modeling a microclimate within vegetation
DESCRIPTION
Modeling a Microclimate within Vegetation. Hisashi Hiraoka Academic Center for Computing and Media Studies Kyoto University. NATO ASI, KIEV 2004. 1. Outline. ◊ introduction • background • review • objective ◊ explanation of our microclimate model ◊ validation of the model - PowerPoint PPT PresentationTRANSCRIPT
Modeling a Microclimate within Vegetation
Hisashi Hiraoka
Academic Center for Computing and Media Studies
Kyoto University
NATO ASI, KIEV 20041
NATO ASI, KIEV 2004
Outline
◊ introduction• background• review• objective
◊ explanation of our microclimate model◊ validation of the model◊ application of the model to a single tree
• the environment around the tree• the heat budget within the tree
2
Introduction
3 NATO ASI, KIEV 2004
NATO ASI, KIEV 2004
Background of this study
numerically investigatng the effect of vegetation on a heat load of a building, thermal comfort, an urban thermal environment and the like.
• trees beside a house (heat load)• roof garden (heat load, thermal comfort)• garden (microclimate, thermal comfort)• street trees (thermal comfort)• park (microclimate, thermal comfort)• wooded area in a city (urban thermal environment)• woods (effect on urban thermal environment)• forest (effect on urban thermal environment)
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NATO ASI, KIEV 2004
Review of researches
• Waggoner and Reifsnyder (1968)• Lemon et al. (1971)• Goudriaan (1977)• Norman (1979)• Horie (1981)• Meyers and Paw U (1987)• Naot and Mahrer (1989)• Kanda and Hino (1990)
Necessary sub-models
* turbulence model* radiation transfer model* stomatal conductance model* model for water uptake of root* model for heat and water diffusion in soil
◊ soil respiration model◊ root respiration model
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Problems of the above models
• These models are not completely applicable to 3dim.• Short wave radiation is not separated into PAR and the other.
Objective of this study
• Proposing a model for simulating a microclimate within three-dimensional vegetation
• Examining the validity of the model by comparing with measurement
• Applying the model to a single model tree and investigating the microclimate produced by the tree
6
Microclimate Model for Vegetation
7 NATO ASI, KIEV 2004
NATO ASI, KIEV 2004
Outline of our microclimate model
• turbulence model the present model [Table 1]
• Ross’s radiation transfer model
assumption 1: A scattering characteristic of a single leaf is of Lambertian type.
Diffusion Approximation
• stomatal conductance model by Collatz et al. (1991)
assumption 2: Vegetation is adequately supplied with water from soil.
8
: surface harmonic series expanded up to the first-order
NATO ASI, KIEV 2004
Formulation of turbulence model
(1) Basic equations are first ensemble-averaged and then spatially averaged.
(2) The turbulence equations for dispersive componentand real turbulent component are derived from thebasic equation and the averaged equations.
(3) These two kinds of equations are combined intothe turbulence equation.
(4) And the unknown quantities are modeled by the semi-empirical closure technique.
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Definition of spatial average:
f ≡1
Va x( )H x− ′ x ( ) f ′ x ( )d ′ x ∫
Va x( )
[formulas]
∂ f∂ xi
=1G
∂ G f∂ xi
+1Va
f ni f ni = H x− ′ x ( ) f ′ x ( ) ′ n ids ′ x ( )s∫(1)
∂ f∂t
=1G
∂G f∂t
−1Va
f vjnj f vj nj = H x− ′ x ( ) f ′ x ,t( )vj ′ x ( ) ′ n jds ′ x ( )s∫(2)
, whereG =
Va x( )V0
V0 : the averaged volume
: the fluid volume in V0
vi : the i-th component of the velocity on leaf surface
H x( ) : filter function
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G =1 in this study.
NATO ASI, KIEV 2004
An example of a filtering function (1 dimension)
H x( )dx−∞
∞
∫ =V0
1
xM
H xM −x( )
f x( )
solidfluid fluid
sufficiently smooth
volumeV0
V0 −Va
sufficiently smooth
Only the part of fluid should be integrated in case of spatial integration. So,we set quantity f(x) =0 in the solid part even if f(x) has a value in the solid including the surface. f(x) may be discontinuos on the interface between the solid and the fluid, but the limit value of f(x) on the inetrface must be bounded.
