5 6 Evpotnpition The meuement of K e nd K b n be mde by pefoming dily wte blne, nd ue of the following eqution fom FAO Ppe 56 (Allen et l., 1998). The oil evpotion (E) n be lulted uing the eqution (8) ET (K b +K e ) ET o (6) K b (ET /ET o )-K e (7) E K e ET o ; (8) nd K e i equl to K e E/ET o (9) The oil evpotion (E) n be meued uing the wte blne (eqution 10) I f (10) i i E De, i 1 ( Pi ROi ) + + Tew, i + DPe, i fw few whee: D e,i-1 i the umultive depth of evpotion following omplete wetting fom the expoed nd wetted ftion of the topoil t the end of dy i-1 (mm), P i i the peipittion on dy i (mm); RO i i peipittion unoff fom the ufe on dy i (mm), I i i the iigtion depth on dy i tht infiltte into the oil (mm), E i i evpotion on dy i (i.e., E i K e /ET o ) (mm), T ew,i i depth of tnpition fom the expoed nd wetted ftion of the oil ufe lye on dy i (mm), f w i ftion of oil ufe wetted by iigtion (0.01-1), nd f ew i the expoed nd wetted oil ftion ( ). The tio of efeene evpotion to efeene tnpition depend on the development tge of the lef nopy expeed the dimenionle ftion of inident bem dition tht penette the nopy (Cmbell &Nomn, 1998; mentioned by Zhng et l. 2004). δ exp(. LAI ) (11) whee i the dimenionle nopy extintion oeffiient, nd theefoe evpotion nd tnpition n be lulte how: E o δ. ET o (12) T ( 1 δ ).ET o Hunke, (1999) found tht ET in otton w highe when the op w ubmitted to high depth of iigtion ( mm) tht when hve low depth of iigtion level ( mm), imil to the K b K uve, obtining highe vlue thn the tetment with high fequeny (i.e.; K b K 1.5, 90 dy fte plnting) thn the low fequeny (i.e.; K b K 1.4, 90 dy fte plnting). (13) 2.2 Limittion in the ue of K Kteji & Rn, (2006) eviewed eent litetue elted to K nd found diffeene of ± 40% between K vlue epoted in the FAO-56 ppe (Allen et l., 1998) nd the vlue expeimentlly obtined, epeilly in the mid gowth tge. Aoding to the utho, thee lge diffeene e ttibutble to the omplexity of the oeffiient K, whih tully integte evel fto: eodynmi fto linked to the height of the op, biologil fto linked to the gowth nd eneene of the ufe leve, phyil fto linked to evpotion fom the oil, phyil fto linked to the epone of the tomt to the

6 Wte Vpo Flux in Agoeoytem Method nd Model Review 7 vpou peue defiit nd gonomi fto linked to op mngement (ditne between ow, uing mulh, iigtion ytem, et.). Fo thi eon K vlue need to be evluted fo lol ondition. The vition in op development te between lotion nd ye hve been expeed oeltion between op oeffiient nd indie uh the theml be index, gound ove, dy fte emegene o plnting, nd gowth te (i.e., Wight & Jenen, 1978; Hunke, 1999; Bown et l., 2001; Nb et l., 2004; Hnon & My 2004; Mdeio et l., 2001; Mdeio et l., 2005; nd Rmíez, 2007). The K i well elted with the gowing degee gde-gdd nd with the ftion of the oil ove by vegettion (f ) (Fig. 1), nd depend on the genotype nd plnt denitie (Rmiez, 2007). The eqution fo two ommon ben genotype nd two plnt denitie e: The eqution bed on CGDD nd f fo ommon ben genotype Mole with 13.6 plnt.m -2 e: K 3x10 6 CGDD CGDD 0.053; R ; p < (14) K f f ; R 0.70; p < (15) The eqution bed on CGDD nd f fo ommon ben genotype SER 16, with 6.4 plnt.m -2 e: K 3x10 6 CGDD CGDD ; R ; p < (16) K f f ; R 0.60; p < (17) 2.3 Wte te oeffiient (K ) The oil wte te oeffiient, K, i minly etimted by it eltionhip to the vege oil moitue ontent o mti potentil in oil lye, nd it n uully be etimted by n empiil fomul bed on oil wte ontent o eltive oil wte vilble ontent (Jenen et l., 1970, ited by Zhng et l., 2004). The K i n impotnt oeffiient beue it indite the enitivity of the op to wte defiit ondition, fo exmple on gin yield i epeilly enitive to moitue te duing telling nd ontinuing though gin fill. Roygd et l., (2002) obeved tht depletion of oil wte to the wilting point fo 1 o 2 dy duing telling o polleniztion edued yield by 22%. Six to eight dy of te edued yield by 50%. Allen et l. (1998), peented the following methodology fo etimting K : K TAW D TAW D TAW RAW ( 1 p ) (18) TAW whee TAW i totl vilble wte nd efe to the pity of the oil to etin wte vilble fo plnt (mm), D i oot zone depletion (mm), RAW i the edily vilble oil wte in the oot zone (mm), p i the ftion of TAW tht the op n extt fom the oot zone without uffeing wte te. TAW 1000( θ θ ) Z FC WP t (19)

7 8 Evpotnpition Mole A SER B 0.6 K Cumultive gowing degeee dy (CGDD) Cumultive gowing degee dy (CGDD) 1.2 Mole 1.2 SER K C Ftion oveed by vegettion (f ) Ftion oveed by vegettion (f ) D Fig. 1. Cop oeffiient (K ) elted to umultive gowing degee dy (CGDD) nd ftion oveed by vegettion (f ) fo two ommon ben genotype: A. Mole CGDD v K, B. SER 16 CGDD v K, C. Mole f v K, D. SER 16 f v K. The uve wee fitted fom gowth peiod V1 to R9 (Dt fom: Rmiez, 2007). (Thee dt wee obtined unde the pojet ponoed by NOAA-CREST (NA17AE1625), NASA-EPSCoR (NCC5-595), USDA- TSTAR-100,USDA Hth Pojet H-402, nd Univeity of Pueto Rio Expeiment Sttion) whee FC i the wte ontent t field pity (m 3.m -3 ), WP i the wte ontent t wilting point (m 3.m -3 ), nd Z t i the ooting depth (m) RAW ptaw (20) Allen et l. (1998) give vlue to diffeent op (FAO, 56.p163). Roygd et l. (2002) nd Zhng et l. (2004), epoted tht K i logithmi funtion of oil wte vilbility (Aw), nd n be etimted follow. K ln( Aw +1) / ln(101) (21) nd Aw i lulted oding to the eqution θ θwp Aw 100 (22) θfc θ wp

8 Wte Vpo Flux in Agoeoytem Method nd Model Review 9 whee i vege oil wte ontent in the lye of the oot zone depth. An exmple of the eltionhip between K nd vilble oil wte hnge, etimted oot zone depletion, i peented by Rmiez (2007). The oot zone depletion (D ), n be lulted uing the wte blne eqution: ( P RO) Ii + ETi DPi D D +, i, i 1 i, (23) whee D,i i the oot zone depletion t the end of dy i; D,i-1 i wte ontent in the oot zone t the end of the peviou dy, i-1; (P-RO) i i the diffeene between peipittion nd ufe unoff on dy i; I i i the iigtion depth on dy i; ET,i i the op ET on dy i nd DP i i the wte lo fom the oot zone by deep peoltion on dy i; ll the unit e in mm. The oot zone depletion oited with K 1.0 (i.e., no wte te), w up to 10 mm fo oot depth between 0 to 20 m, nd up to 15 mm fo oot depth of 0 to 40 m in ommon ben. Fifty peent of the tnpition edution w ehed fo D 22 mm nd 25 mm fo the ommon ben genotype Mole nd genotype SER 16, epetively. Tnpition eed ompletely (K 0) when D 37 mm nd 46 mm, epetively, fo Mole nd SER 16 (Rmíez, 2007). 3. Lyimete diet wte vpou flux meuement The wod lyimete i deived fom the Geek oot lyi, whih men diolution o movement, nd meton, whih men to meue (Howell, 2005). Lyimete e tnk filled with oil in whih op e gown unde ntul ondition to meue the mount of wte lot by evpotion nd tnpition (Allen et l., 1990). A lyimete i the method of detemining ET dietly. The lyimete e tnk buied in the gound to meue the peoltion of wte though the oil. Lyimete e the mot dependble men of dietly meuing the ET te, but thei intlltion mut meet fou equiement fo the dt to be epeenttive of field ondition (Chng, 1968). Requiement 1. The lyimete itelf hould be fily lge nd deep to edue the boundy effet nd to void etiting oot development. Fo hot op, the lyimete hould be t let one ubi mete in volume. Fo tll op, the ize of the lyimete hould be muh lge. Requiement 2. The phyil ondition within the lyimete mut be ompble to thoe outide. The oil hould not be looened to uh degee tht the oot mifition nd wte movement within the lyimete e getly filitted. If the lyimete i unloed on the bottom, peution mut be tken to void the peitene of wte tble nd peene of n bnoml theml egime. To enue pope dinge, the bottom of n iolted oil olumn will often equie the tifiil pplition of moitue ution, equivlent to tht peent t the me depth in the ntul oil (Colemn, 1946) Requiement 3. The lyimete will not be epeenttive of the uounding e if the op in the lyimete i eithe tlle, hote, dene, o thinne, o if the lyimete i on the peiphey of no-opped e. The effetive e of the lyimete i defined the tio of the lyimete ET pe unit e of the uounding field. The vlue of thi tio, othe thn unity, e ued by the in homogeneity of the ufe. The mintenne of unifom op height nd denity i not n ey tk in tll op, ped in ow. If the ufe i indeed inhomogeneou, thee i no dequte wy to etimte the effetive e fom tnk e ovelp oetion o plnt ount.

9 10 Evpotnpition Requiement 4. Eh lyimete hould hve gud-ing e ound it mintined unde the me op nd moitue ondition in ode to minimize the lotheline effet. In id limte, Thonthwite in 1954, uggeted tht gud-ing e of ten e my o my not be lge enough. Whee evel lyimete e intlled in the me field, the guding diu my hve to be bout ten time the lyimete eption (Chng, 1968). Lyimete uounded by idewlk o gvel will not povide elible dt, no will lyimete plnted to tll op if it i uounded by hot g, o plnted to g nd uounded by tll op. Diffeene in gowth nd mtuity between the lyimete plnt nd uounding plnt n eult in ignifint diffeene in meued ET in nd outide the lyimete (Puitt & Louene, 1985; mentioned by Allen et l., 1990). The lyimete e divided billy in two type: Weighing nd Non-weighing, eh of whih e deibed below. 3.1 Non-Weighing Lyimete Alo lled Dinge lyimete, they opete on the piniple tht ET i equl to the mount of infll nd iigtion wte dded to the ytem, minu peoltion, unoff nd oil moitue hnge. Sine the peoltion i low poe, the dinge lyimete i ute only fo long peiod fo whih the wte ontent t the beginning extly equl tht t end. The length of uh peiod vie with the infll egime, fequeny nd mount of iigtion wte pplition, depth of the lyimete, wte movement, nd the like. Theefoe, eod of dinge lyimete hould be peented only in tem of long-peiod moe thn one dy (Chng, 1968), nd they e not ueful fo etimting houly ET. Allen et l. (1990) diue two type the non-weighing lyimete: ) non- weighing ontnt wte-tble type, whih povide elible dt in e whee high wte tble nomlly exit nd whee the wte tble level i mintined eentilly t the me level inide outide the lyimete; b) Non-weighing peoltion type, in whih hnge in wte toed in the oil e detemined by mpling o neuton method o othe oil humidity eno like TDR, nd the infll nd peoltion e meued. Genel piniple of dinge lyimete: Poviion e mde t the bottom of the lyimete ontine to ollet nd meue volumetilly the deep peoltion. Peipittion i meued by in guge(). Evpotnpition i onideed the diffeene mong wte pplied, wte dinge nd oil wte hnge. (Tee et l., 1973; Xingf et l., 1999) When filling-in lyimete, the oil dug out fom the lyimete pit i epled in the ontine, peil peution e needed to etun the oil to it oiginl ttu by etoing the oet oil pofile nd ompting the oil lye to the oiginl denity. It i deible to hve imil oil tte inide the lyimete eltive to the outide. Howeve if the oot e well developed nd nutient e vilble, nd long the wte upply to the oot i unetited, diimil oil will not give ignifint vition in wte ue nd yield, povided othe ondition e imil.(xingf et l. 1999). Although ditubed oil in filled-in lyimete doe not poe eiou poblem in ET meuement, the oil n ffet plnt gowth. Beking up the oil, will hnge oil tutue, etion, nd oil moitue etention hteiti. The lyimete hould povide noml ooting pofile. It hould be lge enough to ende the effet of the im inignifint. It n give eltively lge eo in the ET meuement if the ontine i mll. Howeve, the gete the lyimete e, the moe otly nd omplited the intlltion nd opetion beome. (Xingf et l., 1999).

