The cocfficient of water-vapor transfer from the leaf interior to the surrounding air was evaluated in relation to wind speed and stomatal aperture, and the relation between transpiration rate and wind speed was quantitatively interpreted, after the simulation of the heat-budget of a leaf. The change in tht transpiration rate in the range of low wind speed was revealed, since the effect of transfer by free convection for the heat and water-vapor transfer over a leaf was added to that by forced convection. Moreover, the boundarylayer transfer coefficients including the factors of temperture variation on a leaf surface and the turbulence within a plant canopy were used for the calculation.
From a plant leaf, water is transported through stomates and cuticle, and then across the boundary layer on a leaf surface. Using the internal coefficient for internal transfer of vapor,
DL, and the external one for the bouneary layer,
DB, the transpiration rate,
w, is expressed as follows;
w=2D
L⋅D
B/D
L+D
BΔ
cL, D
TR=D
L⋅D
B/D
L+D
B,
where DTR is called “transpiration-transfer-coefficient”.
D
B=D
n+D
f,
Dn and
Df are the water-vapor transfer coefficients for free and forced convections, respectively.
Dn is given from the following formula,
D
n=A⋅f(Gr, Sc)d/l,
where
f (Gr, Sc) is a graphical function of Gr·Sc, Gr; Grashof number decided from leaf-air temperature difference and vapor-concentration departure of the leaf interior from the ambient air, Sc; Schmidt number,
d; molecular diffusivity of water vapor to air,
l; characteristic length of a leaf.
Df is written as follows,
D
f=Bu
0.5,
where u is wind speed,
A and
B; numerical coefficients.
Δ
cL is difference in water-vapor concentration between the leaf interior on the mesophyll cell walls and the ambient air outside the boundary layer, Δ
cL is expressed as follows, Δ
cL=C
L-r
A⋅C
A,
where
CL and
CA are the saturated concentration of water-vapor at temperatures of leaf and air, respectively,
rA; relative humidity of the air.
In still air, the transpiration-transfer-coefficient has a value determined from the internal vapor transfer coefficient and the external one for free convection.
In flowing air, increasing wind speed causes an increase in transpiration-transfer-coefficient. The increasing rate of the coefficient is large in the range of low wind speed and becomes gradually smaller with an increase in wind speed, until the coefficient approaches asymptotically to the value of the internal coefficient. The effect of wind speed on the increase in transpiration-transfer-coefficient is fairly large as stomatLs open.
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