Chapter 3: Radiation in Common Land Model

Transcription

1 1 Sep Chapter 3: Radiation in Common Land Model 1. Introduction Radiation is enery transfer in space by means of electro-manetic waes, the mechanism which doesn t inole mass transfer (in contrast to other forms of enery transport, conection and conduction). The physical properties of radiation hihly depend on the waelenth: isible, infrared, thermal, radio, etc. The objectie of this chapter is to describe how shortwae (isible and infrared) and lonwae (thermal) radiation are presented in the Common Land Model (CLM, cf. Tech Notes)- Land boundary layer model for the General Circulation Model (GCM), which simulates climate in the Earth System. CLM identifies two components in the Land boundary layer: eetation canopy (denoted by V in the followin) round surface (denoted by G) Veetation is represented by its two sub-components: Photosynthesizin eetation (reen leaes). Its density is characterized by LAI- Leaf Area Index- one-sided reen leaf area per unit round area in broadleaf canopies and as the projected needle leaf area in the coniferous canopies Non-Photosynthesizin eetation (stems, branches and twis, senescent eetation). Its density is characterized by SAI- Stem Area Index- area of stems, senescent eetation, per unit round area. Ground is represented by its two sub-components: Soil (soil itself, laciers, frozen/unfrozen lakes and wetlands) Snow CLM models two components of the radiation fluxes, which interacts with eetation and round: shortwae (solar) and lonwae (terrestrial). The Net radiation flux (cf. Fi. 3.1) is: NET NET ( A + A )( L L ) Net radiation +, where A V and A G are shortwae (solar) enery fluxes absorbed by eetation and round, and NET NET L V and L G are net (flux OUT- flux IN) lonwae (terrestrial) radiation at eetation and round G V G Veetation A V NET L V Fiure 3.1: Net radiation in CLM. Ground A G L N G

2 2 2. Shortwae Fluxes 2.A. BACKGROUND Def: Radiation Flux, (F) - amount of enery propaatin throuh spatial location per unit area and per unit time, [Wm -2 ]. Def: Radiation Intensity in a ien ection, ) - radiation flux per unit solid anle, propaatin throuh spatial location in a ien ection per unit projected area in that ection, [Wm -2 Sr -1 ]. Fiure 3.2: Radiation Intensity ection df - flux inside d d - solid anle alon ection 1 / cos( ) - projected unit area df I(r, ") # radiation intensity at spatial location r, in ection (Fi. 3.2) d" cos( ) Solid anle, d # sin( ")d" d ( - zenith, - azimuth) (whole sphere), % + 2" & " 2# + 2 and F I(r, #) cos( $ ) d# - flux up (Fi. 3.3) F I(r, $ ) cos( %) d$ - flux down (Fi. 3.3) 2 " (upper and lower hemispheres, respectiely) + 2 F Fiure 3.3: Enery fluxes up and down F 2 "

3 3 2.B. VEGETATION AND GROUND FLUXES Interaction of shortwae radiation with eetation and underlyin round is described with Radiatie Transfer (RT) theory. Detailed modelin of radiation intensity in heteroeneous eetation is accomplished with 3-D equation. Such leel of details is unrealistic to implement at the lobal scale, and CLM ealuates only hemispherically interated fluxes with two-stream model, as will be described in Section 3. In this section we introduce two-stream fluxes: reflected, absorbed and transmitted fluxes. Estimation of those fluxes is needed to ealuate CLM s key ariables: canopy albedo, Fraction of Photosynthetically Actie Radiation absorbed by eetation (FPAR), and soil forcin fluxes. Direct Incomin Radiation Diffuse Incomin Radiation I R ) I R ) Veetation A V ) Veetation A V ) T ) T ) T ) Ground A Ground G ) AG ) Fiure 3.: CLM modelin of shortwae enery fluxes for ect and fuse incomin radiation. Refer to Fi. 3. for the followin discussion about enery fluxes. The notations are as follows: I and I - incomin ect and fuse solar flux, R ) and R ) - reflected fuse flux due to input I and I, A V ) and A V ) - eetation absorptance due to input I and I, A G ) and A G ) - round absorptance due to input I and I, T ), T ), T ) - transmitted ect and fuse fluxes due to input I and I, and - round albedos for ect and fuse fluxes.