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Symbols
: instantaneous value of˜ f f
f : ensemble mean of f
f : spatial mean of f
′ f =˜ f −˜ f
′ ′ f =f − f
: time fluctuation, or deviation from ensemble mean
: deviation from spatial mean
U i =˜ u i , U i =Ui Θ =̃ θ , Θ =Θ
q =q C =C
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Table 1 Turbulence model for moist air within vegetation
∂U j
∂xj=Svap+SO2 −SCO2(1) (2)
(3)
(4) (5)
(6)
DεDt
=εk
⎛ ⎝ ⎜ ⎞
⎠ ⎟ cε1Pk +cε3Gk +cεpak1.5 −cε2ε[ ]+
∂∂xj
νt
σε
∂ε∂xj
⎡
⎣ ⎢
⎤
⎦ ⎥ (7)
: represents the vegetation terms which are originally expressed as leaf-surface integral except that in the equation.
: represents the modeled terms.
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DUi
Dt=−
1ρ
∂P∂xi
−∂uiuj
∂xj−Fj
DΘDt
=−∂θuj
∂xj+
aρ cp
⎛
⎝ ⎜
⎞
⎠ ⎟ H +Hvap+HO2 −HCO2[ ]
DqDt
=−∂quj
∂xj+Svap
DCDt
=−∂cuj
∂xj−aAn
DkDt
=Pk +Gk −ε +∂
∂xj
νt
σk
∂k∂xj
⎡
⎣ ⎢
⎤
⎦ ⎥ +U jFj
These terms are derived analytically from the basic equationsby averaging spatially.
drag forcetranspiration photosynthesis
sensible heat heat transfer due to photosynthesis
photosynthesisphotosynthesis
drag force
NATO ASI, KIEV 2004
The vegetation terms (1): leaf-surface integral
Fi =1Va
H x− ′ x ( ) P ′ x ( )δij +τ ij ′ x ( )[ ] ′ n jdS ′ x ( )leaf surface
∫ , τ ij =−ν∂U i∂xj
+∂U j∂xi
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
aH =1Va
H x− ′ x ( )κ∂Θ ′ x ( )
∂ ′ x j′ n jdS ′ x ( )
leafsurface∫
aHvap=−1Va
H x− ′ x ( ) ˆ H θvcv ′ x ( )uj
v ′ x ( ) ′ n jdS ′ x ( )leafsurgace
∫
=−ˆ H θ
v
VaH x− ′ x ( )cv ′ x ( )uj
v ′ x ( ) ′ n jdS ′ x ( )leafsurface
∫ = ˆ H θvaE=aCp
vaporTl −Θ( )E
aHO2 =−ˆ H θ
O2
VaH x− ′ x ( )cO2 ′ x ( )uj
O2 ′ x ( ) ′ n jdS ′ x ( )leafsurface
∫ = ˆ H θO2aAn =aCp
O2 Tl −Θ( )An
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aHCO2 =−ˆ H θ
CO2
VaH x− ′ x ( )cCO2 ′ x ( )uj
CO2 ′ x ( ) ′ n jdS ′ x ( )leafsurface
∫ = ˆ H θCO2aAn =aCp
CO2 Tl −Θ( )An
NATO ASI, KIEV 2004
The vegetation term in the k equation (2):
′ ′ U i =U i − U i , ′ ′ τ ij =τ ij − τ ij , ′ ′ P =P − P
U i leaf surface=0, ∴ ′ ′ U i leaf surface
=−U i =−Ui( )
U i =const., P =const., τ ij =const. inV0