10 Wte Vpo Flux in Agoeoytem Method nd Model Review 11 Intlltion nd wll: The wll n be diffeent mteil: einfoed onete, polyete einfoed with teel, fibegl o plti. The intlltion poeed in the following tep: Exvtion (e.g. 1m*1m*1.2m) in the expeimenttl ite. Eh lye of oil (e.g m, 30-60m nd m) i epted. One the exvtion it ompleted, the lyimete i pled in the exvted hole with 4 wooden bod outide. Befoe epking the oil lye, mke V-hped lope t the bottom nd ple 25 mm inide dimete pefoted PVC pipe (hoizontl). Thee hould be een mteil pled ound the pefeted pipe to void the oil ptile fom enteing the pipe. Connet n e tube (25 mm PVC), ppoximtely 1 m long (vetil). Cove the hoizontl pipe with fine gvel ppoximtely 3-5 m thik. Fill the ontine with the exvted oil whee eh lye i epked inide the lyimete to mth the oiginl vetil oil tte. (Xingf et l. 1999). 3.2 Weighing Lyimete A weighing Lyimete i pble of meuing ET fo peiod hot ten minute. Thu, it n povide moe dditionl infomtion thn dinge lyimete n. Poblem uh diunl ptten of ET, the phenomenon of middy wilt, the hot-tem vition of enegy ptitioning, nd the eltionhip between tnpition nd oil moitue tenion, n be invetigted only by tudying the eod obtined fom weighing lyimete. (e.g.; Chng, 1968; Rithie & Bunett, 1968; Tkh & Rudge, 1970; Pton et l., 1981; Steine et l., 1991; Allen et l., 1998; Loo et l., 2007; von Unold &Fnk, 2008) Weighing lyimete mke diet meuement of wte lo fom gowing op nd the oil ufe ound op nd thu, povide bi dt to vlidte othe wte vpo flux pedition method (e.g.; Dug et l., 1985; Puege et l., 1997; López-Ue et l., 2006; Vughn et l., 2007). The bi onept of thi type of lyimete i tht it meue the diffeene between two m vlue, the m hnge i then onveted into ET (mm) (Mlone et l., 1999; Jhonon et l., 2005). Duing peiod without infll, iigtion nd dinge, the ET te i omputed indited by Howell (2005), : [ Al [( Mi Mi 1 )/ Al ]/ Af ] Ti ET / (24) whee ET i in unit of (mm.h -1 o Kg.m 2 ) fo time intevl i; M i the lyimete oil m, (Kg); A l i lyimete inne tnk ufe e (m 2 ); A f i lyimete folige e (mid wll-i gp e) (m 2 ); T i the time peiod (h). The tio A f /A l i the oetion fto fo the lyimete effetive e. Thi oetion fto ume the outide nd inide vegettion folige ovelp evenly on ll of the ide o edge. If thee i no ovelp, ou in hot g, the A f /A l 1.0 (Howell, 2005). Weighing lyimete povide the mot ute dt fo hot time peiod, nd n be detemined utely ove peiod hot one hou with mehnil le, lod ell ytem, o floting lyimete (Allen t l., 1990). Some weighing lyimete ue weighing mehnim oniting of le opeting on leve nd pendulum piniple (Hold & Deibelbi (1951), mentioned by Mlone et l. (1999)). Howeve, ome diffiultie e vey ommon like: eletoni dt logge eplement, dt logge epi, lod ell eplement, multiflexo intlltion et. (Mlone et l., 1999). The meuement ontol in thee lyimete e impotnt beue of the following iue: ) e-libtion equiement, b) meuement dift (e.g., lope dift, vine dift), ) intument poblem (e.g., lolized non-lineity of lod ell, lod ell dmge, dt logge

11 12 Evpotnpition dmge), d) humn eo (e.g.; inoetly eoding dt duing libtion) nd e) onfidene in meuement eult (Mlone et l. 1999). A lod ell i tndue tht ovet lod ting on it into n nlog eletil ignl. The eletil ignl i popotionl to the lod nd the eltionhip i detemined though libtion, employing line egeion model (mv/v/mm wte), nd it i ued to detemine m hnge of lyimete ove the peiod inteet (e.g. dy, hou, et.). The lyimete hteiti n be diffeent, fo exmple: Mlone et l., (1999) built lyimete of the following fom: 8.1 m 2 in ufe e nd 2.4 m depth, the lyimete i ontuted without ditubing the oil pofile nd the undelying ftue bedok. The oil monolith i uppoted by le fme tht inlude 200:1 leve ytem nd ounteweight fo the dedweight of the oil monolith. The gp between the oil in the lyimete nd the djent oil i between 5.1 m nd 7.0 m exept t the bottom lope whee the unoff tough i loted, thi me utho h given intution fo hieving good libtion fo thi type of lyimete. Tygi et l., (2000) in whet nd oghum ued two etngul tnk, n inne nd oute tnk, ontuted fom 5-mm welded teel plte. The dimenion of the inne tnk wee x x m nd thoe of the oute tnk wee x x m. The lyimete wee ituted in the ente of 20-h field. The ize tio of the oute tnk to the inne tnk i 1.03, o the eo due to wll thikne i miniml. The effetive e fo op ET w 4 m 2. The height of the lyimete im w mintined ne gound level to minimize the boundy lye effet in nd ound the lyimete. The lyimete tnk w upended on the oute tnk by fou lod ell. The lod ell wee mde out of the teel he bem type with 40,000-kg deign lod pity. The totl upended m of the lyimete inluding tnk, oil, nd wte w bout 14,000 kg. Thi povided fety fto of The high fety fto w povided to llow eplement of lod ell without the dnge of oveloding nd lo to ount fo hok loding. A dinge embly onneted with vetil tnd nd gvel bedding to filitte pumping of dinge wte w povided. The tnd pipe lo n be ued to ie the wte tble in the lyimete. To lulte the ET uing Lyimete, we need to employ the oil wte blne (B) eqution: ET R +I -P- Rff +/- SM (25) Whee: R i the in, I i the iigtion, Rff i the unoff, nd +/- SM oil moitue hnge, ll in mm. The ize of the Lyimete i n impotnt element to be onideed in wte vpo flux tudie with thi method. Fo exmple, Dug & Blnd (1989) evluted mll lyimete (<1.0 m 2 ) nd epoted ignifint diffeene in the ET etimtion, billy oited with the diffeene in the lef e index (LAI) inide the lyimete, whih diffeed mong lyimete, thi poblem n be ddeed uing LAI oetion. 3.3 Clibtion of the weighing Lyimete Seyfied et l.,(2001) mde weighing lyimete libtion by pling known weight on the lyimete nd then eoding the eultnt peue hnge. The weight ued in tht tudy wee follow: 19.9 kg fo uppotive blok pled on the lyimete, 43.4 kg fo the tnk whih ontined the weight, nd then twenty-fou 22.7 kg k of ok dded in fouk inement. The weight of eh k oeponded to bout 13 mm ddition of wte;

12 Wte Vpo Flux in Agoeoytem Method nd Model Review 13 o tht weight inement wee equivlent to ~52 mm nd the totl nge w~360 mm of wte. Meuement wee mde both weight w dded nd emoved. The min gument gint the ue of weighing lyimete fo monitoing wte blne pmete nd meuing olute tnpot pmete in the oil nd untuted zone h been the diuion of potentil oue of eo, uh the well known oi effet, pefeentil flow pth t the wll of the lyimete ylinde due to n inuffiient fit of oil monolith inide the lyimete, o the influene of the lowe boundy ondition on the outflow te (Fnk, 2008). 4. The miometeoologil method Fo mny giultul pplition, miometeoologil method e pefeed ine they e genelly non-intuive, n be pplied on emi-ontinuou bi, nd povide infomtion bout the vetil fluxe tht e ouing on le nging fom ten of mete to evel kilomete, depending the oughne of the ufe, the height of the intumenttion, nd the tbility of the tmophee ufe lye. Meye nd Bldohi (2005) hve epted miometeoologil method into fou tegoie: 1) eddy ovine, 2) flux-gdient, 3) umultion, nd 4) m blne. Eh of thee ppohe e uitble fo pplition tht depend on the l of inteet nd ufe type, nd intumenttion vilbility. Some of thee method e deibed in the following etion of thi hpte. 4.1 Humidity nd tempetue gdient method Movement of enegy, wte nd othe ge between field ufe nd tmophee epeent fundmentl poe in the oil-plnt-tmophee ontinuum. The tubulent tnpot in the ufe boundy lye ffet the enible (H) nd ltent (λe) het fluxe, whih long with the dition blne, goven the evpotnpition nd nopy tempetue (Hm nd Heilmn, 2003). Monteith nd Unwoth (1990) peented the funtionl fom of the gdient flux eqution, nd whih h been pplied by Hmen et l. (2006), Rmíez et l. (2008) nd Hmen et l. (2009): ( ) ρ p ρ vl ρ vh ET (26) γρ w ( + ) whee ρ w i the denity of wte, ρ v i the wte vpo denity of the i, ρ i the i denity, γ i the pyhometi ontnt, p i peifi het of i, nd e eodynmi nd bulk ufe eitne (ll thee vible e diued in detil below). L nd H e vetil poition bove the nopy (L: low nd H: High poition), fo exmple in mll op like ben o g, poible vlue of L nd H ould be 0.3 m nd 2 m bove the gound, epetively. Hmen et l. (2006) developed n utomted elevto devie (ET Sttion) fo moving tempetue nd eltive humidity eno (Temp/RH) between the two vetil poition (Fig.2). The devie onited of plti (PVC) fme with 12 volt DC moto (1/30 hp) mounted on the be of the fme. One end of 2-m long hin w tthed to hft on the moto nd the othe end to poket t the top of the fme. Wtepoof limit withe

13 14 Evpotnpition wee loted t the top nd bottom of the fme to limit the nge of vetil movement. Fo utomting the elevto devie, pogmmble logi ontolle (PLC) w ued whih w ompoed of n input nd n ely output. To pogm the devie, ldde logi w ued whih i honologil ngement of tk to be omplihed in the utomtion poe. The Temp/RH eno w onneted to the elevto devie, whih meued eltive humidity nd tempetue in the up poition fo two minute then hnged to the down poition whee meuement wee tken fo two minute. Thi poe tted eh dy t 0600 hou nd ended t When the elevto move to the up poition it tivte the limit with whih end n input ignl to the PLC. Tht input tell the pogm to top nd emin in tht poition fo two minute. At the me time it tivte n output whih end 5 volt ignl to the ontol pot C2 in the CR10X dt logge in whih mll uboutine i exeuted. Thi uboutine ign 1 in the eult mtix whih indite tht the tempetue nd eltive humidity oeponding to the up poition. At the end of the two minute peiod, the elevto move to the down poition nd epet the me poe, but in thi e ending 5 volt ignl to the dt logge in the ontol pot C4, whih then ign 2 in the eult mtix. All infomtion w toed in the wethe ttion dt-logge CR-10X (Cmpbell Sientifi, In) fo lte downloding to peonl ompute. A B Fig. 2. Automted elevto devie developed fo moving the Temp/RH eno between the two vetil poition. A. Temp/RH eno in down poition nd B. Temp/RH eno in up poition. Meuing ove ommon ben (Pheolu vulgi L.). (Thee dt wee obtined unde the pojet ponoed by NOAA-CREST (NA17AE1625), NASA-EPSCoR (NCC5-595), USDA- TSTAR-100,USDA Hth Pojet H-402, nd Univeity of Pueto Rio Expeiment Sttion) 4.2 The Bowen-tio enegy blne method The bi fo thi method i tht the lol enegy blne i loed in uh wy tht the vilble net ditive flux (Rn) i titly ompoed of the enible (H), ltent (λe), nd gound het (G) fluxe, othe toed tem uh thoe elted to nopy het toge nd photoynthei e negligible (Meye nd Bldohi, 2005). Thi method ombine meuement of etin tmophei vible (tempetue nd vpou onenttion gdient) nd vilble enegy (net dition nd hnge in toed theml enegy) to detemine etimte of evpotnpition (ET) (Lloyd, 1992). The method inopote enegy-budget piniple nd tubulent-tnfe theoy. Bowen