4 Accordin to Fi. 3., the incomin ect radiation is partitioned into ect and fuse fluxes after enterin eetation. Diffuse component arises due to scatterin of ect incomin beam by eetation elements. In eneral, the incomin flux inside of canopy can be reflected upward, transmitted downward (two components of scatterin) or absorbed by eetation. Portion of the flux, transmitted to the bottom of canopy, will be absorbed by round. Upward flux at the top of canopy is due to reflectance by canopy and round and has only fuse component. Similar processes occur for fuse incomin radiation, with the only ference is that fluxes inside of eetation hae no ect component. Independently from the type of incomin radiation the followin enery conseration law is alid: I R + A V + A G, (1) or A V I R A G, (2) where I - incomin solar enery flux, R - reflected flux, A V - absorptance of eetation, and A G - absorptance of round The specific formulas for R, T, and A appearin in the CLM scheme for shortwae radiation (Fi. 3.) are deried usin a two-stream approximation (cf. Section 3). The two-stream Radiatie Transfer (RT) model soles for upward and downward fluxes, and thus establishes formulas for transmitted and reflected radiation (R and T). Absorptance is calculated from the enery conseration law (Eq. 2). 2.C. VEGETATION AND GROUND ABSORPTANCES In this section we derie absorptance of eetation and round (A V and A G ) from enery conseration law for ect and fuse incomin fluxes, and, eneralize deriations for the arbitrary incomin flux. Below we assume that the incomin, transmitted and reflected fluxes, T, and R) are know (cf. Section 3). Unit Direct Incomin Radiation Referencin Fi. 3. and takin into account enery conseration law (Eq. 2) we can specify eetation and round absorptances (A V and A G ) for unit ect illumination 1), [ 1# " ] T ) + [ 1# " ] T ) A G ), A V ) 1 R ) A G ).

5 5 Unit Diffuse Incomin Radiation Calculations for unit fuse illumination 1) are similar: Arbitrary Incomin Radiation [ 1# " ] T ) A G ), A V ) 1 R ) A G ). Now we consider enery conseration law for arbitrary incomin flux which consist of ect 1), and fuse components 1). We assume that II +I 1, thus I and I can be thouht as weihts. The eetation and round absorptance (A V and A G ) in the eneral case of illumination conditions are calculated as weihted aerae of those quantities for ect and fuse illumination, A V I A V ) + I A V ) A G I # (1 " ) # T ) + [ I # T ) + I # T )]# (1 " ). Consider special case of no eetation. In this case, A V 0, [ I # 0 + I # 1] # (1 " ) A G I # (1 " ) # 1+ Accordin to enery conseration law, Eq. (1), I # (1 " ) + I # (1 " ). I R + A + A, Therefore, in the eneral case of ect and fuse incomin radiation, V V [ I R ) + I R )] + A V A G I + I +. G

6 6 Sep Two-Stream Radiatie Transfer Modelin 3.A. BACKGROUND In preious section we discussed CLM s radiatie transfer fluxes at the boundary of eetation. Gien fluxes enterin eetation (downward incomin radiation) and exitin eetation (transmitted and reflected fluxes) we calculated absorptance of eetation and round. While the incomin flux is ien, the exitin fluxes need to be calculated. To ealuate the unknown exitin fluxes, CLM sets up RT two-stream equation to sole for downward and upward fluxes inside of canopy. The upward flux at the top of canopy ies canopy reflectances, while downward flux at the bottom of canopy ies transmittance. The two-stream equations are deried from radiatie transport equation for ectional intensity ( I () ), by interation such equation oer upper and lower hemisphere resultin in equation for upward ( F ) and downward ( F ) fluxes, F % I( #) cos( $ ) d#, + 2" F & I( $ ) cos( %) d$. " 2# To derie specific form of two-stream equations one should specify assumptions/ approximations. Simplest ersion of two-stream equations is for horizontal leaes: ' F (L) & " F % (L) + ( $ # 1) " F (L), (3) ' L ' # F (L) & " F % (L) + ( $ # 1) " F (L), ' L and boundary conditions (as specified by incomin flux at the top and round albedos at the bottom): F (L 0) F + F F # (L L total ) " F, where: F (L) and F (L) - total radiation fluxes up and down (ect+fuse) L - leaf area index - a round albedo - leaf reflectance (Fi. 3.6) - leaf transmittance (Fi.3.6)