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U jFj
=Ui
VaH x− ′ x ( ) P ′ x ( )δij +τ ij ′ x ( )[ ] ′ n jdS ′ x ( )
leafsurface∫ =U jFj
€
U jF j ⇐ −1
Va
H x − ′ x ( ) ′ ′ U i ′ x ( ) ′ ′ P ′ x ( )δ ij + ′ ′ τ ij ′ x ( )[ ] ′ n jdS ′ x ( )leaf surface
∫
The equation of k’:
€
′ k ≡ 12
′ u j ′ u j
€
∂ ′ k
∂ t+
1
G
∂ GUk ′ k
∂ xk
=−′ u i ′ u k
G
∂ GUi
∂ xk
− ′ u i ′ u k( )′′∂ ′ ′ u i∂ xk
− ν∂ ′ u i∂ xk
∂ ′ u
∂ xk
− βgk ′ θ ′ u k +1
G
∂
∂ xk
G ′ u i∂ ′ u i∂ xk
+∂ ′ u k∂ xi
⎛
⎝ ⎜
⎞
⎠ ⎟
€
−1
G
∂
∂ xk
G′ p ′ u i
ρδ ik + 1
2 ′ u i ′ u i ′ u k + uk′′ 1
2 ′ u i ′ u i( )′′
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥−
1
Va
′ p ′ u nρ
+ 12 ′ u k ′ u k ′ u n − ν ′ u k
∂ ′ u i∂ xn
+∂ ′ u n∂ xi
⎛
⎝ ⎜
⎞
⎠ ⎟
production frommean shear flow
production fromdispersive component
viscousdissipation
buoyancy moleculardiffusion
turbulent diffusion surface integral term
16 NATO ASI, KIEV 2004
: Real turbulent component
The equation of k”:
€
′ ′ k ≡ 12
′ ′ u j ′ ′ u j
€
∂ ′ ′ k
∂ t+
1
G
∂ GUk ′ ′ k
∂ xk
=−′ ′ u i ′ ′ u kG
∂ GUi
∂ xk
+ ′ u i ′ u k( )′′∂ ′ ′ u
∂ xk
− ν∂ ′ ′ u i∂ xk
+∂ ′ ′ u k∂ xi
⎛
⎝ ⎜
⎞
⎠ ⎟∂ ′ ′ u i∂ xk
− βgk ′ ′ θ ′ ′ u k +UkFk
€
+1
G
∂
∂ xk
G ν∂ ′ ′ u i∂ xk
+∂ ′ ′ u k∂ xi
⎛
⎝ ⎜
⎞
⎠ ⎟ ′ ′ u i
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥−
1
G
∂
∂ xk
G′ ′ p ′ ′ u iρ
δ ik + 12 ′ ′ u i ′ ′ u i ′ ′ u k + ′ u i ′ u k( )
′′′ ′ u i
⎡
⎣ ⎢
⎤
⎦ ⎥
production from mean shear flow
dissipation toward real turbulent component
viscous dissipation buoyancy productionby dragforce
molecular diffusion turbulent diffusion
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: dispersive component of turbulent energy
The equation of turbulent energy k:
€
k ≡ ′ k + ′ ′ k = 12
′ u j ′ u j + 12
′ ′ u j ′ ′ u j ≡ 12 u ju j
€
∂ k
∂ t+
1
G
∂ GUk k
∂ xk
= Pk + Pl →s −ε l →s( ) +UkFk − βgkθ uk −ε +dt +dν +ds
€
Pk =−uiuk
G
∂ GUi
∂ xk
€
Pl →s =ε l →s = − ′ u i ′ u k( )′′∂ ′ ′ u i
∂ xk
€
dt =−1
G
∂
∂ xk
G 12 ′ u i ′ u i ′ u k + 1
2 ′ u i ′ u i( )′′
′ ′ u k + ′ u i ′ u k( )′′
′ ′ u i + 12 ′ ′ u i ′ ′ u i ′ ′ u k +
′ p ′ u i
ρδ ik +
′ ′ p ′ ′ u iρ
δ ik
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
€
dν =ν
G
∂
∂ xk
G ′ u k∂ ′ u i∂ xk
