LI-COR LI-8100A - Calculating the Flux from Measured Data

Theory of Operation
4-5
(mol m
-3
). The soil and chamber must be isothermal for equation (4-8) to hold. A
correction for non-isothermal conditions could be included if one is needed.
Combining equation (4-8) with equation (4-7), considering all variables except c
c
'
to be constant, and rearranging, gives
∂
∂
c
t
sg
v
c
sg
v
c
c
cs
'
''+=
4-9
where c
s
' = c
s
(1-w
c
)
-1
. When w
c
= w
s
, c
s
' gives the dilution-corrected CO
2
mole
fraction in the soil layer communicating with the chamber. We do not expect w
c
to equal w
s
exactly, but most of the time they will differ by less than 0.02 mol/mol
or so, which introduces only a small uncertainty in c
s
'. If c
s
' is taken as a constant,
then equation (4-9) can be integrated to give
c
c
'(t) = c
s
' + [c
c
'(0) - c
s
']e
-At
4-10
where A = sg v
-1
is a rate constant (s
-1
) and c
c
'(0) is the initial value of the dilution-
corrected CO
2
mole fraction when the chamber closes. The rate of change in c
c
'(t)
at any time can be computed from the derivative of equation
(4-10).
∂
∂
c
t
Ac c e
c
sc
At
= −
[]
−
'()0
4-11
Calculating the Flux from Measured Data
In the LI-8100A, equations (4-7), (4-10) and (4-11) are implemented in a form that
presents the variables in more familiar and intuitive units. Equation (4-7) is
computed as
F
c
=
10VP
0
1
W
0
1000






RS(T
0
+ 273.15)


C
 t
4-12
where F
c
is the soil CO
2
efflux rate (μmol m
-2
s
-1
), V is volume (cm
3
), P
0
is the
initial pressure (kPa), W
0
is the initial water vapor mole fraction (mmol mol
-1
), S is
soil surface area (cm
2
), T
0
is initial air temperature (°C), and C'/t is the initial rate
of change in water-corrected CO
2
mole fraction (μmol mol
-1
).