GEOG 402 SURFACE ENERGY FLUXES

Some Point of Confuion Net Rdition Incident t the Sufce R n = K ( 1α + ( 4 εl εσ K L Veg Lye αk εl 4 εσ Soil

Some Point of Confuion Veticl empetue Pofile

Some Point of Confuion Soil et Flux Upwd nd downwd conduction of enible het Diven by veticl tempetue gdient in oil Modulted by oil theml popetie Diection of gdient chnge ufce tempetue chnge K L αk εl 4 εσ G

Enegy, Cbon, nd Wte Sufce Enegy Blnce R n = K ( 1α + ( 4 εl εσ = + λe + G K L λe αs εl 4 εσ Note light diffeence in ymbol ued fo hotwve dition nd lbedo in the text: 4 R n = S ( 1 + ( εl εσ = + λe + G (Eq. 13.2 in Bonn, 2008 G

Enegy, Cbon, nd Wte Sufce Enegy Blnce R n = + λe + G K L λe αk εl 4 εσ G

Enegy, Cbon, nd Wte Sufce Enegy Blnce Ove 24-h peiod G = ~0 R n = + λ E λe R n Enegy Ptitioning

Globl Enegy Blnce

Regionl Enegy Blnce

Diunl Cycle

Enegy Blnce

Ltent et of Vpoiztion λ = 2.454 x 10 6 J kg -1 t 20ºC Exmple fom the book: ypicl umme evp. te: 5 mm pe dy Wte denity: 1000 kg m -3 5 mm = 5 kg pe que mete kg 1dy J 5 2454000 = m 2 dy 86400 kg 142 W m 2

Ltent et of Vpoiztion λ = 2.454 x 10 6 J kg -1 t 20ºC Anothe wy of tting the ltent het of vpoiztion: he mount of ltent het flux pe mm/dy of evp: λ = 28.36 W m -2 pe mm dy -1 Exmple: ( 5 mm pe dy: λe = 5 mm dy -1 x 28.36 W m -2 pe mm dy -1 = 141.8 W m -2 (b λe = 110 W m -2 : E = 110 W m -2 / 28.36 W m -2 pe mm dy -1 = 3.88 mm dy -1

Sufce Enegy Blnce Recll tht in it implet fom, the ufce enegy blnce cn be expeed : R = + n λe At the Me S ttion in nothen hilnd, R n veged 150 W m -2 duing unny peiod in Mch. Auming i poitive, λe mut be le thn 150 W m -2, i.e. E mut be le thn 5.3 mm dy -1

Sufce Enegy Blnce 900 800 700 600 500 hilnd: 25-y Secondy Vegettion Kd Rn 700 600 500 400 300 Bzil: Be Soil Kd Rn 400 E 300 200 100 0 G -100 0:00 4:00 8:00 12:00 16:00 20:00 0:00 200 100 0 G E -100 0:00 4:00 8:00 12:00 16:00 20:00 0:00

Men enegy fluxe. Sufce Enegy Blnce Site Kd Rn G λe dy ll + dy ll dy ll dy ll dy ll Bzil --------------------------------------------------- (W m -2 --------------------------------------------------- ( Slhed vegettion 463 251 280 142 7 0 25 11 240 126 (b Buned lh 409 221 216 107 21 5 26 10 169 91 (c Be oil 361 195 209 102 9-3 106 55 93 50 (dmtue cv 453 245 279 136 12-4 54 29 212 111 (e Unued ptue 526 288 314 157 5-1 142 73 166 85 (f 1/2 y. Secondy vegettion 453 245 --- --- 5 2 182 95 113 59 (g1-y Secondy Vegettion 452 245 269 129 26 3 140 71 102 54 (h1-y Secondy vegettion 489 264 309 154 8 2 180 88 120 64 (i 2-y Secondy vegettion 397 218 245 119 2-4 167 88 74 30 (j 2-y Secondy vegettion 409 225 246 122 2-5 189 103 47 21 (k10-y Secondy vegettion 422 228 273 134 2 0 145 75 126 59 hilnd (l veted bley 457 248 265 116 18 6 68 21 193 96 (m Fllow ice pddy 450 245 306 150 27 1 171 93 56 30 (n Iigted be oil 448 243 322 152 31 5 266 171 33-18 (o 2-y Secondy vegettion 252 137 162 72 2 0 155 90 19-8 (p 3-y Secondy vegettion 392 213 235 100 10 4 144 80 79 14 (q 8-y Secondy vegettion 454 246 318 136 0-3 313 158 7-18 ( 25-y Secondy vegettion 413 225 297 141 2 0 274 168 9-27 + Dy efe to 12-hou peiod 6:00-18:00