+∂ ′ u k∂ xi
⎛
⎝ ⎜
⎞
⎠ ⎟ + ′ ′ u k
∂ ′ ′ u i∂ xk
+∂ ′ ′ u k∂ xi
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
€
ds =−1
Va
′ p ′ u nρ
+ 12 ′ u k ′ u k ′ u n − ν ′ u k
∂ ′ u i∂ xk
+∂ ′ u k∂ xi
⎛
⎝ ⎜
⎞
⎠ ⎟
18 NATO ASI, KIEV 2004
• production from dispersive component• dissipation toward real turbulent component
€
=ν ∂ ′ u i∂ x j
∂ ′ u i∂ x j
+ν∂ ′ ′ u i∂ x j
∂ ′ ′ u i∂ x j
≈ν∂ ′ u i∂ x j
∂ ′ u i∂ x j
The equation :
€
≡ν ∂ ′ u i∂ x j
∂ ′ u i∂ x j
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€
∂∂ t
+1
G
∂ GUkε
∂ xk
=− 2ν∂ ′ u i∂ xj
∂ ′ u k∂ xj
+∂ ′ u j∂ xi
∂ ′ u j∂ xk
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
1
G
∂ GUi
∂ xk
− 2νβgi
∂ ′ θ
∂ xj
∂ ′ u i∂ xj
€
−2ν∂ ′ u i∂ xj
∂ ′ u k∂ xj
⎛
⎝ ⎜
⎞
⎠ ⎟′′
+∂ ′ u j∂ xi
∂ ′ u j∂ xk
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
′′ ⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
∂ ′ ′ u i∂ xk
− 2ν∂ ′ u i∂ xj
∂ ′ u i∂ xk
∂ ′ u k∂ xj
− 2∂
∂ xk
ν∂ ′ u i∂ xj
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
2
€
−1
G
∂ G ′ u k ′ ε 1 + ′ ′ u k ′ ′ ε 1[ ]
∂ xk
−2ν
ρ G
∂
∂ xk
G∂ ′ u k∂ xj
∂ ′ p
∂ xj
+ν
G
∂ 2 Gε
∂ xk2
€
−2ν ′ u k∂ ′ u i∂ xj
1
G
∂ 2 GUi
∂ xj∂ xk
− 2ν ′ u k∂ ′ u i∂ xj
⎛
⎝ ⎜
⎞
⎠ ⎟′′
∂ 2 ′ ′ u i∂ xj∂ xk
€
−1
Va
′ u k ′ ε 1 nk +ν
Va
∂ ε1
∂ xk
nk +ν
Va
∂ε1
∂ xk
nk −2ν
Vaρ
∂ ′ u k∂ xj
∂ ′ p
∂ xj
nk − 2ν ′ u k∂ ′ u i∂ xj
1
Va
∂ u i∂ xj
nk
production from mean shear flow buoyancy
production from dispersive component vortex stretching molecular dissipation
turbulent diffusion turbulent diffusion molecular diffusion
production from mean flow production from dispersive component
NATO ASI, KIEV 2004
NATO ASI, KIEV 2004
The modeled terms: Modeling
[Reynolds stress] uiuj = ′ u i ′ u j + ′ ′ u i ′ ′ u j
[other turbulent fluxes] θui = ′ θ ′ u i + ′ ′ Θ ′ ′ U i =−νt
Prt
∂Θ∂xi
qui = ′ q ′ u i + ′ ′ q ′ ′ U i =−νt
σ v
∂q∂xi
cui = ′ c ′ u i + ′ ′ C ′ ′ U i =−νt
σc
∂C∂xi
[the vegetation term in the equation]
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=−νt∂Ui
∂xj+
∂U j
∂xi
⎛
⎝ ⎜
⎞
⎠ ⎟ +
23
kδij +23
νtδij Svap+SO2 −SCO2( )
−2ν∂ ′ u i∂xj
∂ ′ u k∂xj
⎛
⎝ ⎜
⎞
⎠ ⎟ ′′
+∂ ′ u j∂xi
∂ ′ u j∂xk
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
