METER SC-1 - Page 35

31
SC-1
Using C (from Equation2) and g
d2
(from Equation4) values, Equation1 can be solved for
theflux:
Equation9
F
vapor
=
ρ
!
D
vapor
d
2
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
1
P
atm
h
r1
e
s
(T
a1
) − h
r 2
e
s
(T
a 2
)
⎡
⎣
⎤
⎦
Now that F
vapor
has been solved, the stomatal conductance (g
s
) can be determined. This
requires some assumptions. First, the RH within the leaf tissue is assumed to be 1.0, so
Equation2 becomes
Equation10
=C
eT
P
()
sa
atm
leaf
Second, all conductance values are assumed to be in series, so the flux is constant between
any two nodes. Third, the temperature of the leaf is equal to the temperature of the first RH
sensor (the sensor block head is aluminum to eliminate the temperature difference).
These assumptions mean Equation1 can be written for node 1 and the leaf node
(Equation11, Equation12) and then set equal to Equation9 (Equation13).
Equation11
=−
+
FgCC()
sdvapor 1leaf 1
Equation12
F
vapor
= g
s+ d1
1
P
atm
⎛
⎝
⎜
⎞
⎠
⎟
e
s
(T
a1
)(1− h
r
)
⎡
⎣
⎤
⎦
Equation13
g
s+ d1
P
atm
e
s
(T
a1
)(1− h
r
)
⎡
⎣
⎤
⎦
=
1
P
atm
ρ
!
D
d
2
⎛
⎝
⎜
⎞
⎠
⎟
h
r1
e
s
(T
a1
) − h
r 2
e
s
(T
a2
)
⎡
⎣
⎤
⎦
Solving for g
s+d1
,
Equation14
g
s+ d1
=
ρ
!
D
d
2
⎛
⎝
⎜
⎞
⎠
⎟
h
r1
e
s
(T
a1
) − h
r 2
e
s
(T
a2
)
⎡
⎣
⎤
⎦
e
s
(T
a1
)(1− h
r1
)
Then solve for g
s
using the rule for series combination of conductance (Equation15).
Equation15
=−
+
gg g
111
ssdd11
Hence,
Equation16
1
g
s
=
e
s
(T
a1
)(1− h
r1
)d
2
ρ
!
D h
r1
e
s
(T
a1
) − h
r 2
e
s
(T
a 2
)
⎡
⎣
⎤
⎦
−
d
1
ρ
!
D