FAO PENMAN-MONTEITH EQUATION: CALCULATIONS
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1 Pg 1 of 1 FAO PENMAN-MONEIH EQUAION: CALCULAIONS AND OPIONS FO SUBSIUIONS FO MISSING DAA h FAO Pnmn-Montith qution llow for dt tht i miing to b timtd or clcultd uing othr vilbl dt. In om c thr i mor thn on option of how to clcult or timt th miing dt. hi ction dcrib ll th option vilbl. Appndix B focu on th clcultion rquird to clcult E o uing only tmprtur dt. Summrizd from Crop vpotrnpirtion, Guidlin for computing crop wtr rquirmnt (FAO ppr 56, 1998 E o Δ ( n 900 G + γ u + 73 Δ + γ ( u ( VPD E o dily rfrnc E [mm/d], for longr priod 900 bcom 37 ir tmprtur t m high [ C] VPD vpor prur dficit [kp] u wind pd t m high [m/] m/ n nt rdition t th crop urfc [MJ m - d -1 ] Δ lop vpour prur curv [kp C -1 ] γ pychomtric contnt [kp C -1 ] G oil ht flux dnity [MJ m - d -1 ] EMPEAUE, h mn of th imum nd th imum rcordd tmprtur. + Whr imum tmprtur [ C] imum tmprtur [ C] Adjut tmprtur of non-rfrnc climt ttion, whr dw i vilbl Climt ttion ud to mk obrvtion for rfrnc E o hould b urroundd by wll wtrd crop. A thi i not th c with mot climt ttion in BC. hrfor, th tmprtur hould b djutd uing th dw point tmprtur nd corrction fctor, K o. K o will b C for ll ttion inc th tmprtur will b tkn from nonrfrnc ttion.
2 Pg of 1 Δ - K o ( ( cor ob Δ - K o ( ( cor ob K o C K o 0 C if th non-rfrnc ttion i not comprd to rfrnc ttion Δ dw if Δ i clcultd uing rfrnc ttion dt Δ ( dw n/rf ( - dw rf dw cor ob imum dily tmprtur [ C] imum dily tmprtur [ C] dw point tmprtur [ C] corrctd vlu obrvd vlu VAPOU PESSUE DEFICI, VPD [kp] VPD ( xp SAUAED VAPOU PESSUE, [kp] Sturtd vpour prur i givn by howvr, whn clculting for 4 hour tim priod imum nd imum dily tmprtur hould b ud: + ( (
3 Pg 3 of xp xp ( ( Actul vpour prur whr dw i vilbl, [kp] 17.7 dw xp dw Actul vpour prur whr H i vilbl, [kp] H 100 mn + ( ( H mn mn rltiv humidity [%] Actul vpour prur whr only i vilbl, [kp] h qution um tht th dw point tmprtur ( dw i nr th imum tmprtur (. hi um tht t unri whn th ir i clo to, th ir i nrly turtd with wtr vpour nd rltiv humidity i nr 100%. hi umption hold for loction whr th covr crop i wll wtrd. For rid rgion th ir my not b turtd whn th tmprtur i. Subtrcting to 3 C from would bttr pproximt th vlu ud for in th qution. plc dw with ( - K o ( Ko xp ( Ko K o 0 C for humid nd ub-humid climt K o C for rid nd mi-rid climt. WIND SPEED Whr wind pd dt i vilbl, u [m/] Mtorologicl nmomtr rcord informtion t 10m from th ground urfc.