14 Wte Vpo Flux in Agoeoytem Method nd Model Review 15 howed tht the tio of the enible- to ltent-het flux (β) ould be lulted fom the tio of the vetil gdient of tempetue nd vpou onenttion ove ufe unde etin ondition. Often the gdient e ppoximted fom i-tempetue nd vpou-peue meuement tken t two height bove the nopy. The Bowen-tio method ume tht thee i no net hoizontl dvetion of enegy. With thi umption, the oeffiient (eddy diffuivitie) fo het nd wte vpou tnpot, kh nd kw, epetively, e umed to be equl. Unde dvetive ondition, kh nd kw e not equl (Vem et l., 1978; Lng et. l., 1983 ited by Tomilon, 1997) nd the Bowen-tio method fil to utely etimte ET. Bed on the umption tht Kh nd Kw e equl, nd by ombining evel tem to fom the pyhometi ontnt, the Bowen-tio tke the fom to the eqution 28. Although the theoy fo thi method w develop in the 1920 by Bowen (Bowen, 1926), it ptil pplition h only been poible in eent dede, due to the vilbility of ute intumenttion (Pyeo et l., 2003). The Bowen tio initil onept i hown below: dt PC p Kh β dz de (27) λεkw dz If it i umed tht thee i no net hoizontl dvetion of enegy, equ. 27 n be implified hown below: dt PC p β de dz (28) λε dz whee P i the tmophei peue (kp), C p i the peifi het of i (1.005 J/g C), ε i the tio moleul weight of wte to i nd λ i the ltent het of evpotion (Jg -1 ). One the Bowen tio i detemined, the enegy blne (equ. 29) n be olved fo the enible-het flux (H) nd ltent-het flux (λe). Rn λe + H+G (29) whee R n Rn i the net dition, λe i the ltent-het flux, H i the enible-het flux nd G i the oil-het flux (W.m -2 ). H βλe (30) ( Rn G) λe (1 + β ) (31) The ltent het flux n be epted into two pt: the evpotive flux E (g m -1 dy-1) nd the ltent het of vpoiztion λ (Jg -1 ), whih n be expeed funtion of i tempetue (T- C) (λ 2, T). The ltent-het of vpotion (λ) i defined the mount of enegy equied to onvet 1 gm of liquid wte to vpou t ontnt tempetue T. Senible-het flux (H) i tubulent, tempetue-gdient diven het flux

15 16 Evpotnpition eulting fom diffeene in tempetue between the oil nd vegettive ufe nd the tmophee. The oil-het flux (G) i defined the mount of enegy moving downwd though the oil fom the lnd ufe, ued by tempetue gdient. Thi flux i onideed poitive when moving down though the oil fom the lnd ufe nd negtive when moving upwd though the oil towd the ufe (Tomilon, 1994). The oil het flux i obtined by meuing two oil het flux plte below the oil ufe t 2 nd 8 m, oil moitue t 8 m, nd oil tempetue t 6 m between the two oil het flux plte (Cmpbell Sientifi, In. 1998). Beue the oil-het flux i meued below the oil ufe, ome of the enegy oing the oil ufe ould be toed in, o ome fom, the lye of oil between the ufe nd flux plte loted loet to the ufe, fo thi eon hnge in toge tem, S i dded to the meued het flux (equ. 33). (Cmbell Sientifi, In. 1991): ΔT S d ( C + ( WCw )) b t ρ (32) Δ whee S i the het flux going into toge (Wm -2 ), t i the time intevl between meuement (e), T i the oil tempetue intevl between meuement, d i the depth to the oil-het-flux plte (0.08m), ρ b i the bulk denity of dy oil, C i the peifi het of dy oil (840 J/Kg C), W i the wte ontent of oil (kg the wte/ Kg the oil) nd C w i the peifi het of wte (4,190 J/Kg C). The oil het flux (G) t the ufe i obtined by inluding the effet of toge between the ufe nd depth, d, uing eqution 11. FX1+ FX 2 G + S 2 whee FX 1 i the oil-het flux meued 1 (Wm -2 ), FX 2 i the oil-het flux meued 2 (Wm -2 ). One of the equiement fo uing the Bowen-tio method i tht the wind mut p ove uffiient ditne of imil vegettion nd tein befoe it ehe the eno. Thi ditne i efeed to the feth, nd the feth equiement i genelly onideed to be 100 time the height of the eno bove the ufe (Cmpbell, 1977). Moe detil bout detemintion of the minimum feth equiement i peented lte in thi hpte. Hnk et l. (1968), deibed by Fnk (2003), epoted λe/rn of 0.16 fo dy oil ondition nd 0.97 fo wet oil ondition; On the othe hnd he found λe/rn to be lowet in gzed piie, uggeting tht defolition hnge the nopy tutue nd enegy budget omponent, whih my hve ontibuted to inee wte lo though evpotion omped with the non-gzed piie tetment. Hnon nd My (2004), uing the Bowen Rtio Enegy Blne Method to meue ET in tomtoe, found tht ET te deeed ubtntilly in epone to dying of the oil ufe. Peez et l. (2008) popoed imple model fo etimting the Bowen tio (β ) bed on the limti eitne fto: (33) Δ + γ 1+ S β. 1 (34) Δ 1+ C

16 Wte Vpo Flux in Agoeoytem Method nd Model Review 17 C. Δ. i γ (35) γ S. Δ + γ (36) whee i the nopy eitne ( m -1 ) bed on the big lef onept, nd i the eodynmi eitne ( m -1 ). Thee eitne fto e deibed in detil in the next etion. The fto i i the limtologil eitne epoted by Montheith (1965): i ρcpvpd γ ( R G) n (37) whee ρ i the i denity t ontnt peue (Kg.m -3 ), C p i the peifi het of moit i t ontnt peue (1004 J.Kg -1 0 C -1 ), VPD i the vpou peue defiit of the i (P), γ i the pyhometi ontnt (P. 0 C -1 ) nd R n nd G e in W.m -2. Fo homogeneou nopie, the effetive op ufe nd oue of wte vpou nd het i loted t height d + z oh, whee d i the zeo plne diplement height nd z oh i the oughne length govening the tnfe of het nd vpou (Allen et l. 1998). 4.3 The Penmn-Monteith Method The impotnt ontibution of Monteith nd Penmn` oiginl eqution w the ue of eitne fto, whih w bed on n eletil nlogy fo the potentil diffeene needed to dive unit flux ytem tht involve the tnpot of momentum, het, nd wte vpou (Monteth nd Unwoth, 1990; Monteith, 1997). The eitne hve dimenion of time pe unit length, will be deibed lte. Thi methodology lulte the ltent het flux uing the vpou peue defiit, the lope of the tuted vpou-peue uve nd eodynmi eitne to het, nd nopy eitne in ddition to the enegy-budget omponent of the net dition, oil het flux, nd enible het flux. Field meuement of i tempetue, eltive humidity, nd wind peed e needed to detemine thee vible (Tomilon, 1997). Eqution 38 deibe the Penmn-Monteith (P-M) method to etimte the λe (Allen t l., 1998, Kjelgd nd Stokle, 2001) VPD Δ( Rn G) + ρcp λ E (38) Δ + + γ 1 whee λe, R n, nd G in Wm -2, VPD i vpou peue defiit (kp), ΔSi lope of tution vpo peue uve (kp C -1 ) t i tempetue, ρ i denity of i (Kgm -3 ), C p in J Kg -1 C - 1, in kp C -1, i eodynmi eitnt ( m -1 ) ufe eitne to vpou tnpot ( m -1 ). Aoding to Monteith (1997), the ppene of wind-dependent funtion in the denominto well in the numeto implie tht the te of evpotion lulted fom the P-M model i lwy le dependent on wind peed thn the te fom the

17 18 Evpotnpition oeponding Penmn eqution when othe element of limte e unhnged. In genel, etimted te e uully inenitive to the mgnitude of nd the eo geneted by negleting the influene of the buoyny oetion i often mll. In ontt, the evpotnpition te i uully tong funtion of the ufe eitne ( ). Kjelgd nd Stokle (2001) y the ufe eitne ( ) pmete in the P-M model i ptiully diffiult to etimte due to the ombined influene of plnt, oil nd limti fto tht ffet it vlue. The mgnitude of the tomtl eitne n be etimted in piniple fom the numbe of tomt pe unit lef e nd fom the dimete nd length of poe, whih i diffiult nd theefoe ely meued; theefoe, the tomtl eitne i uully lulted fom tnpition te o etimted gdient of vpou onenttion (Monteith, 1997). Knowing the vlue of the eodynmi eitne ( ) pemit etimtion of the tnfe of het nd wte vpou fom the evpoting ufe into the i bove the nopy. The eodynmi eitne fo ingle lef to diffuion though the boundy lye uounding the lef, within whih the tnfe of het, wte vpou, et., ou, poeed t te govened by moleul diffuion. Povided the wind peed i get enough nd the tempetue diffeene between the lef nd i i mll enough to enue tht tnfe poee e not ffeting by gdient of i denity, the boundy lye eitne depend on i veloity nd on the ize, hpe, nd ltitude of the lef with epet to the i tem. In vey light wind, the te of tnfe e detemined minly by gdient of tempetue nd theefoe by denity, o tht the depend moe on the men lef-i tempetue diffeene thn on wind peed. Aoding to Thom (1975), the fo het tnfe n be detemined by: h ρ Cρ( T T ) (39) H At the field level, fo homogeneou ufe, uh be oil o op nopie, thee i lge-le nlogou boundy lye eitne, whih n be etimted o deived fom meuement of wind peed nd fom knowledge of the eodynmi popetie of the ufe i deibed lte (Monteith, 1997). The n be detemined given vlue of oughne length (Z o ) nd zeo plne diplement height (d), tht depend minly on op height, oil ove, lef e nd tutue of the nopy (Mmn, 1987; Peie, 1982; Shw nd Peei, 1982 ited by Alve et l. 1998), Ln ( Z d ) ( Z d ) m Z Ln h Z om oh (40) 2 K uz whee Z m i height of wind meuement (m), Z h i height of humidity meuement (m), d i zeo diplement height (m), Z om i oughne length govening momentum tnfe of het nd vpou (m) i 0.123h, Z oh i oughne length govening tnfe of het nd vpou (m) i 0.1Z om, K i the von Kmn` ontnt (0.41), u z i win peed t height z. Thi eqution i etited fo neutl tbility ondition, i.e., whee tempetue, tmophei peue, nd wind peed veloity ditibution follow nely dibti ondition (no het exhnge). The pplition of the eqution fo hot time peiod (houly o le) my equie the inluion of oetion fo tbility. Howeve, when pediting ET o

18 Wte Vpo Flux in Agoeoytem Method nd Model Review 19 in the well wteed efeene ufe, het exhnge i mll, nd theefoe the tbility oetion i nomlly not equied (Allen et l., 1998). Alve et l. (1998) tte tht though thi i the mot ued expeion fo, in ft it i not entiely oet, ine it ume logithmi pofile fom the oue height (d + Z oh ) with ineing z in the tmophee, uing the onept to the big lef, equ. 40 n be modified follow: z d z d Ln Ln h d Z om (41) 2 K uz whee h i the height of the op nopy. Aoding to Tollk et l. (1995), the to momentum tnpot in the bene of buoyny effet (neutl tbility) follow the eqution: m 2 [( Zi d )/ Zom ] 2 / k uz ln (42) Unde dibti ondition, the eqution mut be oeted uing the Rihdon numbe fo tbility oetion, uming imility in tnpot of het nd momentum, yielding: h m ( 1+ R ) 5 (43) The Ri fo tbility ondition i onideed when ( R i 0.008) nd i lulted by R i 2 [ g( T T )( Z d )]/ T. u z i (44) whee g i the eletion of the gvity (9.8 m. -2 ), T i the i tempetue (K), T i the plnt nopy tempetue (K), T v i the vege tempetue tken ((T +T )/2). The dvntge of the R i ove othe tbility oetion i tht it ontin only expeimentlly detemined gdient of tempetue nd wind peed nd doe not depend dietly on enible het flux (Tolk et l., 1995). The bulk ufe eitne ( ) deibe the eitne of vpou flow though tnpiing op leve nd evpotion fom the oil ufe. Whee the vegettion doe not ompletely ove the oil, the eitne fto hould indeed inlude the effet of the evpotion fom the oil ufe. If the op i not tnpiing t potentil te, the eitne depend lo on the wte ttu of the vegettion (Vn Bvel, 1967; Allen et l., 1998), nd fo thi e they popoed the ue of the following ppoximte: v L (45) LAItive whee LAI tive i 0.5 time the lef e index (m 2 of lef pe m 2 of oil), nd L i bulk tomtl eitne, whih i the vege eitne of n individul lef, nd n be meued uing n intument lled poomety, the fit tomtl eding wee developed by Fni Dwin who develop hi hon hygomete (Tune, 1991). The L eding e highly vible nd depend on evel fto, uh : op type nd development tge, the wethe nd oil moitue vibility, the tmophei pollutnt nd the plnt phytohomone blne (Tune, 1991). Typilly to detemine minimum L