7 7 Note, durin interaction of photon with leaf, photon can be absorbed with probability a or scattered with probability. The photon scatterin includes reflectance with probability and transmittance with probability. Accordin to enery conseration law: a + 1, and $ # " +, a + " + 1. () Leaf transmittance, reflectance and absorptance are shown at Fi. (3.6) transmittance 0.2 Reflectance absorptance Transmittance Fiure 3.6: Typical spectra of leaf transmittance and reflectance from field measurements reflectance Waelenth, nm Physical meanin of the two-stream equations (Eq. 3) is as follows (cf. Fi. 3.7). Consider the first equation. Chanes in the downward flux at particular canopy layer (L+S) are due to downward scatterin ( ) of the upward flux (the ain term) and attenuation of the downward flux, caused by reflectance and absorbtance ( a + # 1" ) (loss term). Similar meanin has the second equation. F ( # " 1) F "F F absorbed reflected reflected Leaf absorbed Layer L+S Veetation "F (# " 1) F Ground Fiure 3.7: Physical processes underlyin the two-stream equation. Downward Flux is attenuated due to absorptance and reflectance ( " ( a + %)F $ (# " 1) F ) and enhanced due to reflectance of the Upward Flux ( "F ). Similar processes are applicable to the upward flux

8 8 3.B. CLM S TWO-STREAM MODEL CLM implements a more sophisticated ersion of the two stream equation, compared to the simple ersion for horizontal leaes presented in Section 3A. Namely, CLM equation accounts for ferent types of leaf orientation, eometric effects caused by sunlit and shaded areas, reen photosynthesizin s. non eetation and realistic boundary conditions at canopy bottom (snow, ice, soil, etc). CLM formulates separate equations for ect and fuse fluxes and proides solutions for upward ( F ) and downward ( F ) fluxes in each case (cf. Fi. 3.). Equation for Direct Fluxes The ect fluxes arise in the case of ect illumination. While propaatin throuh eetation, some portion of the input ect flux is scattered (conerted to the fuse flux), while the rest remains unsacttered (ect flux). There is only downward ect flux F : (the upward flux oriinates only after scatterin of ect downward flux, and thus this is a fuse flux). The equation and correspondin boundary conditions are simple: $ F (L + S) # K " F (L + S), F (L + S 0) I 1, (5) $ (L + S) where L is LAI and S is SAI (cf. Section 1). K is a coefficient, describin extinction of solar enery, G( µ ) K 1", µ where G is a mean projection of leaf normals in ection, µ cos( ), is a leaf albedo. The solution of Eq. (5) is simply a Beer s law for canopy transmittance for the attenuation of ect solar radiation: F ( K(L + S) ) ) " exp. (6) Equation for Diffuse Fluxes The fuse fluxes arise due to 1) fuse illumination and/or 2) due to scatterin of ect flux. The CLMs two-stream equations for fuse fluxes were oriinally introduced by Dickinson (1983) for its BATS land model and the analytical solution was deried by Sellers (1985). The equations are as follows: ' µ F % (L) $# F & "[1 " (1 " #) $ ] F % (L) + $ µ K (1 " # 0 ) exp( " K (L + S)), '(L + S) source term due to ect beam ' " µ F % (L) $# F & "[1 " (1 " #) $ ] F % (L) + $ µ K # 0 exp( " K (L + S)), (7) '(L + S) source term due to ect beam