Men enegy fluxe. Sufce Enegy Blnce Site Rn G E dy ll dy ll dy ll dy ll hilnd (l veted bley 265 116 18 6 68 21 193 96 (m Fllow ice pddy 306 150 27 1 171 93 56 30 (n Iigted be oil 322 152 31 5 266 171 33-18 (o 2-y Secondy veg 162 72 2 0 155 90 19-8 (p 3-y Secondy veg 235 100 10 4 144 80 79 14 (q 8-y Secondy veg 318 136 0-3 313 158 7-18 ( 25-y Secondy veg 297 141 2 0 274 168 9-27 + Dy efe to 12-hou peiod 6:00-18:00

Sufce Enegy Blnce o include oil het flux effect on the diunl nd nnul cycle, the ufce enegy blnce cn be expeed : o: R = G + + λe n R G = + λe n

Bowen Rtio One wy to decibe the ptitioning of enegy between nd LE (me λe i by tking the tio (clled the Bowen Rtio: β = LE igh vlue of β indicte etiction on the evpotnpition poce, i.e. limited wte vilbility. Low vlue of β indicte uneticted evpotion, i.e. bundnce wte vilbility.

Bowen Rtio β = LE We ll ee lte tht the Bowen Rtio cn be independently etimted fom meuement of the veticl gdient of i tempetue nd humidity. With n independent etimte of β, nd meuement of Rn nd G, LE cn be etimted : LE = Rn G 1+ β

Bowen Rtio β = LE Aid egion e chcteized by high Bowen Rtio vlue, becue limited vilble wte etict evpotion. Wte bodie nd lnd e with bundnce pecipittion nd vegettion cove hve low Bowen Rtio vlue. β > 3 β < 0.5

Bowen Rtio (ß of Defoeted Site in Bzil nd hilnd ß = /LE Bowen Rtio. 10 9 8 7 6 5 4 3 2 1 0 ( Slhed vegettion (b Buned lh (c Be oil (d Mtue cv (e Unued ptue (f 1/2-y Secondy vegettion (g 1-y Secondy vegettion (h 1-y Secondy vegettion (i 2-y Secondy vegettion (j 2-y Secondy vegettion (k 10-y Secondy vegettion (l veted bley (m Fllow ice pddy (n Iigted be oil (o 2-y Secondy vegettion (p 3-y Secondy vegettion (q 8-y Secondy vegettion ( 25-y Secondy vegettion Bzil hilnd

Enegy Blnce Model R = G + J + + λe n Net Rdition Soil et Flux Biom nd Ai Lye et Stoge Flux Senible et Flux Ltent et Flux

Net Rdition (eveting now to the ymbol ued in the text R n = S ( ( 4 + ε L σ 1 Extenl Focing Vible Downwd hotwve dition Downwd longwve dition hee vible e time-dependent nd mut be obtined vi field meuement o climte model imultion.

Net Rdition R n = S ( ( 4 + ε L σ 1 Sufce Pmete nd Stte Vible Albedo (pmete Emiivity (pmete Sufce tempetue (tte vible Albedo nd emiivity depend minly on the type of ufce. he ufce tempetue i contolled by the enegy blnce.

Net Rdition R n = S ( ( 4 + ε L σ 1 Albedo Sufce Albedo Sufce Albedo Ntul Ubn Feh now 0.80-0.95 Rod 0.05-0.20 Old now 0.45-0.70 Roof 0.08-0.35 Deet 0.20-0.45 Wll 0.10-0.40 Glcie 0.20-0.40 Pint Soil 0.05-0.40 White 0.50-0.90 Coplnd 0.18-0.25 Red, bown, geen 0.20-0.35 Glnd 0.16-0.26 Blck 0.02-0.15 Deciduou foet 0.15-0.20 Conifeou foet 0.05-0.15 Wte 0.03-0.10

Net Rdition R n = S ( ( 4 + ε L σ 1 Emiivity (8-12 µm Sufce Ntul Ocen 0.99 Emiivity Feh now 0.986 Melting now 0.99 Deet 0.90 Dy pet oil 0.970 Wet pet oil 0.983 Dy fine nd 0.949 Wet fine nd 0.962 hick geen g 0.986 hin geen g on wet cly oil 0.975 Deciduou foet 0.950 Conifeou foet 0.970 Sufce Emiivity Ubn Aphlt 0.93 Concete 0.85 Roof 0.91 Pint 0.96

Net Rdition R n = S ( ( 4 + ε L σ 1 Sufce empetue he ufce tempetue could be deived fom field meuement o etimted uing n enegy blnce model.