4 Pg 4 of 1 u u y 4.87 ln(67.8 y 5.4 Agromtrologicl nmomtr r loctd -3 m bov th ground. h wind informtion cn b djutd if th hight of th intrumnt i known. (FAO, p55-56 y hight of intrumnt bov ground [m] u y murd wind pd t y mtr bov ground lvl [m -1 ] u wind pd t m bov ground [m -1 ] Whr wind pd dt i not vilbl, u [m/] Whr wind dt in not vilbl, u vlu tht i grtr thn or qul to 0.5 m/ in th E o qution. h vrg worldwid vlu ud tmporry timt i m/. NE ADIAION, N [MJ M - D -1 ] n n nl n nt olr rdition [MJ m - d -1 ] nl nt long wv rdition [MJ m - d -1 ] Nt olr rdition, n [MJ m - d -1 ] ( 1 α n olr rdition [MJ m - d -1 ], ction blow α lbdo or cnopy rflction cofficint which i 0.3 for th hypothticl rfrnc crop. Solr dition if unhin hour, n, i not vilbl, [MJ m - d -1 ] (p60 Bcu th mount of rdition rching th rth i rflctd in th imum nd imum tmprtur th following qution cn b u to timt olr rdition. It i not pproprit to import rdition dt from othr ttion bcu to th diffrnc in xpour du to th mountinou nd cotl r. For ilnd condition uing only tmprtur to timt i not pproprit du to th ffct of th urrounding wtr body. K (
5 Pg 5 of 1 Solr rdition [MJ m - d -1 ], xtrtrrtril rdition [MJ m - d -1 ], ction blow K 0.16 for intrior loction 0.19 for cotl loction K Solr dition if unhin hour, n, i vilbl, [MJ m - d -1 ] (p50 n N n unhin hour rcordd [hour] xtr trrtril rdition, [MJ m - d -1 ] N vilbl durtion of unhin hour [hour] hr r lookup tbl rfrncd by month nd dgr ltitud (FAO 1998, p0 to dtr N. Intrpoltion of th tbl i rquird. Or clcult: 4 N ω π ω unt hour ngl, blow for complt clcultion [rd] xtr trrtril rdition, [MJ m - d -1 ] Extr trrtril rdition, [MJ m - d -1 ] U lookup tbl rfrncd by month nd dgr ltitud (FAO 1998p19, to dtr xtrtrrtril. Intrpoltion of th tbl i rquird. Or clcult: 4 60 G π c d r [ ω in( ϕin( δ + co( ϕco( δ in( ω ] G c 0.08 [MJ m - -1 ], olr contnt invr rltiv ditnc Erth-Sun d r π d r co J 365 ω unt hour ngl [rd] ω rcco [ tn( ϕ tn( δ ]
6 Pg 6 of 1 ϕ δ J ltitud [rd] π ϕ( rd lt( 180 olr dclintion [rd] π δ in J Julin dy J M int D 9 M month D dy (not: 4 x 60 x G c / (not: x 3.14/ Clr Sky Solr dition, o [MJ m - d -1 ] o 5 [ z] z lvtion of climt ttion bov lvl [m] Nt longwv rdition, nl [MJ m - d -1 ] nl ( ( ( σ 35 o Whr ll vribl r clcultd bov or known. σ 4.903x10-9 MJK -4 m - dy -1 SLOPE VAPOU PESSUE CUVE, Δ [KPA C -1 ]
7 Pg 7 of xp Δ 4098 ( mn tmprtur, [ C] PSYCHOMEIC CONSAN, γ [kp/ C] γ P P tmophric prur, [kp] z P z lvtion bov lvl, [m] SOIL HEA FLUX DENSIY, G Ignord for dily clcultion
8 Pg 8 of 1 POCEDUE FO CALCULAING E O USING FAO PENMAN- MONEIH WIH ONLY MINIMUM AND MAXIMUM EMPEAUE DAA EQUIED: Elvtion, mtr [m] Ltitud, dgr [ o ] Minimum mprtur, dgr Cliu [ C] Mximum mprtur, dgr Cliu [ C] Clifiction Cotl or Intrior Clifiction Arid of Humid Julin dy DAA ASSUMED O CONSANS: Wind pd m/ Albdo or cnopy rflction cofficint, α 0.3 Solr contnt, G c 0.08 MJ - -1 Intrior nd Cotl cofficint, K 0.16 for intrior loction 0.19 for cotl loction Humid nd rid rgion cofficint, K o 0 C for humid / ub-humid climt C for rid / mi-rid climt POCEDUE: 1. Clcult mn ir tmprtur, [ C] +. Clcult ctul vpour prur, [kp] U imum tmprtur nd djutmnt fctor dpnding on climt clifiction humid or mi-rid whr: 17.7 ( Ko xp ( Ko K o 0 C for humid nd ub-humid climt K o C for rid nd mi-rid climt Sttion r clifid cotl nd intrior, intrior ttion r conidrd mi-rid, whil cotl ttion r conidrd to b humid.