9 9 and boundary conditions (as specified by incomin flux at the top and round albedos at the bottom): F (L + S 0) F F # (L + S L + S ) " F total total, where: F (L) and F (L) - fuse radiation fluxes up and down per unit incident flux L and S - Leaf Area Index (LAI) and Stem Area Index (SAI) K G / µ - optical depth of ect beam per unit L+S µ cos( ) G () - mean projection of leaf normals in ection. µ - aerae inerse optical depth (K) per unit L+S - effectie albedo of scatterin elements (leaes, stems, and snow). Note for eetation elements albedo includes not only reflectance component but also transmittance and 0 - upscatter parameters for fuse and ect radiation, respectiely. Those parameters are used as coefficients for to account for complex effects of scatterin is a round albedo Note, that CLM s two-stream equations hae a structure similar to that of two-stream equation for horizontal leaes (Eq. (3)). The ference is due to the fact that Eq. (7) is formulated for fuse radiation only, where enery source comes not only from fusion incomin radiation, but also due to scatterin of ect radiation (Eq. (6)) as shown in Fi. 3.. Physical meanin of CLMs two-stream equation (Eq.7) is similar to two-stream equation for horizontal leaes (Eq. 3): Chanes in the downward fuse flux are due to downward scatterin of upward fuse flux (the ain term) and attenuation of the downward fuse flux caused by reflectance and absorptance (loss term) and due to downward scatterin of the ect radiation (ain term). Optical Parameters Next we describe optical parameters of the CLM s two-stream accordin to Sellers (1985). Mean projection of leaes normals in ection : where G ( µ ) a + b µ, a 0.5 # 0.633" # 0.33", b " (1 2a), 2 and is the deiation of leaf anles from a random distribution:

10 10 $ + 1 for horizontal leaes & # 0 for randoml leaes "% 1 for ertical leaes Note that CLM can simulate any cases of leaf normal orientations in between aboe extremes. Aerae inerse optical depth is ien by: µ 1 & a, a + b )# µ. / dµ µ $ - * ' µ / d 1 ln K( ) G( µ ) b % b + a (" 0 Leaf and Stem optical properties are specified separately in CLM (cf. Table 1). 0 # " leaf leaf stem stem leaf leaf stem stem VIS " NIR " VIS " NIR VIS NIR VIS NIR Table 3.1: Optical properties of ferent eetation types (Plant Functional Types) in CLM.

11 11 Leaf (stem) optical properties are characterized by leaf (stem) reflectance, leaf leaf stem ( ), and leaf (stem) transmittance, ( stem ), respectiely. Veetation optical properties are characterized by weihed aerae of leaf and stem optical properties where e leaf leaf stem stem w + w, e leaf leaf stem stem w + w, L w leaf L + S w stem S L + S Gien transmittance and reflectances of eetated elements, its albedo is defined as, e e e # " +. CLM describes complex scatterin effects, which can not be accounted for by usin only effectie albedo,. Instead, upscatterin term,, is used toether with. In the case of eetation only, upscatterin coefficient can be specified as follows. The upscatterin coefficient for fuse radiation is defined as: 2 e 1 e 1 & $ 0 2 $ % e +. e + ( 0 e /. e, 1+ - )* ) ' ( #. " Consider special case of horizontal leaes. In this case 1, and $ #", # 1 " (1 " &) % $ 1" (1 " ) % $ 1" $ + # 1". $ Therefore CLM s two-stream (Eq.7) become identical with Eq. (3) for horizontal leaes. This proides additional means to understand meanin of the upscatterin coefficients- as they were introduced to account for more complex features of radiation scatterin, arisin due to arbitrary orientation of leaf normal compared to simple case of horizontal leaes with sinle ection of orientation of leaf normals. The upscatterin coefficient for ect radiation is defined as: e e e 1+ µ K " µ G( µ ) " # 0 µ µ $ d. K 2 µ G ( µ ) + µ G( µ ) 1 0

