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Com putation of day-tim e atm osph eric turbulent ... · Procedure Com putation of day-tim e atm...
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Proce dure Com putation ofday-tim e atm os ph e ric turbul e ntdiffus ivity ove r com pl e x te rrain Sum m ary A m eth od for th e cal cul ation ofatm os ph e ric turbul e ntdiffus ivity ove r com pl e x te rrain during day-tim e h as be e n de ve l ope d. Th e m ode l is inte nde d for us e in diagnos tic m e te orol ogical m ode l s th atus e h e atfl ux atground l eve l for th e e s tim ate ofth e param e te rs ch aracte rizing atm os ph e ric turbul e nce . Cal cul ation is carrie d outus ing ge ograph ic pos ition and tim e ofth e day, butal s o orograph ic factor, w h ich is ofte n ne gl e cte d. Inde e d s h adow s ge ne rate d from m ountain profil e s produce an e ffe cton th e h e ating ofth e air m as s al ong the vall e y fl oor, w h ich m ay be s ubs tantiall y diffe re ntfrom th e cas e offl atuniform te rrain. Th e propos e d m e th od tak e s into accountth e ge ograph ic l ocation ofth e are a (l atitude and l ongitude ), th e tim e ofth e day, th e incl ination ofth e s urface and its e xpos ition, th e s oil type , th e cl oud cove rage . Th e s urface e ne rgy bal ance is cl os e d us ing diffe re ntwe ll k nown form ul ations in te rm s ofl ocal val ue s ofparam e te rs (e .g. H ol ts l ag and Van Ul de n, 19 83). Th e m ode l al s o tak e s into accountth e variabil ity ofal be do coe fficie ntw ith th e incl ination ofs ol ar be am s upon day h ours . Model cal ibration Gianl uca Antonacci (gianl uca.antonacci@ cis m a.bz .it) - CISM A (Ital y) & Marco Tubino (m arco.tubino@ ing.unitn.it) - De partm e ntofCivil and Environm e ntal Engine e ring, Unive rs ity ofTre nto (Ital y) Form ul ation Com parison w ith radiom e te rs'data A case study: th e Adige Vall e y (Ital y) Inputdata - Digital el e vation m ode l (DEM) ofth e are a - Land us e cate gorie s or re fl e ction coe fficie nts , ifavail abl e - Cl oud cove r (fraction ofcove re d s k y) - Gl obal Radiation [W /m 2 ]atground l eve l m e as ure d by one or m ore w e ath e r s tations (onl y for cal ibration). O utputdata (on th e w h ol e dom ain) Gl obal Radiation [W /m 2 ] Se ns ibl e h e atfl ux [W /m 2 ] Ve rtical diffus ivity coe fficie ntata re fe re nce h e igh tz [m 2 /s ] L istof sym bol s Q g = gl obal s ol ar radiation atground l eve l [W /m 2 ] Q g ' = gl obal s ol ar radiation corre cte d w ith l ocal te rrain e xpos ition to s ol ar be am s [W /m 2 ] Q * = ne ts ol ar radiation atground l eve l [W /m 2 ] f= s ol ar e l e vation angl e [°] l = s ol ar azim uth angl e [°] Q h = s e ns ibl e h e atfl ux atground l eve l [W /m 2 ] z = z /L s tabil ty param e te r [-] K z = ve rtical diffus ivity coe fficie ntatground l eve l [m 2 /s ] Tr = gl obal tras m is s ivity ofth e atm os ph e re [-] E = e xtrate rre s trial s ol ar irradiance atth e top ofth e atm os ph e re [W /m 2 ] d = jul ian day (1 .. 365) B = Bow e n ratio [-] F = s tabil ity function Y = s im il arity function L = Monin - Obuk h ov l e ngth [m ] l t = l ocal te rrain e xpos ition [°] f t = l ocal te rrain incl ination [°] T = te m pe rature [K] a = al be do [-] a' = al be do corrre cte d w ith s ol ar e l e vation [-] f= e arth orbite ll ipticity corre ction function S 0 = s ol ar cons tant(~1350 W /m 2 ) N = cl oud cove rage (fraction ofcove re d s k y) c 1 , c 2 , c 3 , c 4 : cons tants De scription Two e ffe cts are tak e n into cons ide ration: 1) Sh adow e d are as are cons ide re d as not contributing to th e h e ating of th e air m as s above th e ground l eve l ; diffe re nt points l ying on th e oppos ite s ide s of a vall ey show a tim e s h iftin diurnal radiation cycl e . For e ach pointofth e DEM th e m ode l ch e ck s ifitis s h adow e d by s om