′′⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⋅∂ ′ ′ u i∂xk
∝ −εk
⎛ ⎝ ⎜
⎞ ⎠ ⎟ ′ u i ′ u k( )
′′⋅
∂ ′ ′ u i∂xk
=εk
⎛ ⎝ ⎜
⎞ ⎠ ⎟ cεpak1.5
dimensional analysisaccording to Launderproduction from dispersive component
NATO ASI, KIEV 2004
Table 2 The balances of heat, vapor and CO2 on leaves
[a] Heat exchange between leaves and the surrounding air
a QPAR +QNIR +Rnet( ) =a H +lvE +Hvap+HO2 −HCO2( )(1)
[b] The balance of water vapor flux on leaves
(2)
[c] Net photosynthetic rate
E =gses Tl( )
P0−cs
vapor⎛
⎝ ⎜
⎞
⎠ ⎟ =αv
P0
R Θ +273.15( )cs
vapor−cavapor
( )
An =αcP0
R Θ +273.15( )ca
CO2 −csCO2
( ) =gs
1.6cs
CO2 −ciCO2
( )(3)
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transpiration(latent heat)
photosynthesis(sensible heat)
sensible heat transfer between leaves and air
short-wave radiationsabsorbed by leaves
net long-wave radiation
transpiration rate
stomatal conductance
net photosynthetic rate
NATO ASI, KIEV 2004
Ross’s radiation transfer models
(Short wave radiation)
rj∂i x,r( )∂xj
=−a x( )G x,r( )i x,r( )+a x( ) Γ x,r, ′ r ( )i x, ′ r ( )d ′ ω ′ ω =4π∫
(Long wave radiation)
rj∂i x,r( )∂xj
=−a x( )G x,r( )i x,r( ) +a x( ) Γ x,r, ′ r ( )i x, ′ r ( )d ′ ω ′ ω =4π∫ +a x( )
ε x( )π
σ Tl x( ) +273.15( )4
[symbols]
G x,r( )=1
2πg x,rL( ) r ⋅ rL( )dωL
ωL =2π∫
Γ x,r, ′ r ( )=1
2π′ ′ σ r, ′ r ;rL( )g x,rL( ) r ⋅rL( ) ′ r ⋅rL( )dωL
ωL =2π∫
i x,r( )=i x;θ,φ( ) : radiance ,
g x,rL( ) : distribution function of foliage area orientation
′ ′ σ r, ′ r ;rL( ) : scattering function of leaf, ε x( ) : emissivity of leaf
a x( ) : leaf area density , Tl x( ) : leaf temperature
r = θ,φ( ) : direction of radiance
rL = θL ,φL( ) : direction of leaf surface, r ⋅rL( ) : inner product22
NATO ASI, KIEV 2004
Outline of stomatal conductance model by Collatz et al.
gs =mhsAn cs( )+b(1) Ball’s empirical equation
An =gs cs −ci( ) 1.6(2)The value 1.6 means the ratio in molecular diffusivity of CO2 to H2O.
An = f QPAR,Tl ,ci( )(3) simplified Farquhar’sphotosynthesis model
• The photosynthesis model was made on the basis of Rubiscoenzyme reaction in Calvin cycle of C3 plant.
• Refer to the paper by Collatz et al. (1991) for the details.