19 20 Evpotnpition uing poomete, fully expnded, unlit leve ne to the top of the nopy e uveyed duing mximum ol idine (ppoximtely ol noon unde loudle ondition) nd low VPD peiod (Kjelgd nd Stokle, 2001). Thi tndd vlue fom litetue o poomete meuement e heefte identified Lmin. In ddition, L h been hown to inee with ineing VPD nd/o edued ol idine (R ). Adjutment fto fo VPD (f VPD ) nd R (f R ) wee empiilly deived nd ued multiplie of Lmin. The dependene of L on VPD n be epeented by line funtion (Jvi, 1976) f VPD + bvpd (46) whee nd b e line egeion oeffiient, nd f VPD i equl to 1 (no djutment) fo VPD thehold vlue, whih n be tken 1.5 kp. The me utho peented libted fom of eqution 46 fo on, f VPD (VPD). Kjelgd nd Stokle (2001) peented modified fom of the djutment fto: f R R mx C + R 2 (47) whee R nd R mx e the tul nd mximum dily ol idine (MJ m -2 dy -1 ) nd C 2 i fitted ontnt. Tking the mximum of the djutment fto fo VPD nd R, Lmin i modified to give the L (Kjelgd nd Stokle, 2001): L L min { f f } mx, (48) whee f VPD nd f R, e equl to o lge thn 1. Alve et l. (1998) indite tht the ufe eitne tem ( ) h been the mot diued in the litetue. Sevel omponent to be onideed hee inlude: ) The eitne to wte vpou t the evpoting ufe: plnt nd thei tomte ( ) nd oil ( ); b) the eitne to vpou tnfe inide the nopy fom thee evpoting ufe up to the big lef ( ). The eitne, n be ppoximted uing equ. 50. VPD R n i 1 tj LAI 1 1 Whee t i the ingle lef tomtl eitne (m -1 ), n i lef numbe. The bulk ufe eitne n lo be lulted uing the inveion of the Penmn- Monteith eqution with inopotion of the Bowen tio follow (Alve et l. (1998) nd Alve nd Peei, 2000): Δ ρcpvpd β 1 + γ γλe Aute pedition of equie good etimte of the Bowen tio (β). Rmiez (2007) h ued the following inveion fom of the Penmn-Monteith eqution to obtin etimte of : (49) (50)

20 Wte Vpo Flux in Agoeoytem Method nd Model Review 21 VPD Δ( R ) ρ n G + Cp Δ γ λe. (51) γ Similly thee utho, nlying the eitne onept, onluded tht the of dene op nnot be obtined by imply veging tomtl eitne beue the diving foe (vpou peue defiit) i not ontnt within the nopy. Sugie (1977) ddeed nopy eitne ( ), tting tht it i nomlly mixtue of oil nd plnt eitne to evpotion. If the top the oil i vey dy, diet oil evpotion my be negleted nd i ppoximtely equl to the lef eitne ( L ) divided by the LAI. Bldohi et l. (1991), indited tht the invee of the big-lef model (eg., invee of the P- M model) will be good etimte of nopy eitne o ufe eitne if etin ondition e met. Thee ondition inlude: i) tedy-tte envionment; ii) dy, fully developed, hoizontlly homogeneou nopy ituted on level tein; iii) identil oueink level fo wte vpou, enible het nd momentum tnfe, nd negligible utiul tnpition nd oil evpotion. Szeiz nd Long (1969) deibe pofile method to etimted, ρ. Cp, VPD (52) γ. λe Thee method n be ued in the field when the te of evpotnpition i meued by lyimete o lulted fom the Bowen tio enegy blne method, nd the tempetue, humidity nd wind pofile e meued within the boundy lye imultneouly. Oteg-Fi et l. (2004), evluted methodology fo lulting the nopy ufe eitne ( v ) in oyben nd tomtoe, uing only meteoologil vible nd oil moitue eding. The dvntge of thi method i tht it n be ued to etimte λe by the genel Penmn-Monteith model with meteoologil eding t one level, nd without L nd LAI meuement. ρ. p. VPD θ Δ.. FC WP ( R G) ) θi θwp n θ (53) Whee θ FC nd θ WP e the volumeti moitue ontent t field pity (ftion) nd wilting point (ftion), epetively, nd θ i i volumeti oil ontent in the oot zone (ftion) meued eh dy. Kml nd Htfield (2004), ued the eqution 50 to detemine the ufe eitne in Potto: nd tted tht the nopy eitne ( in.m -1 ; men tomtl eitne of op ), n be detemined by dividing the by the effetive LAI defined by othe utho uh Htfield nd Allen (1996) nd fo well wteed op, n be n be etimted uing eqution LAI (54) LAI

21 22 Evpotnpition Kjelgd nd Stokle (2001) diued the etimtion of nopy eitne ( ) fom inglelef eitne ( L ) (eqution 55), oiginlly popoed by Szeiz nd Long (1969): L (55) LAItive Kml nd Htfield (2004) divided the ufe eitne ( ) ued in the P-M model into two omponent, nd oneptulized n exe eitne ( o ) in eie with the nopy tomtl eitne. Thi exe eitne w linked to the tutue of the op, ptiully op height. + o (56) Peei et l. (1999) tted tht the ufe eitne ( ) i the um of two omponent: one oeponding minly to the tomtl eitne ( t ), the othe to the lef boundy lye nd tubulent tnfe inide the nopy ( i ) (eqution 57), thu, ufe eitne i not puely phyiologil pmete: t + i (57) Stomtl eitne n tke vlue fom 80.m -1 to 90.m -1 ommon nge fo giultul op uggeted vlue of 100.m -1 fo mot ble op (Monteith, 1981). The tble 1 lit men vege vlue fo viou op unde well wte ondition. The L i tongly dependent on the time of dy (billy due to the tempol ntue of limti ondition), fo the oil moitue ontent nd by the genotype. Fig. 3A, how how lge diffeene in L ou, with nd without dought te, fte 9:00 m until lte in the ftenoon, nd the mot itil point i t 13:00 hou when the highet VPD oued. Fo thi eon, when thi vible ( L ) i not meued, ppopite pmeteition i equied fo good wte flux o ET etimtion, epeilly unde dought te ondition. In Fig. 3C, it i poible to ee in ommon ben genotype unde dought te ondition, lowe L omped with le dought eitne duing evel dy with dought te. Peie (1975), epoted in Kjelgd nd Stokle (2001), oneptulized the exe eitne ( o ) line funtion of op height nd LAI: h blai (58) o + whee nd b e ontnt. Fo on, Kjelgd nd Stokle (2001) pmeteized equ. 58 follow: o 16.64h +0.92LAI. Cnopy eitne n lo be detemined fom lef o nopy tempetue ine it i ffeted by plnt hteiti, eg. Lef e index (LAI), height, nd mtuity. Soil fto (Avilble oil wte-a, nd oil olution linity) nd wethe fto (R n nd wind peed) lo ffet the nopy eitne. Montheith (1965) howed tht tnpition te phyilly depend on eltive hnge of ufe tempetue nd, nd onluded tht depend on the Reynold numbe of the i nd n be detemined fom wind peed, the hteiti length of the plnt ufe, nd the kinemti vioity of the i. An inee in fo Whet w ued by deee in totl lef e, by n inee in the eitne of individul leve due to eneene, o by ombintion of both effet; in Sudn g, ineed with plnt ge nd deee in oil moitue. Vn Bvel (1967) tudied Alflf thoughout n iigtion yle nd found

22 Wte Vpo Flux in Agoeoytem Method nd Model Review 23 tht nopy eitne ineed linely with deeing oil wte potentil. Kml nd Htfield (2004) found n exponentilly invee eltionhip between nopy eitne nd net dition, nd line invee eltionhip between nopy eitne nd vilble oil wte. Cove op L Soue Cove op L Soue /m /m Con 200 Sunflowe 400 Soyben nd potto 350 Sogum 300 Millet 300 Apen 400 Mize 160 Alflf 80 Clipped g (0.15 m) Common ben Con 264 Coffee 149 Whet 134 Kikhm et l. (1985) Kikhm et l. (1985) Kikhm et l. (1985) Kikhm et l. (1985) Kikhm et l. (1985) Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Rmiez et l. (2007) Rmiez nd Hmen (2007). Unpublihed dt. Rmiez nd Jmillo (2008). (Clulted) Howell et l. (1994) Cv 714 Between 476 to 1428 Eulyptu Mple Cop-Genel Gim oghum 200 Soyben 120 Bley Sug beet 100 Clipped nd Iigted g ( m) 75 Soghum 192 Ande Topil Foety 132 Coffee 150 Con 252 Soghum 280 Tble 1. Avege vlue of the tomtl eitne ( L ) fo evel op. Oguntunde (2005). Thi dt unde limited oil wte ondition. Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Peei nd Alve (2005) Stine et l. (1991) Rmiez nd Jmillo (2008). (Clulted) Angeloi et l. (1983) Howell et l. (1994) Howell et l. (1994)

23 24 Evpotnpition The Dinge nd Iigtion Ppe-FAO 56 (Allen et l., 1998) eommend the Szeiz nd Long (1969) method fo lulting (eqution 55), in whih n vege of L fo diffeent poition within the op nopy, weighted by LAI o LAI effetive i ued. Thi method eem to give good eult only in vey ough ufe, like foet nd ptil ove op with dy oil (Monteith, 1981). Alve et l. (1998) onluded tht of dene op nnot be obtined by imply veging tomtl eitne ( L ) beue VPD, whih i the diving foe, i not ontnt within the nopy. Alve nd Peei (2000) hve tted The PM model n be ued to pedit ET if ute methodologie e vilble fo detemining the tht tke into ount the enegy ptitioning. In ddition to the lk of vlue fo op, quetion hve been ied eltive to the ppopitene of uing the PM model fo ptil o pe nopie beue the oue/ink fluxe my be ditibuted in non-unifom mnne thoughout the field (Hm nd Heilmn, 1991; Kjelgd et l., 1994; Fhmi nd Buh, 1995; Oteg-Fi et l.; 2006). Adequte pmeteiztion of the ufe eitne mke the P-M model good etimto of ET (i.e., Sugie nd Kteji, 1991; Rn et l., 1997; Alve nd Peei, 2000; Oteg-Fi et l., 2004). Rmiez (2007), epoted tht the dily ET etimtion with the P-M model with bed on L nd LAI effetive gve good etimtion in two ommon ben genotype with vible LAI, without nd with modete dought te fo both ye (2006 nd 2007). Rmiez et l. (2008) n epoted invee eltion between nd nd L in ben (Pheolu vulgi L), well thoe epoted by Alve nd Peei (2000) (Fig. 4), whih implie tht with low (windy ondition), the L (nd theefoe ) inee. The Alve nd Peei (2000) tudy did not meue the L, the the w etimted bed on miometeoologil pmete. Dipitie in the meued uing the P-M invee model ie fom: ) impefet mpling of leve nd the bity method of veging lef eitne ove the whole nopy, b) fom the dependene of on non-tomtl fto uh evpotion fom wet oil o tem, o othe nd ) the omplex eodynmi behviou of nopie (Monteith, 1995). Lowe LAI index (LAI <1.0) nd dought te lo ffet the peiion in the etimtion (eg., Rmiez, 2007). Ue of the LAI effetive when LAI < 1.0 i not neey nd tend to oveetimte the nd unde-etimte the ET. Kteji nd Peie (1985) found fo LAI >1.0 good geement between meuement vlue of evpotnpition ove lflf op uing the enegy blne method, nd vlue lulted with P-M eqution uing vible. Kteji nd Peie (1983) popoed to imulte uing the following eltion: * + whee nd b e line oeffiient tht need empiil detemintion, *(.m -1 ) i limti eitne (Kteji nd Rn, 2006) giving by: Tble 2 peent vlue of nd b fo evel op. b ( R G) (59) Δ + γ ρcpvpd *. (60) Δλ n

24 Wte Vpo Flux in Agoeoytem Method nd Model Review 25 A B LAI 4,50 4,00 3, ,00 (m -1 ) ,50 2,00 1,50 1,00 0,50 LAI (m 2.m -2 ) 0 V2 V4 V8 R1 R3 R4 R6 R8 0, Mole SER 16 C L (/m) Fig. 3. Reltionhip between A. Chnge in the tomtl eitne duing the dy with nd without dought te in Pheolu vulgi L. genotype Mole. B. Sufe eitne nd Lef e index, nd C. Stomtl behviou epeented in tomtl eitne ( L ) unde dought te ondition fo two ommon ben genotype - Mole let dought tolent nd SER 16 dought te tolent. DOY