12 12 Boundary Conditions at the Ground Ground surface below eetation may sinificantly influence radiatie transfer processes, especially for the sparse eetation. CLM discriminates between two components of the round: Soil (laciers, frozen/unfrozen lakes and wetlands, soil) Snow Key round ariable for the purpose of modelin shortwae fluxes is albedo, as it seres to specify boundary conditions for the two-stream model. CLM models albedo as function of: Ground type (soil and snow) Illumination condition (ect and fuse) Waelenth (VIS and NIR) Total round ect ( ) and fuse ( ) albedos are modeled in CLM as a weihted combination of soil and snow albedos, soil snow snow # (") # (") (1 $ f ) + # (") f, soil snow snow snow # (") # (") (1 $ f ) + # (") f, snow where is a waelenth. Coefficient f snow is the fraction of the round coered with snow, f snow zsnow 10 z + z. 0 snow Aboe, z snow is the depth of snow (in meters), z [m] is the momentum rouhness lenth for soil. Estimation of the snow fraction is an approximation. CLM assumes that if effectie rouhness lenth (10 z 0 ) of soil is comparable to snow depth, wind can blow away snow and expose bare soil ( f snow <1). Solution of the CLM s two stream-model The solution of the CLM s two-stream equation for fuse fluxes has components: downward and upward fluxes due to fuse illumination and ect sources. The eneral form of solution is as follows: F F [" (L + S) ] + B exp[ (L + S) ] ) # A exp # #, [ "(L + S) ] + B # exp[ "(L + S) ] + C exp[ K(L + S) ] ) # A exp # #,

13 13 F F [" (L + S) ] + B exp[ (L + S) ] ) # A exp # #, [" (L + S) ] + B exp[ (L + S) ] ) # A exp # #, where A, A, A, A, B, B B, B, C, and are alebraic combination of coefficients of CLMS s two-stream equations as specified in CLM tech notes (WWW1). Physical meanin of each term of solution on the riht-hand side is as follows: contributions from fuse downwellin and upwellin radiation are ien by first and second terms, respectiely, and the contribution from ect radiation is ien by the third term (when applicable). Gien the solution of the two-stream equations for ect and fuse illumination we can specify the unknown fluxes appearin in the equation (cf. Section 2.C) for net shortwae fluxes (eetation and round absorptances): F F F F F ) " R ), ) " R ), ) " T ), ) " T ), ) " T ). 3.C. EXAMPLES OF TWO-STREAM SIMULATIONS Consider the followin examples which illustrate dependence of top of canopy albedo, canopy absorptance, and below canopy transmittance as function of arious parameters in the eetation canopy + round system. Simulations were performed with the Stochastic RT model (Shabano et al., 2000), run in the two-stream mode. The canopy was presented by the homoeneous medium comprised with reen leaes (no stems) with random leaf normal orientations. Note, that the examples are intended only for conceptual understandin; some discrepancy with CLM s two-stream simulations is possible. Fi. 3.8 shows ariation of the surface albedo as function of LAI of eetation and soil optical properties. In the case of no eetation, albedo of the total system is equialent to the soil albedo. Typically, round albedo at VIS and NIR waelenths are linearly related (cf. soil line). If soil albedo is constant, the albedo of total system is chanin as function of LAI alon trajectories, called soil isolines. If LAI is lare, independently from soil albedos, all trajectories conere to a sinle point in VIS-NIR spectral space. If LAI is constant, total albedo aries alon LAI isolines.

14 1 Fiure 3.8: Simulated Albedo in Red-NIR spectral space. Input flux: ect radiation only, Solar Zenith Anle, SZA0. Leaf albedos are ( red) 0. 10, ( NIR) Fiure 3.9 shows albedo, absorptance and transmittance as function of LAI for Red and NIR waelenth and two alues of Solar Zenith Anle (SZA+0 and 60 derees). Note that albedo at Red is decreasin as LAI is increasin because relatiely briht soil is replaced with darker eetation. The opposite trend is obsered for albedo at NIR waelenth. Canopy absorptance is increasin as LAI is increases, because more leaes are able to absorb more radiation. As LAI is increasin, leaes more efficiently coer the round and transmittance declines both for Red and NIR waelenth. With respect to SZA, canopy albedo is always hiher for na beam illumination compared to off na ections, as at na ection, the density of intercepted photons is hiher, and therefore eetation is able to trap liht more efficiently. The absorptance is hiher for the off-na ections, because the optical path inside of eetation canopy is hiher compared to one for na ection. Likewise, transmitted to the bottom canopy flux is lower for off-na ections.