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Verification of the Model
24 NATO ASI, KIEV 2004
NATO ASI, KIEV 2004
Verification of the present model
The measurement by Naot and Mahrer (1989)• plant: cotton field (1.4m high, 1-dimension)• location: Gilgal (25Km north of the Dead Sea), Israel• period: August 18 - 20, 1987 (3 days)• weather: fair during the period
Comparison with the measurement• physical quantities compared with the measurement (1) wind velocity at the height of 1.4m, and 2.5m (2) air temperature at the height of 1.4m (3) net radiant flux
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0 1 2 3 4 50
0.5
1
1.5
2
2.5
3
3.5
4
Optimization of the coefficient cp 21:00at h
[ / ]velocity m s
: circles mesured data
( ): Svensson and Haggkvist or Yamada cp=2.49
: present cp=1.5
: present cp=2.5
( ): Svensson and Haggkvist or Yamada cp=2.50
Fig. 1 Optimization of the coefficient cp in the equation
the model by Svensson andHaggkvist (or Yamada):
DεDt
=L +εk
⎛ ⎝ ⎜ ⎞
⎠ ⎟ cεpU jFj
the present model:
DεDt
=L +εk
⎛ ⎝ ⎜ ⎞
⎠ ⎟ cεpak1.5
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NATO ASI, KIEV 2004
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70
time [hour]
circle : measured (4m : boundary condition)diamond : measured (2.5m), triangle : measured (1.4m)dotted line : model (2.5m), solid line : model (1.4m)
Fig. 2 Measured and calculated diurnal changes in wind velocity
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NATO ASI, KIEV 2004
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70
time [hour]
circle : measured (4m : boundary condition)triangle : measured (1.4m)solid line : model (1.4m)
Fig. 3 Measured and calculated diurnal changes in air temperature at the height of 1.4m
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NATO ASI, KIEV 2004
-200
0
200
400
600
800
0 10 20 30 40 50 60 70time [hour]
circle : measured data, solid line : model
Fig. 4 Measured and calculated diurnal changes in net radiant flux
29
Application of the Model to a Single Model Tree
30 NATO ASI, KIEV 2004
NATO ASI, KIEV 2004
Application of the model to a single tree (1)
Outline of computation
• computational domain: 48m(x-axis)X30m(y-axis)X30m(z-axis)• tree: 6m cubical foliage whose center is at a point(15m, 15m, 7m) leaf area density: 1[m2/m3] distribution function of foliage area orientation: uniform leaf transmissivity: 0.1(PAR), 0.5(NIR) <- short wave reflectivity: 0.1(PAR), 0.4(NIR) <- short wave emissivity: 0.9 <- long wave• sun: the solar altitude (h): 60 [degree] the atmospheric transmittance (P): 0.8• the diffused solar radiation: <- Berlarge’s equation• PAR conversion factor at h=60: 0.425(direct), 0.7(diffuse) <- Ross• the downward atmospheric radiation <- Brunt’s equation• calculation method: FDM, SMAC, QUICK, Adams-Bashforth
<- Bouguer’s equation
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NATO ASI, KIEV 2004
Application of the model to a single tree (2)
Results of computation: the microclimate produced by the tree the atmospheric conditions: • wind velocity: 2 [m/s] • air temperature: 20 [C] • relative humidity: 40 [%] • CO2 mole fraction: 340 [mol/mol]
Figures: • Fig. 5 wind velocity vectors • Fig. 6 distribution of air temperature • Fig. 7 distribution of specific humidity • Fig. 8 distribution of CO2 mole fraction
All figures are illustrated as graphs in (x-z) cross sectionthrough the center of the tree.
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NATO ASI, KIEV 2004
a tree
sun
60°
10 20 30 40
25
20
15
10
5
0
x [m]
z [m]
= 2.000e+00
Wind velocity vectors
Fig. 5 Wind velocity vectors
[m/s]
33
Wind Velocity Vectors
34 NATO ASI, KIEV 2004
Wind Velocity Vectors
35 NATO ASI, KIEV 2004
NATO ASI, KIEV 2004
19.9719.9619.95
a tree
sun
60°
10 20 30 40
25
20
15
10
5
0
x [m]
z [m]
19.96 19.98 20.00[C]
Distribution of air temperature
Fig. 6 Distribution of air temperature36
NATO ASI, KIEV 2004
5.84
5.966.00
5.885.92
a tree
sun
60°
10 20 30 40
25
20
15
10
5
0
x [m]
z [m]
5.85 5.90 5.95 6.00[g/Kg]
Distribution of specific humidity
Fig. 7 Distribution of specific humidity37
NATO ASI, KIEV 2004
339.0338.4337.8
a tree
sun
60°
10 20 30 40
25
20
15
10
5
0
x [m]
z [m]
337 338 339 340[micro-mol/mol]
Distribution of CO2 mole fraction
Fig.8 Distribution of CO2 mole fraction
38
Pressure Distribution
NATO ASI, KIEV 200439
NATO ASI, KIEV 2004
Application of the model to a single tree (3-1)
Results of computation: the heat budget within foliage
Figures:• Fig. 9 PAR absorbed by leaves• Fig. 10 NIR absorbed by leaves• Fig. 11 net long wave radiation• Fig. 12 distribution of latent heat• Fig. 13 distribution of sensible heat• Fig. 14 distribution of sensible heat of water vapor due to transpiration
All figures are illustrated as graphs in (x-z) cross sectionthrough the center of the tree.
