METER SC-1 - Page 34

30
SYSTEM
For the SC-1, the two distances are d
1
= 3.35 mm and d
2
= 11.43 mm.
The stomatal conductance (
g
s
) is the variable the SC-1 ultimately measures. The derivation
below shows how the variables above yield stomatal conductance.
First, the vapor flux (
F
vapor
) along the diffusion path will be determined using the RH
difference between nodes 1 and 2 as given in Equation1.
Equation1
=−
FgCC()
dvapor 21 2
C values are related to RH by Equation2
Equation2
=C
he T
P
()
i
rs a
atm
where h
r
is RH, e
s
(T
a
) is the saturated vapor pressure at air temperature, and P
atm
is
atmospheric pressure.
e
s
(T
a
) is calculated by the Tetens formula with appropriate coefficients
for water vapor:
Equation3
e
s
(T
a
) = 0.611exp
17.502T
T + 240.97
⎛
⎝
⎜
⎞
⎠
⎟
NOTE: T must be in degrees Celsius.
Next, the value of g
d2
(Equation1) must be determined by Equation4
Equation4
ρ
=g
D
d
d 2
vapor
2

where
ρ

is the molar density of air (Equation5) and D
vapor
is the diffusivity of water vapor
(Equation6).
Equation5
ρ
!
= 44.6
P
a
101.3
273.15
T
⎛
⎝
⎜
⎞
⎠
⎟
Equation6
D
vapor
(T , P
a
) = D
ref
(273.15,101.3)
101.3
P
a
⎛
⎝
⎜
⎞
⎠
⎟
T
273.15
⎛
⎝
⎜
⎞
⎠
⎟
1.75
Both of these quantities are temperature and pressure dependent; however, when multiplied
together as in Equation4, some of this dependency drops out.
Next, solve for the numerator in Equation4. If
Equation7
=×
−
D (273.15,101.3) 2.12 10 (m /s)
ref
52
then
Equation8
ρ
!
D
vapor
= 44.6
( )
2.12 × 10
−5
( )
T
273.15
⎛
⎝
⎜
⎞
⎠
⎟
0.75