15 15 Fiure 3.9: Impact of Solar Zenith Anle on simulated Albedo, Absorptance and Transmittance as function of LAI at Red and NIR waelenths. Simulations with SZA0 0 are shown in BLACK, while simulation with SZA60 0, are in shown in RED. Input flux: ect radiation only. Ground albedo (soil) was set to 0.1. Leaf albedos are ( red) 0. 17, ( NIR)

16 16 Oct-2 and Lonwae Fluxes.A. BACKGROUND Def: Black body - ideal object, which absorb all the incomin radiation. Def: Thermal equilibrium- such a state of the system that incomin and outoin radiation fluxes are in balance (equal) and temperature of the system is not chanin with the time. Def: Absorptiity of surface, a, is the fraction of incident radiation absorbed by a surface. For black body a1. Def: Emissiity of a surface,, is the ratio of the actual radiation, emitted by a surface to that amount, emitted by a black body. For black body 1. Kirchhoff Law - In the state of thermal equilibrium absorptiity, a, is equal to emissiity,. Plank Equation - Spectral radiation flux, emitted by a black body is where - waelenth, [ µ m ], 8# hc L( "), 5 " [exp(hc / k" T) 1] L () - spectral radiation flux, [W m -2 µ m 1 ], T - temperature of the object, [K], h Plank constant, 6.63x10-3, [J] c - speed of liht in acuum, x10 8, [ms -1 ] k - Boltzman constant, 1.381x10-23 [J K -1 ], Stefan-Boltzman Law: Enery flux, emitted by unit area of a plane surface of black body into a hemisphere is proportional to the fourth power of its absolute temperature, L T, where L is enery flux [W m -2 ], T is a temperature [K], is a Stefan-Boltzman constant, 5.67x10-8 [W m -2 K -1 ] Stefan-Boltzman law can be deried from Plank equation by interation oer emitted spectrum,

17 17 " " 8& hc L L( $ )d$ L d$ # T $ [exp(hc / k$ T) % 1] Typical terrestrial objects (soil, eetation, water, snow, ice) hae such rane of temperatures (around 300K) such that emitted radiation is confined mostly in the thermal rane of waelenths (3-100 µ m ). In contrast, temperature of Sun is much hiher (6000K) and, therefore, maximum emitted radiation occupies VIS-NIR waelenth band ( nm). Schematic plot for lonwae enery fluxes for typical terrestrial object is ien in Fi Note that this scheme preseres enery conseration law: Absorbed Flux Emitted Flux " # L # T " L T, Input Output $ L (1 " )L + # T (1 " )L + L. ( 1# ") L Scattered flux L Incomin flux " L Absorbed flux # " T Emitted flux Fiure 3.10: Lonwae fluxes- Incomin, Scattered (Reflected/Transmitted), and Emitted at equilibrium..b. VEGETATION AND GROUND FLUXES Consider propaation of lonwae radiation fluxes (heat transfer) in the two-component system (Fi 3.11): Veetation Ground The system is illuminated from the top with incomin lonwae radiation from the atmosphere. In the followin discussion round seres as a bottom boundary for lon wae radiation in the eetation canopy. Analysis of the more complex processes of heat transfer deep into the round (thermal conductiity) is beyond the scope of this lecture notes. Note also, that CLM describes system not in equilibrium- temperature of eetation and round may chane from preious (T n ) to the next step (T n+1 ) in the CLM run. Neertheless CLM assumes that absorptiity is equal to emissiity.

18 18 Veetation Fluxes Accordin to Fi there are two input fluxes into Veetation layer: downward flux from atmosphere ( L atm ) at the atmosphere-eetation border and upward flux from Ground ( L G, cf. next section) at the eetation-round border. Two output fluxes from Veetation layer are as flows. The downward flux from eetation at the eetation-round border, $ (1 % # ) Latm $ +# " T, (1) L and the upward flux from eetation+round at the atmosphere-eetation border, L $ (1 % # ) Latm & + (1 % # ) L $ +# " T +, (2) where Latm - downward flux from atmosphere at the top of eetation L - downward flux at the eetation-round border L - upward flux at the eetation-round border L+ - upward flux at the atmosphere-eetation border - emissiity ( absorptiity) of eetation T - temperature of the eetation Note that due to radiatie couplin of eetation and round, the upward flux from eetation includes the round component (this explains the subscript notation, V+G). L atm L V+G NET L Veetation L G Ground NET L G L Fiure 3.11: Lonwae Fluxes in Veetation + Ground system.