40
NATO ASI, KIEV 2004
200160
120
80
40
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
50 100 150 200[W/m3]
PAR absorbed by leaves
Fig. 9 PAR absorbed by leaves
41
NATO ASI, KIEV 2004
45
36
27
18
9
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
10 20 30 40[W/m3]
NIR absorbed by leaves
Fig. 10 NIR absorbed by leaves
42
NATO ASI, KIEV 2004
-80
-60
-40
-20
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
-80 -60 -40 -20negative value : emission [W/m3]
Net long wave radiation
Fig. 11 Net long wave radiation43
NATO ASI, KIEV 2004
150
120
90
60
30
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
25 50 75 100 125 150[W/m3]
Distribution of latent heat
Fig. 12 Distribution of latent heat
44
NATO ASI, KIEV 2004
-15.0
0.0
-15.0
0.0
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
-25 -20 -15 -10 -5 0 5negative value : inflow [w/m3]
Distribution of sensible heat
Fig. 13 Distribution of sensible heat
45
NATO ASI, KIEV 2004
-0.02
0.00
-0.04-0.02
0.00
-0.04
-0.02
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
-0.050 -0.025 -0.000 0.025negative value : inflow [W/m3]
Sensible heat of water vapor due to transpiration
Fig. 14 Distribution of sensible heat of water vapor due to transpiration
46
NATO ASI, KIEV 2004
Application of the model to a single tree (3-2)
Summary of the heat budget within foliage
• A great deal of the short wave radiation absorbed by leaves is released through latent heat due to transpiration.
• Long wave radiation is not negligible.
• Air sensible heat (that is, heat convection term) is much less than latent heat.
• Sensible heat of water vapor due to transpiration is negligible.
47
NATO ASI, KIEV 2004
Application of the model to a single tree (4)
Results of computation: the others
Figures:• Fig. 15 transpiration rate within foliage• Fig. 16 net CO2 assimilation rate • Fig. 17 stomatal conductance• Fig. 18 leaf temperature
These figures are illustrated as graphs in a (x-z) cross sectionthrough the center of the tree.
48
NATO ASI, KIEV 2004
3.2
2.4
1.6
0.8
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
0.5 1.0 1.5 2.0 2.5 3.0 3.5[mmol/sm3]
Transpiration rate
Fig. 15 Transpiration rate within foliage49
NATO ASI, KIEV 2004
30
24
18
12
6
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
5 10 15 20 25 30[micro-mol/sm3]
Net CO2 assimilation rate
Fig. 16 Net CO2 assimilation rate50
NATO ASI, KIEV 2004
0.8
0.6
0.4
0.2
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
0.2 0.4 0.6 0.8[mol/sm2]
Stomatal conductance
Fig. 17 Distribution of stomatal conductance
51
NATO ASI, KIEV 2004
20.1
18.9
19.2
19.5
19.8
19.5 19.8
19.8
1.25 2.50 3.75 5.00
5.00
3.75
2.50
1.25
x [m]
z [m]
19.0 19.5 20.0[C]
Distribution of leaf temperature
Fig. 18 Distribution of leaf temperature
52
Summary
53 NATO ASI, KIEV 2004
NATO ASI, KIEV 2004
Summary
1] The model for simulating a microclimate produced by three-dimensional vegetation was proposed.
2] The model was examined in comparison with the measurement. The results from the model agreed with the measurement.
3] The model was applied to a single model tree. And the heat budget within foliage was investigated. The results from the computation were:
◊ A great deal of the short wave radiation absorbed by leaves was released through latent heat due to transpiration.
◊ Long wave radiation was not negligible.◊ Air sensible heat was much less than latent heat.◊ Sensible heat of water vapor due to transpiration was negligible.
This fact suggests that the results from a turbulence model for dry air are almost equal to those from the present model.
54