e oth e r point of th e dom ain, at a give n date and h our. Th is ch e ck is carrie d out ve rifying if th e l ine s s tarting from th e ground and h aving th e s ol ar incl ination inte rce pts om e h igh e r pointbe l onging to th e dom ain [3]. Sol ar e l e vation and azim uth de pe nd on l atitude , l ongitude , date and tim e ofth e day 2) Th e l ocal incl ination ofth e te rrain w ith re s pe ctto s ol ar be am s im pl ie s a s patial variation of e ne rgy fl ux at ground l e ve l. Th e ve ry im portant point is th at a corre ction for th e re l ative angl e be tw e e n th e s ol ar be am s and th e ground is com pute d at e ach point of th e digital el e vation m ode l (e q . 3). As a cons e q ue nce th e dis tribution of gl obal radiation is no m ore cos tant ove r th e dom ain, but varie s , at a give n tim e , de pe nding on th e l ocal e xpos ition. Th e s patial dis tribution of ne t radiation, s e ns ibl e h e atfl ux and turbul e ntdiffus ivity vary accordingl y. Point1: S. Mich e l e (radiom e te r + m ode l ) Point2: Tre nto airport(radiom e te r + m ode l ) Point3: W e s ts ide ofth e Adige Vall e y (m ode l ) Point4: ce nte r ofth e Adige Vall e y (m ode l ) Point5: Eas ts ide ofth e Adige Vall e y (m ode l ) 1. Cal cul ation ofe xtratte rre s trial irradiance [1] with : 2. Cal cul ation ofgl obal s ol ar radiation atground l eve l [5] with : 3. Corre ction ofs ol ar radiation w ith e xpos ition to th e s un;ifa pointis 5. Cal cul ation ofgl obal ne tradiation atground l eve l [3] 6. Cal cul ation ofs e ns ibl e h e atfl ux [4] 7. Ite rative cal cul ation of s tabil ity param e te rs [1] 8. Cal cul ation ofve rtical turbul e ntdiffus ivity ata re fe re nce h e igh t[6] with : Ave rage l atitude ofth e dom ain: 46 °N Ave rage l ongitude ofth e dom ain: 11° E Dim e ns ion: 10 x 20 k m Cell re s ol ution for com putation: 100 m Th e cal ibration of th e m ode lw as carrie d out by de te rm ining th e param e te rs of e q uation (3) for th e tras m is s ivity of atm os ph e re . Th e be st fitting val ues where a 1 =0.59 , a 2 =0.20, a 3 =0.47, w h ich are ve ry s im il ar to th e one s found in l ite rature [1, 6]. s h adow e d, a null val ue is as s igne d to Q g for th atl ocation Tim e s h iftdue to diffe re nt l ocation ofpoints cl oudy day s unny day 4. Corre ction ofth e al be do w ith s ol ar incl ination angl e [7]
Transcript of Com putation of day-tim e atm osph eric turbulent ... · Procedure Com putation of day-tim e atm...
Proce dure
Com putation of day-tim e atm os ph e ric turbule nt diffus ivity ove r com ple x te rrain
Sum m aryA m e th od for th e calculation of atm os ph e ric turbule nt diffus ivity ove r com ple x te rrain during day-tim e h as be e n de ve lope d. Th e m ode l is inte nde d for us e in diagnos tic m e te orological m ode ls th at us e h e at flux at ground le ve l for th e e s tim ate of th e param e te rs ch aracte riz ing atm os ph e ric turbule nce . Calculation is carrie d out us ing ge ograph ic pos ition and tim e of th e day, but als o orograph ic factor, w h ich is ofte n ne gle cte d. Inde e d s h adow s ge ne rate d from m ountain profile s produce an e ffe ct on th e h e ating of th e air m as s along th e valle y floor, w h ich m ay be s ubs tantially diffe re nt from th e cas e of flat uniform te rrain. Th e propos e d m e th od tak e s into account th e ge ograph ic location of th e are a (latitude and longitude ), th e tim e of th e day, th e inclination of th e s urface and its e xpos ition, th e s oil type , th e cloud cove rage . Th e s urface e ne rgy balance is clos e d us ing diffe re nt w e ll k now n form ulations in te rm s of local value s of param e te rs (e .g. H olts lag and Van Ulde n, 19 83). Th e m ode l als o tak e s into account th e variability of albe do coe fficie nt w ith th e inclination of s olar be am s upon day h ours .