25 26 Evpotnpition Windy L ( / ) R ; p< L (.m -1 ) A Low wind ( L /LAI effetive ) Windy (.m -1 ) ( / ) R ; P<0.031 B 200 Low wind (.m -1 ) Fig. 4. Aeodynmi eitne ( ) funtion of: A. Stomtl eitne ( L ) nd B. Meued ufe eitne: L /LAI effetive, (Dt fom: Rmiez, 2007). Cop b Soue G Kteji nd Rn (2006) Tomto Kteji nd Rn (2006) Gin oghum Kteji nd Rn (2006) Soyben Kteji nd Rn (2006) Sunflowe Kteji nd Rn (2006) Sweet oghum Kteji nd Rn (2006) G (Topil limte) Goe (1976) in Rn et l. (1997) G (Meditenen limte) Rn et l. (1994) Alflf Kteji nd Peie (1983) in Rn et l (1997) Soghum Rn et l. (1997)b Sunflowe Rn et.l (1997)b Tble 2. Coeffiient nd b fo evel op

26 Wte Vpo Flux in Agoeoytem Method nd Model Review 27 The Penmn-Monteith model i onideed ingle-lye model, Shuttlewoth nd Wlle (1985) developed double-lye model, elying on the Penmn-Monteith model onept to deibe the ltent het flux fom the nopy (λt) nd fom the oil (λe) follow: VPDo Δ( Rn Rn ) + ρcp λ T (61) Δ + γ 1 + VPDo Δ( Rn G) + ρcp λ E (62) Δ + γ 1 + whee R n i the bobed net dition t the oil ufe, i the bulk boundy lye eitne of the nopy element within the nopy, i the bulk tomtl eitne of the nopy, i the eodynmi eitne between the oil nd the men nopy height, i the ufe eitne of the oil nd VPD o i the vpou peue defiit t the height of the nopy i tem. 4.4 The double-lye Shulttlewoth-Wlle model The Shulttlewoth-Wlle Model (S-W) ume tht thee i blending of het fluxe fom the leve nd the oil in the men nopy iflow t the height of the effetive nopy oue (Shulttlewoth nd Wlle,1985). The full expeion of the Shulttlewoth-Wlle Model (S-W) model i peented by Zhng et l. (2008) follow: PM λet PM + C S PM S λe + λt C` ΔA p + ΔA S P PM P [( ρcpd Δ )( ASw A )/( + )] Δ + γ [ 1+ /( + )] + p p [( ρcpd Δ A )/( + )] p Δ + γ [ 1+ /( + )] p (63) (64) (65) C C P S P S [ R R / R ( R + R )] 1 P S P [ R R / R ( R + R )] 1 (66) (67) R R S P ( Δ + γ ) + γ (68) p p ( Δ + γ ) + γ (69)

27 28 Evpotnpition R P ( Δ + γ ) (70) whee λe i the ltent het flux of evpotion fom the oil ufe (W/m 2 ), λt the ltent het fluxe of tnpition fom nopy (W/m 2 p ), the nopy eitne (/m), p the eodynmi eitne of the nopy to in-nopy flow (/m), the oil ufe eitne (/m), nd the eodynmi eitne fom the efeene height to innopy het exhnge plne height nd fom thee to the oil ufe (/m), epetively, A w A e the totl vilble enegy nd the vilble enegy to the oil (W/m 2 ), epetively nd defined follow: Aw n R G (71) A R G (72) nw whee R i the net dition fluxe into the oil ufe (W/m 2 ), nd n be lulted nw uing the Bee lw follow: (. LAI ) n.exp (73) w R n R whee i the extintion oeffiient of light ttenution (e.g.; Sene, 1994 indite 0.68 fo fully gown plnt, 0 fo be oil; Zhng et l., 2008 ue 0.24 fo vineyd op). The ufe eitne i lulted follow: p t min (74) LAI ΠF ( X ) effetive whee t min i the miniml tomtl eitne of individul leve unde optiml ondition. LAI effetive i: equl to LAI fo LAI 2.0; LAI/2 fo LAI 4.0 nd 2 fo intemedite vlue of LAI, X i i peifi envionmentl vible, nd F i (X i ) i the te funtion with 0.0 F i (X i ) 1.0 (fom: Jvi, 1976). i i i S F 1( S) (75) 1100 S + 1 ( )( ) ( TH ) ( ) 2 / 2 TL T TL TH T ( )( ) ( TH ) ( T ) 2 / 2 L T T F2 ( T ) (76) 2 L H 2 3 F ( D 2 ) D e (77) 1 if θ θf θ θ W F4 ( θ) if θf < θ < θ W θf θ W 0 if θ θw (78)

28 Wte Vpo Flux in Agoeoytem Method nd Model Review 29 whee S i the inoming photoynthetilly tive dition flux (W/m 2 ), T i the i tempetue ( o K), θ F i the oil moitue t field pity (m 3 /m 3 ), θ w i the oil moitue t wilting point (m 3 /m 3 ), nd θ i the tul oil moitue in the oot zone. (m 3 /m 3 ). T H nd T L e uppe nd lowe tempetue limit outide of whih tnpition i umed to ee ( o C) nd e et t vlue of 40 nd 0 o C (e.g.; Hi et l., 2004; Zhng et l., 2008). The 1, 2, nd 3 e deived by multi-vite optimiztion, nd e 57.67,25.78 nd 9.65, epetively (Zhng et l., 2008). The eodynmi eitne nd e lulted fom the vetil wind pofile in the field nd the eddy diffuion oeffiient. Above the nopy height, the eddy diffuion oeffiient (K) i given by: ( z d ) K ku * (79) whee u* i the wind fition veloity (m/), k i the vn-kmn ontnt (0.41), z i the efeene height (m), nd d the zeo plne diplement (m). The exponentil deee of the eddy diffuion oeffiient (K) though the nopy i given follow: z K kh. exp n 1 (80) n whee k h i the eddy diffuion oeffiient t the top of the nopy (m 2 /), nd n i the extintion oeffiient of the eddy diffuion. Butet (1982) ited by Zhng et l., (2008) indite tht n 2.5 when h <1 m; n 4.25 when h >10 m, line intepoltion ould be ued fo op with h between thoe vlue. k h i detemined follow. k h ( h d ) ku * (81) The eodynmi eitne nd e obtined by integting the eddy diffuion oeffiient fom the oil ufe to the level of the pefeed ink of momentum in the nopy, nd fom thee to the efeene height (Shutllewoth nd Guney, 1990, mentioned by Zhng et l., 2008) follow: 1 z d h zo + d ln + exp n 1 1 Ku * h d nkh h (82) h exp ( n) nz exp h ' + z d exp n h o 0 nkh The bulk boundy lye eitne of nopy i lulted follow: (83) p b (84) 2LAI whee b i the men boundy lye eitne (/m) (e.g.; Bion et l., 1998, eommend ue 50 /m). The oil ufe eitne i the eitne to wte vpou movement fom the inteio to the ufe of the oil, nd i tongly depending of the wte ontent (θ ), nd i lulted uing the Annditki et l. (2000) expeion:

29 30 Evpotnpition ( θ ) f (85) min whee θ i oil volumeti wte ontent (m 3 /m 3 ), nd i the minimum oil ufe min eitne, tht oepond with the oil field pity (θ FC ) nd i umed equl to 100 /m (e.g.; Cmilo nd Guney, 1986; Zhng et l., 2008). f θ i expeed oding with Thompon (1981) nd mentioned by Zhng et l. The ( ) (2008) follow: θ FC f ( θ ) (86) θ 4.5 Clumping model The Clumping model i bed in the Shulttlewoth-Wlle model, thi model epte the oil ufe into ftionl e inide nd outide the influene of the nopy, nd inlude the ftion of nopy ove (f) in hi lultion. Benne nd Inoll (1997) nd Zhng et l. (2008) expe the model follow: λe λ λ λ p p b b ( C PM + C PM ) + ( f ) C PM b E + E + T f 1 (87) whee λ E i the ltent het of evpotion fom oil unde the plnt (W/m 2 b ); λe i the ltent het of evpotion fom be oil (W/m 2 ); f i the ftionl vegettive ove nd the othe tem e expeed follow: C C p PM PM p PM ΔA p ( ρcpd Δ A ) + Δ + γ p p + p p ( ρcpd Δ A ) ΔA + + Δ + γ b ( ρcpd) b ΔA + + b Δ + γ b b b p R R ( R + R ) p b p b b p [ R R R + ( 1 f ) R R R + fr R R + fr R R ] b p R R ( R + R ) p b p b b p [ R R R + ( 1 f ) R R R + fr R R + fr R R ] (88) (89) (90) (91) (92)

30 Wte Vpo Flux in Agoeoytem Method nd Model Review 31 C b p b RR ( R + R ) p b p b b p [ R R R + ( 1 f ) R R R + fr R R + fr R R ] (93) R R R p b ( Δ + γ ) + γ (94) p p ( Δ + γ ) + γ (95) b b ( Δ + γ ) + γ (96) R ( Δ + γ ) p Whee A, A, A nd unde hub nd be oil (W/m 2 ) epetively, b (97) b A e enegy vilble to evpotnpition, to the plnt, to oil the eddy diffuion eitne fom in- the oil ufe eitne b nopy het exhnge plne height to the oil ufe (/m), of be oil (/m). The Avilble enegy fo thi model, the net dition (R n ) i divided i divided into net p dition in the plnt ( R ) nd the net dition in the oil ( n R ). If the enegy toge in the n plnt i umed to be negligible, then: R n Rn exp ( CLAI / f ) (98) R A A p n b R R (99) n n Rn G (100) b Rn G (101) A R (102) p p Whee R nd n R e the dition bobed by the plnt nd the dition by the oil n (W/m 2 b ) epetively, G nd G e the oil het flux unde plnt nd be oil (W/m 2 ) epetively, C i the extintion oeffiient of light ttenution oding fo Sene (1994) i equl to 0.68 fo fully gown plnt. The eitne fo the be oil ufe b n be lulted eqully in the S-W model, mentioned befoe. The eodynmi eitne between the be oil ufe nd the men b ufe flow height ( ) n be lulted uming tht the be oil ufe i totlly b unffeted by djent vegettion o tht i eodynmi eitne equl to nd defined fo: p n Z m Z' (103) b o ln 2 k Um Whee Z m i the men ufe flow height (m), nd ould be umed equl to 0.75h, nd u m i the wind peed t the Z m (m/). 2

31 32 Evpotnpition Aoding with Zhng et l. (2008), the eodynmi eitne ( b b ) vie between nd f vie fom 0 to 1, nd the funtionl eltionhip of thi hnge i not know. 4.6 Combintion model Theoetil ppohe to ufe evpotion fom the enegy blne eqution ombined with enible het nd ltent het exhnge expeion give the following definition fo tul evpotnpition (Peei et l., 1999). Δ ρcp ET Δ + n VPD γ Δ ( R G) + Hu( VPD ) (104) Whee R n - G vilble enegy (MJ/m 2 ) fo the nopy, ompied of net dition, R n nd the oil het flux, G; H(u) exhnge oeffiient (m/) between the ufe level nd efeene level bove the nopy but tken inide the onevtive boundy ublye; VPD nd VPD (kp) vpou peue defiit (VPD) fo the ufe level nd the efeene level, epetively; ρ tmophei denity (kg/m3); Cp peifi het of moit i (J/kg7C); lope of the vpou peue uve (P/ºC); nd pyhometi ontnt (P/ºC). To obtin evpotnpition with (104) the mot diffiult tem to etimte i VPD, epeenting the vpou peue defiit t the evpotive ufe. If VPD n be oited with ufe eitne tem ( ), then ET n be lulted dietly fom the flux eqution: ET ρcp VPD (87) (105) γ nd 1 (106) Hu n be lulte uing the eqution diued lte. Two min olution n be defined fom (104) uing limti dt: 1. The e of full wte vilbility oeponding to tution t the evpotive ufe. Then VPD 0 nd beome null. Eq. (104) then give the mximum vlue fo ET, the potentil evpotion (EP), whih depend only on limti diving foe: Δ( R EP G) + ρcpf( uvpd Δλ n ) In whee F(u) 1/. The ombintion the eqution n get: (107) ET EP γ (108) (1 + ) Δ + γ 2. The e fo equilibium between the ufe nd the efeene level oepond to VPD VPD. In thi e, the evpotnpition i efeed to the equilibium evpotion (Ee).