19 19 Ground Fluxes The Ground is modeled by semi-infinite space: startin from the top boundary (Ground surface) it expands infinitely in downward ection (cf. Fi. 3.11). The input flux to the Ground layer is ien by downward fux from eetation layer ( L V, cf. Eq. (1)) at the eetation-round border. The output flux at the same border is ien by upward flux from the Ground layer, L (1 % # ) L $ +# " T where L - upward flux at the eetation-round border L - downward flux at the eetation-round border - emissiity ( absorptiity) of round &, (3) T - temperature of the round Note, that accordin to Eq. (3) round upward flux does not depend ectly on the flux from atmosphere ( L atm ). The round is coupled with atmosphere only inectly throuh eetation flux ( L ). Emissiity of Veetation and Ground in CLM CLM uses the followin alues of eetation and round emissiity. Emissiity of round is: % $ 0.96 for soil, 0.97 for laciers, # 0.96 for wetlands, " 0.97 for snow. The emissiity of eetation is calculated as, & L + S # ( 1' exp$ ', % µ " where L is LAI, S is SAI, and µ is aerae inerse optical depth for lonwae radiation. Temperature and Fluxes increments Durin CLM runs temperatures of the eetation and round are updated incrementally. Temperature updates results in correspondin updates of emitted fluxes for eetation and round, $ " # " n + 1 n n 3 n + 1 ( T ) $ " # "( T ) + " $ " # "( T ) "( T T ) n, ()

20 $ " # " n + 1 n n 3 n + 1 ( T ) $ " # "( T ) + " $ " # "( T ) "( T T ) Note, formulas aboe are obtained accordin to standard Taylor expansion technique, n 20. (5) and " f (T) f (T + T) f (t) + T, " T f (T) # " T, $ f (T) 3 # " T $ T n + 1 n " T T T.,

21 21 Oct C. UPWAR FLUX FROM VEGETATION AND GROUND Consider Eqs. (1)-(3) for eetation and round lonwae fluxes and note the interdependencies. Upward flux from total system of eetation + round at the eetation-atmosphere border ( L +, Eq. (2)) depends on upward flux from round ( L, Eq. (3)), which in turn depends on the downward flux from eetation ( L, Eq. (1)). System of Eqs. (1)-(3) can be soled for L + in terms of known input ariables, L atm, T, T,,. For the purpose of representation of solution in terms of CLM s incremental temperature chanes we will use Eq. ()-(5) as well in the followin deriations. Consider two cases. In the simplest case of no eetation, L + &' L & (1 % # ) Latm $ +# " T n n 3 n + 1 n ( T ) + $ " # "( T )(T T ) (1 $ ) " Latm % +$ " # " In the second case, round is coered by eetation, and Eq. (6) is alid, (1 $ ) " L L + atm $ (1 % # ) Latm & + (1 % # ) L & + (1 $ ) " L % +$ " # " $ +# The unknown L can be deried by combinin Eqs. (1) and (3), ( 1 $ # ( 1 % # ) ) (1 $ # L & (1 % # ) L $ +# " T n n 3 n + 1 n ( T ) + $ " # "( T )(T T ) " T [(1 % # ) Latm $ +# " T ] + # " T n n ) Latm % + (1 $ # ) # " ( T ) + # " ( T ) + n 3 n + 1 n n 3 n + 1 n ( T )(T T ) + " $ " # "( T )(T T ) + " (1 $ ) " $ " # " Finally, substitutin the deried expression in the aboe equation for L +, we will et, L + (A) ( 1$ # ) " L + atm (B) + ( 1$ # ) " (1 $ # ) " (1 $ # ) " Latm + (C) + ( 1$ # ) (1 $ # ) # " ( T ) + (D) + ( 1$ # ) # " ( T ) + n n...

