LI-COR LI-8100A - Page 68

Theory of Operation
4-13
f gCC g wCC g wC
pc
l
ci c
l
cc i c
l
cc
= − = −
′
−
′
= −
′
− ρρ ρ α ( ) ()( ) ()()111
4-20
Where f
p
is photosynthesis rate (mol m
-2
s
-1
), g
l
is the total leaf conductance (mol
m
-2
s
-1
) including stomatal and leaf boundary layer conductance, C
i
’ is intercellular
CO
2
mole fraction (mol mol
-1
),  is C
i
/C
a
ratio. We assume  to be constant over a
wide range of CO
2
concentrations (around 0.6 for C
3
-species, and 0.3 for C
4
species) (Wong et al., 1979; Morison, 1987; Xu and Hsiao, 2004).
V
s
w
c
t
g w C C LAI g w C R
c
c
c
cs c s c c
l
cc
h
ρ
∂
∂
ρρα
()
'
()( ) ()()11 11− = −
′
−
′
−−
′
− +
4-21
where R
h
is total above-ground biomass respiration. Rearranging Equation 4-21, we
have
∂
∂
α
′
++ −
[]
′
=
′
+
c
t
S
V
g LAIg C
S
V
gC R
c
s
l
css
h
() ( )1
4-22
Let
N
S
V
g LAIg M
S
V
gC R
s
l
ss
h
=+ −
[]
=
′
+() ( )1 α and
∂
∂
′
+
′
=
c
t
NC M
c
c
4-23
Equation (4-23) can be integrated to have
′
=+
′
−
−
Ct
M
N
C
M
N
e
co
Nt
() ( )
4-24
Let
′
=C
M
N
m
, we have
′
=
′
+
′
−
′
−
Ct C C C e
cmom
Nt
() ( )
4-25
The following equation will be used to fit the time series of C
c
’ (see earlier in this
section for explanation of the original of t
o
)
′
=
′
+
′
−
′
−−
Ct C C C e
cmom
Nt t
o
() ( )
()
4-26
Equation 4-25 is exactly the same as Equation 4-10 for opaque chambers. For the
LI-8100A, we use a generic exponential equation to fit the time series of chamber
CO
2
concentration. For a clear chamber, when C’
m
< C’
o
, net carbon uptake is
observed. When C’
s
> C’
o
from fitted equation 4-10, net carbon release is observed.