32 Wte Vpo Flux in Agoeoytem Method nd Model Review 33 ρcp VPD Ee (109) γ Whee w enmed e, temed the equilibium ufe eitne, inditing tht the tem, in thi e, epeent the ufe eitne fo equilibium evpotion. The vlue fo e depend pedomintely on limti hteiti lthough thee hteiti e influened by R n nd G of the vegettive ufe. Fo pupoe hee, the e tem n be lled the limti eitne fo the ufe. e EP n be etimte: ρcp Δ + γ VPD e γ Δ R G n (110) nd ET n be etimte uing: γ e EP Ee (111) Δ + γ ET EP(36) γ 1+ Δ + γ (112) 4.7 Pitley nd Tylo model Pitley nd Tylo (1972), popoe to negleted the eodynmi tem nd fix the dition tem by intoduing dimenionle oeffiient (α). Δ ET α ( Rn G) (113) Δ + γ whee ET i wte flux unde efeene ondition (well wteed g) in mm.dy -1 ; R n nd G e net dition nd oil het flux epetbly in mm.dy -1 ; Δ nd in kp. C -1. The tem α i given 1.26 fo g field in humid wethe ondition, nd w dopted by Pitley nd Tylo (1972) fo wet ufe; howeve α i nging between 0.7 to 1.6, ove viou lndpe (Flint nd Child, 1991). Aoding with Zhng et l. (2004), the tem α n be lulted follow: λ α Δ E( Δ + γ ) Δ + γ ( R G) Δ( 1+ β ) n (114) Alo de α tem enible t the oil moitue hnge (Eg.; Ggo nd Butet, 1992; Ggo 1996; nd Zhng et l., 2004), tht eltion n be etimted uing model like: θ d α k 1 exp (115) θfc whee k, nd d e pmete of the model, θ i the tul volumeti oil moitue ontent (m 3.m -3 ) nd θ i the volumeti moitue ontent t field pity (m 3.m -3 ). FC

33 34 Evpotnpition 4.8 Eddy ovine method The eddy ovine method i, in genel, the mot pefeed beue it povide diet meue of the vetil tubulent flux o the men hoizontl temline, povided by ft eno (~10 Hz) (Meye nd Bldohi, 2005). Relizing the limittion of the Thonthwite-Holzmn type of ppoh, Swinbnk (1951) ited by Chng (1968) w the fit to ttempt diet meuement by the o-lled eddy oeltion tehnique. The method i bed on the umption tht the vetil eddy flux n be detemined by imultneou meuement of the upwd eddy veloity nd the flutution in vpou peue. Atully i outinely tehnique fo diet meuement of ufe lye fluxe of momentum, het, nd te ge (CO 2, H 2 O, O 3 ) between the ufe nd the tubulent tmophee (Mmm, 2000). Thi ytem eognize tht the tnpot of het, moitue, nd momentum in the boundy lye i govened lmot entiely by tubulene. The eddy oeltion method i theoetilly imple uing n ppoh to meue the tubulent fluxe of vpou nd het bove the nopy ufe. The eddy oeltion fluxe e lulted nd eoded in 30 min o le tempol eolution. Auming the net ltel dvetion of vpou tnfe i negligible, the ltent het flux (evpotnpition) n be lulted fom the ovine between the wte vpou denity (ρ ν ) nd the vetil wind peed (w). λ E λw' ρv ' (116) λ E i the ltent het flux (W m -2 ), λ i the ltent het of vpoiztion (J kg -1 ), ρ ν i the whee flutution in the wte vpou denity (kg m -3 ), nd w i the flutution in the vetil wind peed (m -1 ). The ove b epeent the vege of the peiod nd pime indite the devition fom the men vlue duing the veging peiod. Aoding with Weve (1992) the eddy oeltion method depend on the eltion between the dietion of i movement ne the lnd ufe nd popetie of the tmophee, uh tempetue nd humidity. The enible het flux n be lulted fom the ovine of i tempetue nd the vetil wind peed. H C w't' (117) ρ p Whee H the enible het flux (W m -2 ), ρ the i denity (kg m -3 ), C p the peifi het of moit i (J kg -1 o C -1 ) nd T the flutution in the i tempetue ( o C). The fine wie themoouple (0.01 mm dimete) e not inluded in the eddy oeltion ytem. The i tempetue flutution, meued by the oni nemomete, e oeted fo i tempetue flutution in etimtion of enible het fluxe. The oetion i fo the effet of wind blowing noml to the oni outi pth. The implified fomul by Shotnu et l. (1983) i follow: ( T ) w ' w T wt 0.51 q (118) Whee w T i otted ovine of wind peed nd oni tempetue (m o C -1 ), T i i tempetue ( o C) nd q i the peifi humidity in gm of wte vpou pe gm of moit i. Two Eddy ovine ytem e ued to meue the wte vpou fluxe, the open pth nd loe pth. Aoding with Anthoni et l. (2001) the Open-pth eddy ovine

34 Wte Vpo Flux in Agoeoytem Method nd Model Review 35 ytem equie oetion fo denity flutution in the mpled i (Mmn nd Lee, 2002; Webb et l., 1980) nd in genel loed-pth ytem equie inopotion of time lg nd oetion fo the lo of high fequeny infomtion, due to the i being dwn though long mpling tube (Mmn nd Lee, 2002; Mooe, 1986). The mot ommon oetion in the eddy ovine ytem i deibed by Wolf et l. (2008) : i) Coodinte ottion, ii) Ai denity oetion, nd iii) Fequeny dependent ignl lo. Etimtion of tubulent fluxe i highly dependent on the uy of the vetil wind peed meuement. Meuement of wind peed in thee othogonl dietion with oni nemomete equie efined oienttion with epet to the ntul oodinte ytem though mthemti oodinte ottion (Sumne, 2001). The veto of wind h thee omponent (u, v, w) in thee oodinte dietion (x, y, z). The z-dietion i oiented with epet to gvity, nd the othe two e bity. Bldohi et l. (1988) povide poedue to tnfom the initil oodinte ytem to the ntul oodinte ytem. Deibed in detil by Sumne (2001), the oodinte ytem i otted by n ngle bout the z-xi to lign u into the x-dietion on the x-y plne, then otted by n ngle bout the y-dietion to lign w long the z-dietion. The eult foe v nd wequl to zeo, nd u i pointed dietly to the i tem. When w gete thn 10 degee, the tubulent flux dt hould be exluded bed on the umption tht puiou tubulene w the ue of the exeive mount of the oodinte ottion. oθ 2 2 ( u + v ) ( u + v + w ) ( u + v + w ) (119) w inθ (120) u oη (121) 2 2 ( u + v ) v inη (122) 2 2 ( u + v ) The ltent het nd enible het fluxe e omputed fom the oodinte ottiontnfomed ovine: w ρv w ρ oθ u ρ inθ oη v ρ inθ inη v v v (123) wt wt oθ ut inθ oη v T inθ inη (124) Afte the oodinte ottion, the finl ltent het flux n be etimted fom eqution (116) plu the following oetion of i denity (C i ) (Webb et l., 1980) nd oetion of oxygen (CO 2 ) (Tnne nd Geene, 1989).

35 36 Evpotnpition C i ρc p ρ H v ( T ) λ (125) FK H CO 2 (126) K w o ( T ) λ Whee F i the fto ued in kypton hygomete oetion tht ount fo moleul weight of i nd oxygen, nd tmophei bundne of oxygen, equl to g o C J -1, K o i the extintion oeffiient of hygomete fo oxygen, etimted m 3 g -1 m -1, K w i the extintion oeffiient of hygomete fo wte, fom the mnuftue i m 3 g -1 m -1. With the meued fou flux omponent fom the enegy blne eqution, the enegy blne hould be loed, howeve, thi i not ptilly the e. A tendeny to undeetimte enegy nd m fluxe h been pevive poblem with the eddy ovine tehnique (Hm nd Heilmn, 2003). Hm nd Heilmn (2003) epoted louue of 0.79 fo piine lotion nd 0.96 fo foet. Rmiez nd Hmen (2007-Dt without publition) indite 0.71 fo g nd 0.75 fo on. The eo in eddy ovine method ould be oited with: 1. Auy of the R n nd G meuement (eo e often 5 to 10%). 2. The length le of the eddie eponible fo tnpot (if i lge, the fequeny epone nd eno eption eo my hve been mlle) 3. Seno eption nd indequte eno epone (n genete 15% of Undeetimtion of λe by (Hm nd Heilmn, 2003) nd 10% epoted by Lubh nd MNuhton (1999). 4. Hm nd Heilmn (2003) onlude The inheent tendeny to undeetimte fluxe when uing eddy ovine my be linked to the eo ued by eno eption nd indequte fequeny epone of the eno. The oetion popoed by Mmn nd Lee (2002) i diffiult to implement fo the non-peilit beue they equie lultion of opet uing high-fequeny (10Hz) dt, nd lo i equied expetie expeiene to intepet the opet popely The enegy blne loue i oeted uing the Bowen tio (Kougi nd Ktuym, 2007) follow: Η β λe (127) λe Rn-G-H (128) Whee: β nd λε me fom eddy ovine ytem, R n nd G e meued. The Mmn nlytil fomule fo petl oetion to meuemed momentum nd l fluxe fo eddy ovine ytem. Mmn (2000) develop n nlytil method fo fequeny epone oetion, bed in the Hot (1997) ppoh develop follow: Fo Stble tmophei ondition (0<ζ 2).. Ft-epone open pth ytem Flux m b b 1 p ( )( ) ( )( ) ( ) ( )( ) 1 Flux + 1 b p b + p p p b. Sl intument with epone (129)

36 Wte Vpo Flux in Agoeoytem Method nd Model Review 37 Flux m Flux 1 b b 1 p p ( )( ) ( )( ) ( ) b p b + p p + 1 ( + 1)( + p) + p. Untble tmophei ondition (ζ 0) (130) α α α α Flux m b b 1 p 1 Flux 1 α α α ( )( ) α α α α ( )( ) α ( ) α α + 1 b p b + p p + 1 ( + )( + p ) α (131) whee the ubipt m efe to the meuement flux, 2 π xτ ; h b 2 π xτ ; b p 2 π xτ, nd τ h nd τ b e the equivlent time ontnt oited with tend emovl ( τ h ) nd blok veging ( τ b ). Fo eltively bod oepet with eltively hllow pek, uh the flt tein neutl/tble flt tein oepetum α0.925, nd fo hpe, moe peked oepet, uh the tble tein oepet α0.925 (Kiml et l., 1972). Thee ppoximtion e lely eie to employ thn numeil ppohe nd e pplible even when fluxe e o mll to pelude the ue of in itu method. Nevethele, thi ppoh i ubjet t the next ondition: i) hoizontlly-homogeneou upwind feth, ii) the vlidity of the o-epetl imility, iii) uffiiently long veging peiod, nd pefebly, iv) eltively mll oetion (Mmn, 2000). 4.9 The infed ufe tempetue method The ufe tempetue h lo been ued fo the etimtion of the enible het flux (H) uing the eitne model (Alve et l., 2000) H To T ρ. Cp (132) Whee ρ i i denity (Kgm -3 ), Cp peifi het t ontnt peue (Jkg -1 ºC -1 ), To i the tempetue t ufe level (ºC), T i the tempetue t the efeene level (ºC), nd i the eodynmi eitne to het flux between the ufe nd the efeene level (m -1 ), the ltent het flux (λe) n be omputed the eidul tem in the enegy blne. λe To T Rn G H Rn G ρ. Cp (133) Alve et l. (2000) y the diotive ufe tempetue h evel dwbk. Theml dition eeived by the intument n oiginte fom the leve but lo fom de oil, nd the meuement n be highly dependent on op ove, inlintion of diomete nd un height nd zimuth, epeilly en ptil ove op, the fit one lie in the ue of n dequte vlue of. Whee d i zeo plne diplement height (m), Z om nd Z OH e the oughne length (m) fo momentum nd het epetively, k i the von Kmn ontnt, u z i the wind peed (m -1 ) t the efeene height z (m), nd ψm nd ψh e the integted tbility funtion fo deibing the effet of the buoyny o tbility on momentum tnfe nd het between the ufe nd the efeene level.