Mode l calibration
Gianluca Antonacci (gianluca.antonacci@ cis m a.bz .it) - CISMA (Italy)&
Marco Tubino (m arco.tubino@ ing.unitn.it) - De partm e nt of Civil and Environm e ntal Engine e ring, Unive rs ity of Tre nto (Italy)
Form ulation
Com parison w ith radiom e te rs' data
A case study: th e Adige Valle y (Italy)
Input data- Digital e le vation m ode l (DEM) of th e are a- Land us e cate gorie s or re fle ction coe fficie nts , if available- Cloud cove r (fraction of cove re d s k y)- Global Radiation [W /m 2] at ground le ve l m e as ure d by one or m ore w e ath e r s tations (only for calibration).
O utput data (on th e w h ole dom ain)� Global Radiation [W /m 2]� Se ns ible h e at flux [W /m 2]� Ve rtical diffus ivity coe fficie nt at a re fe re nce h e igh t z [m 2/s ]
List of sym bolsQg = global s olar radiation at ground le ve l [W /m 2]Qg' = global s olar radiation corre cte d w ith local te rrain e xpos ition to s olar be am s [W /m 2]Q* = ne t s olar radiation at ground le ve l [W /m 2]f = s olar e le vation angle [°]l = s olar azim uth angle [°]Qh = s e ns ible h e at flux at ground le ve l [W /m 2]z = z/L s tabilty param e te r [-]K z = ve rtical diffus ivity coe fficie nt at ground le ve l [m 2/s ]Tr = global tras m is s ivity of th e atm os ph e re [-]E = e xtrate rre s trial s olar irradiance at th e top of th e atm os ph e re [W /m 2]d = julian day (1 .. 365) B = Bow e n ratio [-]F = s tability functionY = s im ilarity functionL = Monin - Obuk h ov le ngth [m ]lt = local te rrain e xpos ition [°]ft= local te rrain inclination [°]T = te m pe rature [K]a = albe do [-]a' = albe do corrre cte d w ith s olar e le vation [-]f = e arth orbit e llipticity corre ction functionS0 = s olar cons tant (~1350 W /m 2)N = cloud cove rage (fraction of cove re d s k y)c1, c2, c3, c4: cons tants
De scriptionTw o e ffe cts are tak e n into cons ide ration:1) Sh adow e d are as are cons ide re d as not contributing to th e h e ating of th e air m as s above th e ground le ve l; diffe re nt points lying on th e oppos ite s ide s of a valle y s h ow a tim e s h ift in diurnal radiation cycle . For e ach point of th e DEM th e m ode l ch e ck s if it is s h adow e d by s om e oth e r point of th e dom ain, at a give n date and h our. Th is ch e ck is carrie d out ve rifying if th e line s s tarting from th e ground and h aving th e s olar inclination inte rce pt s om e h igh e r point be longing to th e dom ain [3].
Solar e le vation and az im uth de pe nd on latitude , longitude , date and tim e of th e day
2) Th e local inclination of th e te rrain w ith re s pe ct to s olar be am s im plie s a s patial variation of e ne rgy flux at ground le ve l . Th e ve ry im portant point is th at a corre ction for th e re lative angle be tw e e n th e s olar be am s and th e ground is com pute d at e ach point of th e digital e le vation m ode l (e q . 3). As a cons e q ue nce th e dis tribution of global radiation is no m ore cos tant ove r th e dom ain, but varie s , at a give n tim e , de pe nding on th e local e xpos ition. Th e s patial dis tribution of ne t radiation, s e ns ible h e at flux and turbule nt diffus ivity vary accordingly.
Point 1: S. Mich e le (radiom e te r + m ode l)Point 2: Tre nto airport (radiom e te r + m ode l)
Point 3: W e s t s ide of th e Adige Valle y (m ode l)Point 4: ce nte r of th e Adige Valle y (m ode l)
Point 5: Eas t s ide of th e Adige Valle y (m ode l)
1. Calculation of e xtratte rre s trial irradiance [1]
w ith :
2. Calculation of global s olar radiation at ground le ve l [5]
w ith :
3. Corre ction of s olar radiation w ith e xpos ition to th e s un; if a point is
5. Calculation of global ne t radiation at ground le ve l [3]
6. Calculation of s e ns ible h e at flux [4] 7. Ite rative calculation of s tability param e te rs [1]
8. Calculation of ve rtical turbule nt diffus ivity at a re fe re nce h e igh t [6]
w ith :
Ave rage latitude of th e dom ain: 46 °NAve rage longitude of th e dom ain: 11° EDim e ns ion: 10 x 20 k mCe ll re s olution for com putation: 100 m
Th e calibration of th e m ode l w as carrie d out by de te rm ining th e param e te rs of e q uation (3) for th e tras m is s ivity of atm os ph e re . Th e be s t fitting value s w h e re a1=0.59 , a2=0.20, a3=0.47, w h ich are ve ry s im ilar to th e one s found in lite rature [1, 6].
s h adow e d, a null value is as s igne d to Qg forth at location
Tim e s h ift due
to diffe re nt
location of points
cloudy day
s unny day
4. Corre ction of th e albe do w ith s olar inclination angle [7]
Re sults (application to th e Adige Valle y)
DiscussionW e can obs e rve th at th e m ajor diffe re nce s due to th e introdution of th e com ple x te rrain m odule m os tly occur at m orning and in late afte rnoon. Th e propos e d proce dure can le ad to an im prove m e nt of diagnos tic m e te orological m ode ls and dis pe rs ion m ode ls : in fact th e pre s e nce of s h adow e d and not s h adow e d zone s de te rm ine s local conve ctive circulations and m odifie s th e local e ne rgy balance of th e air above th e valle y floor and le ad to turbule nt diffus ivitie s w h ich m ay attain value s up to 3-4 tim e s large r at ground le ve l.
Bibliograph y[1] R. Sozz i, T. Ge orgiadis , M. Vale ntini, Introduzione alla turbole nza atm osfe rica, e d. Pitagora, 2002 [2] K.J. Allw ine , C.D. W h ite m an, Extrate rre strial solar radiation on incline d surface s, Environm e ntal Softw are , vol. I, pp. 164-169 , 19 86 [3] A.A. H olts lag, A.P. Van Ulde n, A sim ple sch e m e for daytim e e stim ate s of th e surface fluxe s from routine w e ath e r data, J. Clim . Appl.. Me te or., vol. 22, pp. 517-529 , 19 83[4] J. S.Scire , F.R. Robe , M.E. Fe rnau, R.J. Yam artino, A Use r's Guide for th e CALMET M e toroloigical Mode l, Earth Te ch Inc., 19 9 9[5] W . Bruts ae rt, Evaporation into th e atm osph e re : th e ory, h istory and applications, D. Re ide l Publis h ing Com pany, 19 84[6] B.R. Stull, An Introduction to Boundary Laye r M e te orology, Kluw e r Acade m ic Publis h e rs , 19 89[7] G.W . Paltridge , C.M. Platt, Radiative proce sse s in m e te orology and clim atology, Els e vie r, 19 76
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w ith out com ple x te rrain m ode l
(Qg = cons tant ove r dom ain)
w ith com ple x te rrain m ode l
Q h [W /m 2]
Qg' [W /m 2] Q h [W /m 2]
Qg' [W /m 2]Qg' [W /m 2]
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w ith out com ple x te rrain m ode l
(Qg = cons tant ove r dom ain)
w ith com ple xte rrain m ode l
t=17:0015-08-2002
w ith out com ple x te rrain m ode l
(Qg = cons tant ove r dom ain)
w ith com ple xte rrain m ode l
Q h [W /m 2]K z [m 2/s ] | z=3 m
K z [m 2/s ] | z=3 m
K z [m 2/s ] | z=3 m
Th e introduction of th e com ple x te rrain adjus tm e nt de te rm ine s a ch ange in th e s h ape and a tim e s h ift of th e s e ns ible h e at flux cycle and of th e diffus ivity function. W h e n th e com ple x te rrain corre ction is not us e d th e re m ay s till be a diffe re nce in th e daily e volution of s e ns ible h e at flux (s e e points 3 and 4), but it is only due to th e s patial variation of th e albe do coe fficie nt, th at is of diffe re nt land us e cate gorie s .
Th e tim e s h ift of th e diffus ivity K z is ve ry cle ar and de pe nds on th e diffe re nt location in th e valle y, as for th e oth e r q uantitie s (Qg, Q'* and Qh ).
In th e pre s e nt s tudy a value of z=3m w as us e d as th e re fe re nce h e igh t for calculating K z.