22 22 n T n 3 n + 1 n + " $ " # " T (T T ) n 3 n + 1 ) " (1 $ ) " $ " # " T (T (E) + # " ( ) + (F) ( ) + (G) + " (1 $ ( ) T ) + n 3 n + 1 (H) + " (1 $ ) " $ " # "( T )(T T ) The physical meanin of the terms (A)-(H) is as follows: Term (A) - atmospheric flux reflected by eetation back to atmosphere Term (B) - atmospheric flux transmitted throuh eetation to round, reflected by round back to eetation and transmitted throuh eetation back to atmosphere Term (C) - flux, emitted by eetation to the round, reflected by round back to eetation and transmitted throuh eetation back to atmosphere Term (D) - flux, emitted by round, and transmitted throuh eetation to atmosphere Term (E) - flux, emitted by eetation to atmosphere Term (F) increase/decrease in the flux (due to increase/decrease in eetation temperature), that is emitted by eetation to atmosphere Term (G) increase/decrease in the flux (due to increase/decrease in eetation temperature), that is emitted by eetation to the round, reflected by round back to eetation and transmitted throuh eetation back to atmosphere Term (H) increase/decrease in the flux (due to increase/decrease in round temperature), that is emitted by round and transmitted throuh eetation to the atmosphere..d. NET FLUXES Next, we ealuate net fluxes separately for round and for eetation. Net flux for eetation/round is calculated as a ference between outoin and incomin fluxes. Two cases are considered for round net fluxes: with and without eetation. In the case of no eetation, NET OUT IN L & L $ L # " % " T $ # " Latm, where first tem on the riht (loss) corresponds to emitted flux from round and second term (ain) corresponds to absorbed flux from atmosphere. In the second case, when round is coered by eetation, net round flux is, NET OUT IN L & L $ L # " % " T $ # " L, where first tem on the riht (loss) corresponds to emitted flux from round and second term (ain) corresponds to absorbed flux from eetation. Note, for both cases, the deried net round flux seres as lonwae radiation forcin to chane soil temperature. n. n

23 23 Next, consider net radiation flux for eetation, L NET % L OUT L IN [2 $ $ "$ "#" T " (1 $ )]" $ " # " $ # "[ 1+ (1 $ # ) " (1 $ # )]" L atm. (6) T First term on the riht (loss) is most complex and will be considered last. Second term (ain) corresponds to absorption of emitted by round flux. Third term (ain) corresponds to absorption of atmospheric flux and consists of two sub-terms. First sub-term corresponds to ect absorption of incomin atmospheric flux. Second sub-term corresponds to absorption of atmospheric flux, transmitted throuh eetation, reflected by round back to eetation. T A " C (1 # " )(1 # " )" T Veetation " T Ground ( 1# " )" T B " " T Fiure 3.12: Enery loss by eetation due to interaction with round. First term (loss) is the most complex and can be ealuated as follows. Exitin from eetation flux has three components (A, B, C, refer to Fi. 3.12). Component A corresponds to ect emission of eetation, " T A #, Component B corresponds to emission of eetation flux down toward round and absorptance by round, B # # " T

24 2 Component C corresponds to emission of eetation flux down toward eetation, reflection by eetation and transmission back to atmosphere, C (1 $ # ) (1 $ # ) # " T Now, the sum of A, B and C corresponds to total emission (exitin flux) and can be ealuated as follows A + B + C % # " T + # # " T + (1 $ # ) (1 $ # ) # " T [ 1+ # + (1 $ # ) (1 $ # )] # [ 1+ # + 1$ # $ # (1 $ # )] # " " [ 2 $ # (1 $ # )] # " T, Thus, the sum, A+B+C, corresponds to the first term of Eq. (6). T T 5. CHAPTER 3 REFRENCES CLM Tech notes (pp. 37-0), Dickinson, R.E. (1983) Land surface processes and climate-surface albedos and enery balance. Adanced Geophysics, 25, Sellers, P.J. (1985). Canopy reflectance, photosynthesis and transpiration. International Journal of Remote Sensin: Shabano, N.V., Knyazikhin, Y., Baret, F., Myneni, R.B. (2000). Stochastic Modelin of Radiation Reime in Discontinuous Veetation Canopies. Remote Sensin of Enironment, 7(1):