37 38 Evpotnpition The neey intument e: Wind peed nd dietion eno t (0.85 nd 1.46m), pyhomete t the me height tht wind eno, net diomete plement 1.5 m nd infed themomete pependiul to the ow the op, nd poitioned t n ngle of 60º below hoizontl to view the top leve of the plnt t 0.40 m ditne. (Alve et l., 2000) Senible het flux, H i lulted with the flux pplied to level Z 1 nd Z 2. H T1 T 2 ρ Cp (134) [ ] 2 1 [ ] 2 i the eodynmi eitne to het flux between the two level, nd i omputed 1 uing the eqution [ ] 2 1 Z2 d ln Z1 d (135) ku * with u* the fition veloity, obtined in the poe of detemining eodynmi pmete d nd Z om fom the win pofile meuement. The i tempetue t the ufe level (To) i lulte uing: H To T + (136) ρcp The tbility ondition n be lulted uing the Rihdon numbe 5. Feth equiement The i tht ping ove ufe i ffeted by the field ufe fetue (Roenbeg et l., 1983); the miniml feth equiement n be etimted bed on the thikne of the intenl boundy lye (δ in m ) nd oughne pmete (Z o in m) onideing the miniml nd mximl op height duing the gown eon. The δ n be lulted uing the eltion popoed by Monteith nd Unwoth (1990). 4 / 5 1/ L. Zo δ (137) whee L i the ditne of tvee (feth) o unifom ufe with oughne Z o. The Z o fo op i ppoximtely one ode of mgnitude mlle thn the op height h, nd n be lulted oding with Roenbeg et l. (1983) follow: Log 10 Z o log 10 h (138) A fto of fety height to feth of 1:50 to 1:100 i uully onideed dequte fo tudie mde ove giultul op ufe (Roenbeg et l., 1983, Allen et l., 1998) but my be too onevtive nd diffiult to hieve in ptie. Alve et l. (1998) obtined full pofile development uing 1:48 feth eltion in Whet nd lettue. Heilmn et l. (1989) found tht fo Bowen-Rtio etimte feth 1:20 w uffiient ove g, nd Hm nd Heilmn (1991) nd Fithhen nd Fithen (2005) obtined imil eult.

38 Wte Vpo Flux in Agoeoytem Method nd Model Review Stbility oetion The gdient method need tbility oetion, one of the mot ued i the Monin- Obukhov tbility fto (ζ) deibed by (Roembeg et l., 1983; Cmpbell, 1985; Puege nd Kut;2005). ( k. z. g. H ) ξ (139) 3 (. C. T. u * ) ρ whee k i von Kmn ontnt, z i height of wind nd i tempetue meuement (m), g i the gvittionl ontnt (9.8 m. -2 ), H β.λe, T i i tempetue ( o K), u* i the fition veloity given by Kjelgd et l. (1994) without the tbility oetion fto: k. uz u* z d + Z ln Zom p om (140) flux with negtive ign fo ζ indite untble ondition nd need to be exlude, in flux unde untble ondition the λe i ove R n (Fig.5), when the flux with negtive ζ e exlude, λe i low tht R n (Fig.5b). Pyeo et l. (2003) indite tht fluxe with inoet ign nd β -1 hould not be onideed when etimted the enegy blne omponent by the enegy blne Bowen tio method. The negtive ζ e oeponded with negtive β (Fig.6). The Rihdon numbe (Ri) epeented by the eqution 44, lo i well know tbility fto (e.g.; Alve et l., 2000; Tolk, et l., 1995) nd epeent the tio of the buoyny theml effet to mehnil wind he (Puege nd Kut, 2005). Negtive vlue indite intbility ondition whee ufe heting enhne buoyny effet, nd poitive Ri vlue indite tble ondition whee tempetue ne the ufe e oole thn wy fom the ufe A Rn LE G H B Rn LE G H W.m W.m :48:00 AM 7:12:00 AM 9:36:00 AM 12:00:00 PM 2:24:00 PM 4:48:00 PM 7:12:00 PM Time :48:00 AM 7:12:00 AM 9:36:00 AM 12:00:00 PM 2:24:00 PM 4:48:00 PM 7:12:00 PM Time Fig. 5. Enegy blne omponent meued by Bowen tio method in g A. without tbility oetion nd B. with tbility oetion.

39 40 Evpotnpition Bowen tio (H/LE) E-10-4E-10-3E-10-2E-10-1E E-10 Monin-Obukhov tbility fto (ζ ) Fig. 6. Reltionhip between Bowen tio (β) ) nd the Monin-Obukhov tbility fto 7. Aknowledgement Muh of the dt peented in thi hpte wee obtined unde the pojet ponoed by NOAA-CREST (NA17AE1625), NASA-EPSCoR (NCC5-595), USDA-TSTAR-100, nd USDA Hth Pojet H-402. We e lo gteful with the Univeity of Pueto Rio Expeiment Sttion nd the Ntionl Coffee Reeh Cente (Cenifé-Colombi) fo poviding uppot to finih thi doument. 8. Refeene Alve, I.; Peie, A. nd Peei, L. S. (1998). Aeodynmi nd Sufe Reitente of Complete Cove Cop: How Good i the Big Lef?. Amein Soiety of Agiultul Enginee. 41(2): Alve, I.; Fonte, J.C. nd Peei, L.S. (2000). Evpotnpition Etimtion Fom Infed Sufe Tempetue. I: The Pefomne of the Flux Eqution. Amein Soiety of Agiultul Enginee. 43(3): Alve. L. nd L.S. Peei. (2000). Modeling Sufe eitne fom limti vible?. Agiultul. Wte. Mngement. 42: Allen G.R.; Cuen H.R.; Jenen E.M.; Blthley K.R. & Epenbek M.J. (1990). Evpotnpition nd iigtion wte equiement. Amein Soiety of Civil Enginnee. New Yok (USA).332p. Allen, G.R.; Peei, S.L.; Re, D. & Smith, M. (1998). Cop evpotnpition: Guideline fo omputing op wte equeement. Food nd Agoultul Ogniztion of the United Ntion (FAO).56. Rome.300p. Annditki, M., A.Likt., P. Kekide., S. Rizo., J.Gvnoni. nd A. Poulvili. (2000). Cop wte equiement model teted fo op gown in Gee. Agiultul. Wte Mngement.42: Angeloi, L.R.; BuninI, O. nd Mglhe, A.C.(1983). Vio de eiténi etomáti á difuo de vpo d águ oid o etdo de enegi d águ n folh em

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42 Wte Vpo Flux in Agoeoytem Method nd Model Review 43 Howell, T.A.; Steine, J.L.; Sheide, A.D.; Evett, S.R. nd Tolk. A.J. (1994). Evpotnpition of iigted winte whet, oghum nd on. ASAE Ppe No , ASAE, St. Joep, MI Hot, T.W. (1997). A imple fomul fo ttenution of eddy ovine flux meuement. Boundy Lye Meteoology. 82: Hunke, D.J. (1999). Bl Cop Coeffiient nd Wte Ue Fo Ely Mtuity Cotton. Amein Soiety of Agiultul Enginee.42(4): Hunke, D.J.; Pinte, P.J.J. & Ci, H.(2002). Alflf Bl Cop Coeffiient fo FAO-56 Poedue in the Deet Region of the Southweten U.S. Amein Soiety of Agiultul Enginee.45(6): Jvi, P.G. (1976). The intepettion of the vition in lef wte potentil nd tomtl ondutne found in nopie in the field. Phil Tntion Royl Soiety London Bulletin. 273: Jhonon, R.S.; Willim, L.E.; Ay, J.E. & Tout. T.J. (2005). Weighing lyimete id tudy of wte eltion in tee nd vine op. Clifoni Agiultue.59(2): Kml, H.A. nd Htfield, L.J. (2004). Cnopy Reitne Affeted Soil nd Meteoologil Fto in Potto. Agonomy Jounl. 96: Kiml, J.C.; Wyngd, J.C.; Izumi, Y. nd Cote, O.R. (1972). Deiving powe pet fom thee-omponent oni nemomete. Jounl Applied Meteoology. 7: Kteji, N. nd Peie, A. (1983). Modelling the el evpotnpition in Alflf op. Role of the op oeffiient. Agonomie.3(6): (in: Fenh). Kteji, N. nd Peie, A. (1985). Detemintion of the nopy eitne to the wte vpou diffuion of the ix nopy ove. Agiultul Meteoology 34: (in: Fenh). Kteji, N. nd Rn, G. (2006). Modelling evpotnpition of ix iigted op unde Meditenen limte ondition. Agiultul nd Foet Meteology.138: Kikhm, M.B.; Redelf, M.S.; Stone, L.R. nd Knemu, E.T. (1985). Compion of wte ttu nd evpotnpition of ix ow op. Field Cop Reeh.10: Kjelgd, J.F. nd Stoke, C.O. (2001). Evluting Sufe Reitne fo Etimting Con nd Potto Evpotnpition with the Penmn-Monteith Model. Amein Soiety of Agiultul Enginee.44(4): Kjelgd, J.K.; Stokle, C.O.; Vill Mi, J.M.; Evn, R.G. nd Cmpbell, G.S. (1994). Evlution method to etimte on evpotnpition fom hot-time intevl wethe dt. Tntion of ASAE. 37(6): , Kougi, Y. nd Ktuym. M. (2007). Evpotnpition ove Jpnee ype foet II. Compion of the eddy ovine nd wte budget method. Jounl of Hydology.334: Lubh, J. nd MNuhton (1999). A petum-independent poedue fo oeting eddy flux meuement with epted eno. Boundy Lye Meteotology. 89: Lloyd, W.G. (1992). Bowen-Rtio meuement. Evpotnpition meuement of ntive vegettion, Owen Vlley, Clifoni. U.S Geologil Suvey. Wte-Reoue Invetigtion Repot :5-18

43 44 Evpotnpition López-Ue, R.; Mtin de Snt Olll, F..; Febeio, C. & Motll. A. (2006). Teting evpotnpition equition uing lyimete obevtion in emiid limte. Agiultul Wte Mngement.85(1-2): Loo, C.; S. Ginyle.; E. Piek. (2007). Aement of wte blne imultion fo lgele weighing lyimete. Jounl of Hydology.335(3-4): Mdeio, G.A.; Aud, F.B.; Ski, E. & Fujiw, M. (2001). The influene of the op nopy on evpotnpition nd op oeffiient of ben (Pheolu vulgi L.). Agiultul Wte Mngement 49: Mlone, R.W.; Stewdon, D.J.; Bont, J.V. & Nelen, T. (1999). Clibtion nd Qulity Contol of the Cohoton Weighing Lyimete. Tntion of the ASAE/Amein Soiety of Agiultul Enginiee.42(3): Mmn, W.J. (2000). A imple method fo etimte fequeny epone oetion fo eddy ovine ytem. Agiultul nd Foet Meteoology.104: Mmn, W.J. nd Lee, X. (2002). Eddy ovine flux oetion nd unetintie in long tem tudie of bon nd enegy exhnge. Agiultul nd Foet Meteoology.113: Meye, P.T. nd Bldohi, D.D. (2005). Cuent miometeoologil flux methodologie with pplition in giultue. In: Miometeoology in Agiultul Sytem, Agonomy Monogph no, 47. Amein Soiety of Agonomy, Cop Siene Soiety of Amei, Soil Siene Soiety of Amei, 677 S. Soe Rd., Mdion, W153711, USA: Monteith, L.J. (1965). Evpotion nd the envionment. Symp.So.Expe.Biol.19: Monteith, L.J. (1981). Evpotion nd ufe tempetue. Qutely Jounl of the Royl Meteoology Soiety. 107(451):1-27. Monteith, J.L. (1995). Aommodtion between tnpiing vegettion nd the onvetive boundy lye. Jounl of Hydology. 166: Monteith,, L.J. (1997). Evpotion Model. In: Agiultul Sytem Modelling nd Simultion. Edited by Robet M. Pet nd R. Bue Cuy. Univeity of Floid, Gineville, Floid: Monteith, J. L. nd Unwoth, M. H. (1990). Piniple of Envionmentl Phyi, 2 nd ed., Edwd Anold Publihe. 291 pg. Mooe, C.J. (1986). Fequeny epone oetion fo eddy oeltion ytem. Boundy- Lye Meteoology, 37: Nb, B.S.; Khkuli, H.A.; Khledin, M.R. (2004). Etimtion of Cop Coeffiient fo Sugne (Rtoon) in Hft Tppeh of In. ASAE/CSAE Annul Intentionl Meeting. Fimont Chteu Luie, The Weting, Govenment Cente Ottw, Ontio, Cnd. 1-4 Augut.10p. Oguntunde, G.P. (2005). Whole-plnt wte ue nd nopy ondutne of v unde limited vilble oil wte nd vying evpotive demnd. Plnt nd Soil. 278: Oteg-Fi, S.O.; Antonioletti, R. nd Bion, N. (2004). Evlution of the Penmn- Monteith model fo etimtig oyben evpotnpition. Iigtion Siene 23:1-9.