9 Pg 9 of 1 3. Clcult turtd vpour prur for, ( [kp] ( 17.7 xp Clcult turtd vpour prur for, ( [kp] ( xp Clcult turtd vpour prur, [kp] + whr: ( ( ( Stp 3 ( Stp 4 6. Clcult invr rltiv ditnc Erth-Sun, d r [rd] π d r co J 365 whr: J Julin dy 7. Convrt ltitud to rdin, ϕ [rd] π ϕ ( rd lt( 180 whr: lt ltitud of ttion in dgr 8. Clcult olr dclintion, δ [rd] π δ in J whr: J Julin dy
10 Pg 10 of 1 9. Clcult unt hour ngl, ω [rd] ω rcco whr: [ tn( ϕ tn( δ ] δ Stp 7 ϕ Stp Clcult xtrtrrtril rdition, [MJm - dy -1 ] 4 60 G π whr: c d r [ ω in( ϕ in( δ + co( ϕ co( δ in( ω ] d r Stp 6 ϕ Stp 7 δ Stp 8 ω Stp 9 G c olr contnt 0.08 MJm Clcult clr ky olr rdition, o [MJm - dy -1 ] o whr: 5 ( z Z lvtion of climt ttion bov lvl [m] Stp Clcult olr rdition, [MJm - dy -1 ] U djutmnt fctor K dpnding on ttion loction, cotl or intrior K whr: ( K 0.16 for intrior loction K 0.19 for cotl loction 13. Clcult nt longwv rdition, nl [MJm - dy -1 ] nl ( o 4 4 ( ( σ 35 whr: Stp Stp 1 o Stp 11 σ x 10-9 MJK -4 m - dy -1
11 Pg 11 of Clcult nt olr rdition, n [MJm - dy -1 ] ( 1 α n whr: Stp 1 α Clcult nt rdition, n [MJm - dy -1 ] n n nl whr: n Stp 14 nl Stp Clcult lop vpour prur, Δ [kp C -1 ] xp Δ ( Clcult tmophric prur, P [kp] z P whr: z lvtion bov lvl [m] 18. Clcult pychomtric contnt, γ [kp C -1 ] γ whr: P P Stp Clcult vpotrnpirtion, E o E o Δ n + γ u + 73 Δ + γ ( u (
12 Pg 1 of 1 POCEDUE FO CALCULAING EO USING FAO PENMAN- MONEIH WIH MINIMUM AND MAXIMUM EMPEAUE AND SUNSHINE HOUS DAA EQUIED: Elvtion, mtr [m] Ltitud, dgr [ o ] Minimum mprtur, dgr Cliu [ C] Mximum mprtur, dgr Cliu [ C] Sunhin hour, hour [hr] Clifiction Cotl or Intrior Clifiction Arid of Humid Julin dy DAA ASSUMED O CONSANS: Wind Spd m/ Albdo or cnopy rflction cofficint, α 0.3 Solr contnt, G c 0.08 MJ - -1 Humid nd rid rgion cofficint, K o 0 C for humid / ub-humid climt C for rid / mi-rid climt U th Sm Procdur out lind for Clculting E uing only tmprtur dt. Stp 1, th clcultion of olr rdition, with th following clcultion. 1. Clcult olr rdition, [MJm - dy -1 ] n N n unhin hour rcordd [hour] xtr trrtril rdition, [MJ m - d -1 ] N vilbl durtion of unhin hour [hour] hr r lookup tbl rfrncd by month nd dgr ltitud (FAO 1998, p0 to dtr N. Intrpoltion of th tbl i rquird. Or clcult: N 4 ω π ω unt hour ngl, blow for complt clcultion [rd] xtr trrtril rdition, [MJ m - d -1 ]
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