Soil et Flux Field Meuement Appoch: G ΔCd S = t G = oil het flux t the ufce(w m G 8cm Δ C fc fc = G 8cm + S = oil het flux meued t 8 cm depth (W m = chnge in oil tempetue(k = het cpcity of the moit oil d = depth of oil lye (m t = time intevl ( -2-2 O: Model Simultion Appoch: d S = K = K dz whee : K = theml conductivity of the oil (W m d dz ufce z ufce = the veticl tempetuegdient in the oil = ufce tempetue(k = tempetue t depth z (K z = depth of oil lye (m z z -2 K -1

Biom Enegy Stoge Flux Field Meuement Appoch: hemocouple to meue tempetue chnge in biom nd i lye Meuement of humidity pofile Suvey of biom mount nd ditibution O: Model Simultion Appoch: Simulte tempetue gdient within tee tem nd othe plnt element Simulte veticl tempetue nd humidity pofile Etimte biom mount nd ditibution

Senible et Flux = ρc p ( ufce

Ltent et Flux λe = ρc γ p ( e e [ W ufce ]

Enegy Blnce Model: Linking It All ogethe R = + λe + n G G = K ufce z z λe ρc = γ p ( e e [ W ufce ] R n = S ( ( 4 + εl εσ 1 = ρc p ( ufce

( z K e e C C L S g W p p Δ + = + ] [ ( ( 1 4 γ ρ ρ εσ ε Eqution 13.13, Bonn, 2008, p. 202

S ( 1 + εl = εσ 4 ρc p ( ρc γ p (e e [ ] + W K Δz g he left ide of the eqution h the two extenl focing tem, bobed ol dition nd bobed longwve dition. he ight ide of the eqution h the ufce epone tem. Sufce empetue ( i key vible tht ppe in ll the tem on the ight ide of thi eqution. i detemined by the ufce enegy blnce nd tongly influence the ufce enegy blnce tem. epond to extenl focing to mintin enegy blnce. Fo given chnge in extenl focing, the necey chnge in will depend on ufce chcteitic.

( z K e e C C L S g W p p Δ + = + ] [ ( ( 1 4 γ ρ ρ εσ ε hi eqution cn be ued ufce enegy blnce model. But it cnnot be olved nlyticlly nd ome of the pmete nd vible my be difficult to meue o etimte.

G R E n = ( λ G E R n + + = λ ufce p C ( = ρ Eqution 13.14, Bonn, 2008, p. 202 p n n C G R G R E ( ( ( + = = ρ λ Enegy blnce eqution: Renge the enegy blnce eqution: Subtitute the eitnce fomul fo :

( ] [ ] [ * * e e + = W p e e C E ( ] [ ( * + = γ ρ λ Eqution 13.16, Bonn, 2008, p. 202 Stution vpo peue t the ufce tempetue cn be ppoximted : Whee i the lope of the tution vpo peue v tempetue cuve. Subtituting tht into the eitnce fomul fo λe: W ufce p e e C E ] [ ( = γ ρ λ Reult in:

( ( E G R C n p λ ρ = W p e e C E ( ] [ ( * + = γ ρ λ p n C G R E ( ( + = ρ λ Eq 13.16 Renging Eq. 13.14, we get: Subtituting thi expeion fo into Eq. 13.14, we get: Recll: Eq 13.14 ( ] [ ( ( * W p n e e C G R E γ ρ λ + + = he Penmn-Monteith Eqution (Monteith (1965 Eqution 13.18, Bonn, 2008, p. 202

( ] [ ( ( * W p n e e C G R E γ ρ λ + + = ( * W γ = γ Expeion fo nd cn lo be deived: he Penmn-Monteith Eqution (Monteith (1965 Eqution 13.18, Bonn, 2008, p. 202 * * * * * * ] [ ( ( ] [ ( ( γ ρ γ γ ρ γ + + = + + = e e C G R e e C G R p n p n Eqution 13.19, Bonn, 2008, p. 202 Eqution 13.20, Bonn, 2008, p. 203

Chpte 13 Review Quetion 1. Clculte oil wming te: Rnet 450 W/q m 350 W/q m LE 45 W/q m G 55 W/q m Cρd 1250000 J/(q m deg C d/dt 0.000044 deg C/ 0.1584 deg C/h Rnet 600 W/q m 475 W/q m LE 85 W/q m G 40 W/q m Cρd 1250000 J/(q m deg C d/dt 0.000032 deg C/ 0.1152 deg C/h

Chpte 13 Review Quetion 2. Diet nd wettet ite? Bowen tio:0.5, 1.0, 6.0 (diet, 1.5, 0.2 (wettet 3. Pecip nnul =800 mm Rnet nnul =70 Wm -2 Enegy o wte limit on evpotion? wte 4. Skip. 5. Pecip dily =8 mm Rnet nnul =120 Wm -2 Enegy o wte limit on evpotion? enegy

Chpte 13 Review Quetion 6. Fig. 13.7: Why i the LE/Rnet lope gete fo topicl infoet thn glnd? E i limited t glnd ite becue of lowe oughne, lowe lef e, hllowe oot, lowe wte vilbility. Do poblem 7, 8, nd 9 t home.