44 Wte Vpo Flux in Agoeoytem Method nd Model Review 45 Oteg-Fi, S.O.; Olioo, A.; Fuente, S.; Vlde, H. (2006). Ltent het flux ove fuowiigted tomto op uing Penmn-Monteith eqution with vible ufe nopy eitne. Agiultul Wte Mngement. 82: Pton, W.J.; Luenoth, W.K. & Smith, F.M. (1981). Wte lo fom hotg teppe. Agiultul Meteoology. 24: Pyeo, J.O.; Nele C.M.U.; Wight J.L.nd Allen. R.G. (2003). Guideline fo vlidting bowen tio dte. Amein Soiety of Agiultul Enginiee. 46(4): Penmn; H.L. (1948). Ntul Evpotion fom open wte, be oil nd g. Poeeding of the Royl Soiety of London. Seie A, Mthemtil nd Phyil Siene. 193(1032): Penmn, H.L. (1956). Evpotion: An intodutoy uvey. Nethelnd Jounl Agiultul Siene.1:9-29, 87-97, Peei S. L.; Peie, A.; Allen G, R. & Alve, I. (1996). Evpotnpition: Review of Conept nd Futue Tend. In; Evpotnpition nd Iigtion Sheduling. Poeeding of the Intentionl Confeene. Novembe 3-6. Sn Antonio, TEXAS: Peei S. L.; Peie, A.; Allen G, R.; Alve, I. (1999). Evpotnpition: Conept nd Futue Tend. Jounl Iigtion nd Dinge Enginee.125(2): Peei S.L.; & Alve, I. (2005). Cop wte equiement. In: Soil nd Envioment. Edited by Elevie: Peez, P.J.; Ctellvi, F. nd Mtinez-Cob. A. (2008). A imple model fo etimtion the Bowen tio fom limti fto fo detemining ltent nd enible het flux. Agiultul nd Foet Meteoology. 148: Pietley, C.H.B. nd Tylo, R.J. (1972). On the ement of the ufe het nd evpotnpition uing lge-le pmete. Monthly Wte Review. 100(2): Puege, H.J.; Htfield, J.L.; Ae, J. K. & Pikul J. J.L. (1997). Bowen-Rtio ompion with lyimete evpotnpition. Agonomy Jounl. 89(5): Puege, H.J. nd Kut, P.W. (2005). Aeodynmi method fo etimting tubulent fluxe. In: Miometeoology in Agiultul Sytem, Agonomy Monogph no, 47. Amein Soiety of Agonomy, Cop Siene Soiety of Amei, Soil Siene Soiety of Amei, 677 S. Segoe Rd., Mdion, W153711, USA: Rmíez, B.V.H. (2007). Plnt-Wte Reltionhip fo Sevel Common Ben Genotype (Pheolu vulgi L.) with nd Without Dought Ste Condition. M.S. Thei, Agonomy nd Soil Deptment, Univeity of Pueto Rio Myguez Cmpu. 190 pge. Rmiez, B.V.H.; Hmen, W.E. nd Poh, G.T. (2008). Etimtion of Atul Evpotnpition Uing Meued nd Clulted Vlue of Bulk Sufe Reitne. Poeeding of the Wold Envionmentl nd Wte Reeh Conge. Honolulu (Hwii). 10p. Rmíez, B.V.H. nd Jmillo, R.A. (2008). Modifition in the Supefiil Hydology oited t the ove hnge in the Colombin Topil Ande. In: XIV Colombin Soil Soiety Meeting.13p. (in Spnih).

45 46 Evpotnpition Rn, G.; Kteji, N.; Mtoilli, M.; El Moujbbe,M El. nd N. Bion. (1997). Vlidtion of model of tul evpotnpition fo wte teed oyben. Agiultul nd Foet Meteoology.86: Rn, G.; Kteji, N.; Mtoilli, M. nd El Moujbbe, M. (1997b). A model fo pediting tul evpotnpition unde oil wte te in Meditenen egion. Theoil Applied. Climtolology. 56: Rithie, J.T. & Bunett, E. (1968). A peiion weighing lyimete fo ow op wte ue tudie. Agonomy Jounl. 60(5): Roenbeg, J. N.; Bld, B.L. nd Vem, S.B. (1983). Miolimte; The Biologil Envionment. A Wiley-Inteiene Publition, Jhon Wiley nd Son. Edt. 495p. Roygd, F.R.; Alley, M.M.& Khol, R. (2002). No-Till Con Yield nd Wte Blne in the Mid-Atlnti Cotl Plin. Agonomy Jounl. 94: Sugie, B. (1977). Miometeoology on Cop nd Glnd. Envionmentl Effet on Cop Phyiology. Poeeding of Sympoium held t Long Ahton Reeh Sttion Uviveity of Bitol. Ademi Pe: Sugie, B. nd Kteji, N. (1991). Some plnt fto ontolling evpotnpition. Agiultul nd Foet Meteoology.54: Sene, K.J. (1994). Pmeteition fo enegy tnfe fom pe vine op. Agiultul nd Foet Meteoology.71:1-18. Seyfied, M.S.; Hnon, C.L.; Mudok, M.D. & Vn Vto. S. (2001). Long-tem lyimete dtbe, Reynold Ceek Expeimentl Wtehed, Idho, United Stte. Wte Reoue Reeh.37(11): Shotnu, P.; Nieuwtdt, F. T. M. nd de Buin, H. A. R. (1983). Tempetue meuement with oni nemomete nd it pplition to het nd moitue fluxe. Boundy-Lye Meteoology 50: Shuttlewoth, W.J.; nd Wlle, J.S. (1985). Evpotion fom pe op-an enegy ombintion theoy. Qutely Jounl of the Royl Meteoology Soiety..111: Steine, J.L.A.; Howell, T.A. & Shneide, A.D. (1991). Lyimete evlution of dily potentil evpotnpition model fo gin oghum. Agonomy Jounl.83(1): Suleimn, A. & Cgo, R. (2004). Houly nd Dytime Evpotnpition fom Glnd Uing Rdiometi Sufe Tempetue. Agonomy Jounl.96: Sumne, D. M. (2001). Evpotnpition fom ype nd pine foet ubjeted to ntul fie in Volui County, Floid, U. S. Geologil Suvey Wte- Reoue Invetigtion Repot Whington, D.C.: U.S. Geologil Suvey. Szeiz, C., nd Long, L.F. (1969). Sufe eitne of op nopie. Wte Reoue Reeh. 5(8): Tkh, H.S. & Rudge, A.J. (1970). Evpotion tudie in tndd thment. Jounl of Hydology.11(4): Tnne, C.B. (1960). Enegy blne ppoh to evpotnpition fom op. Soil Siene. Soiety of Amein Poeeding. 24(1):1-9. Tnne, B. D., nd Geene, J. P. (1989). Meuement of enible het flux nd wte vpou fluxe uing eddy oeltion method. Finl epot to U.S. Amy Dugwy Poving Gound. DAAD D-0088.

46 Wte Vpo Flux in Agoeoytem Method nd Model Review 47 Tee, L.D.; H. Shimmulepfenning.; nd R.P.Wlden. (1973). Rinout helte nd dinge lyimete to quntittively meue dought te. Agonomy Jounl. 65(4): Thom, A.S. (1975). Momentum, m nd het exhnge of plnt ommunitie. In: Vegettion nd the tmophee: Edit by Monteith. J.L Ademi Pe, New Yok. Tolk, A.J.; Howell, A.T.; Steine, L.J. nd Kieg, R.D. (1995). Aeodynmi Chteiti of Con Detemined by Enegy Blne Tenique. Agonomy.Jounl.87: Tomilon, A.E. (1994). Intumenttion, Method, nd Peliminy Evlution of Evpotnpition fo Glnd in the Aid Lnd Eology Reeve, Beton County, Whington, My-Otobe U.S. Geologil Suvey. Wte-Reoue Invetigtion Repot nd Whington Stte Deptment of Eology.32p Tomilon, A.E. (1997). Evpotnpition fo Thee Spe-Cnopy Site in the Blk Rok Vlley, Ykim County, Whington, Mh 1992 to Otobe U.S. Geologil Suvey. Wte-Reoue Invetigtion Repot nd Whington Stte Deptment of Eology.88p. Tune, C.N. (1991). Meuement nd influene of envionmentl nd plnt fto on tomtl ondutne in the field. Agiultul nd Foet Meteoology. 54: Tygi, N.K.; Shm, D.K. & Luth, S.K. (2000). Evpotnpition nd Cop Coeffiient of Whet nd Soghum. Jounl of Iigtion nd Dinge Enginee.126(4): vn Bvel, C.H.M. (1967). Chnge in nopy eitne to wte lo fom lflf indued by oil wte depletion. Agiultul nd Foet Meteoology. 4: Vughn, P.J.; Tout, T.J. & Ay, J.E. (2007). A poeing method fo weighing lyimete dt nd ompion to miometeoologil ETo pedition. Agiultul. Wte Mngement. 88(1-2): Von Unold, G. & Fnk, J. (2008). Module deign of field lyimete fo peifi pplition need. Wte Ai Soil Pollut: Fou 8: Weve, L.H. (1992). Eddy-Coeltion meuement t ite C nd F. Evpotnpition Meuement of Ntive Vegettion, Owne Vlley. Clifoni. U.S. Geologil Suvey. Wte-Reoue Invetigtion Repot : Webb, E. K.; Pemn, G. I. nd Leuning, R. (1980). Coetion of flux meuement fo denity effet due to het nd wte vpou tnfe. Qutely Jounl of the Royl Meteoology Soiety.. 106: Wilon, D.; Reginto, R. & Hollet, J.K. (1992). Evpotnpition meuement of ntive vegettion, Owne Vlley, Clifoni. U.S. Geologil Suvey. Wte Reoue Invetigtion Repot :1:4. Wolf,A.; Sliend, N.; Akhlov, K.; Johnon, D.A. nd L, E. (2008). Effet of diffeent eddy ovine blne loue nd ompion with the modified Bowen tio Sytem. Agiultul nd Foet Meteoology.148: Wight, J.L. & Jenen, M.E. (1978). Development nd evlution of evpotnpition model fo iigtion heduling. Tn ASAE. 21(1): Xingf, H.; Viiyenkul, V. & Deho, Z. (1999). Deign, Contution nd Intlltion of Filled-in Dinge Lyimete nd It Applition. Poeeding of 99 Intentionl Confeene on Agiultl Engineeing. Beijing, Chin, Deembe:II-162-II-167.

47 48 Evpotnpition Zhng, Y.; Liu, C.; Yu, Q.; Shen, Y.; Kendy, E.; Kondoh, A.; Tng, C. & Sun, H. (2004). Enegy fluxe nd Pitley-Tylo pmete ove winte whet nd mize in the Noth Chin Plint. Hydology Poe.18 : Zhng, B.; Kng, S.; Li, F. nd Zhng. L. (2008). Compion of thee evpotnpition model to Bowen tio-enegy blne method fo vineyd in n id deet egion of nothwet Chin. Agiultul nd Foet Meteoology.148:

48 Evpotnpition Edited by Pof. Lezek Lbedzki ISBN Hd ove, 446 pge Publihe InTeh Publihed online 16, Mh, 2011 Publihed in pint edition Mh, 2011 Evpotnpition i vey omplex phenomenon, ompiing diffeent pet nd poee (hydologil, meteoologil, phyiologil, oil, plnt nd othe). Fme, giultue dvie, extenion evie, hydologit, gometeoologit, wte mngement peilit nd mny othe e fing the poblem of evpotnpition. Thi book i dedited to futhe undetnding of the evpotnpition poblem, peenting bod body of expeiene, by epoting diffeent view of the utho nd the eult of thei tudie. It ove pet fom undetnding nd onept of evpotnpition, though methodology of lulting nd meuing, to pplition in diffeent field, in whih evpotnpition i n impotnt fto. The book will be of benefit to ientit, enginee nd mnge involved in poblem elted to meteoology, limtology, hydology, geogphy, gonomy nd giultul wte mngement. We hope they will find ueful mteil in thi olletion of ppe. How to efeene In ode to oetly efeene thi holly wok, feel fee to opy nd pte the following: Vićto Hugo Rmiŕez-Buile nd Ei W. Hmen (2011). Wte Vpo Flux in Agoeoytem Method nd Model Review, Evpotnpition, Pof. Lezek Lbedzki (Ed.), ISBN: , InTeh, Avilble fom: InTeh Euope Univeity Cmpu STeP Ri Slvk Kutzek 83/A Rijek, Coti Phone: +385 (51) Fx: +385 (51) InTeh Chin Unit 405, Offie Blok, Hotel Equtoil Shnghi No.65, Yn An Rod (Wet), Shnghi, , Chin Phone: Fx: