4-4
Theory of Operation
f
c
=
v
c
s
c
c
t
+
c
c
1 w
c
w
c
t
4-6
Equation (4-6) has the same form as that used in the LI-6400 Portable
Photosynthesis System for soil respiration; however, it can be simplified by defining
c
c
' = c
c
(1 - w
c
)
-1
, which is the chamber CO
2
mole fraction corrected for water
vapor dilution. This is called Cdry (ppm) in the LI-8100A data output.
Differentiating c
c
' we find,
(1 w
c
)
c
c
t
=
c
c
t
+
c
c
1 w
c
w
c
t
Substituting this into equation (4-6) gives
f
c
=
v
c
s
(1 w
c
)
c
c
t
4-7
Equation (4-7) has an important advantage over equation (4-6) because it is not
necessary to estimate the rate of increase in water vapor mole fraction. In most
measurements, the water vapor mole fraction increases in a highly non-linear
fashion, and the rate is estimated with a linear function. Thus, in effect, equation
(4-6) forces us to use average values for w
c
/t and w
c
. But with equation (4-7),
the dilution correction is made point-by-point, and estimates of the initial values at
time zero are used to estimate f
c
at the instant the chamber closed. This is both
easier and more accurate than the procedure required to implement equation (4-6).
In order to use equation (4-7) the initial values must be known for p and T
K
(to
compute
c
), as well as the initial values for w
c
and c
c
'/t. After the chamber
closes, the LI-8100A performs a linear regression with time on the first 10 values of
each measured variable. The initial values of p, T
K
and w
c
are obtained from the
time zero intercepts of these regressions; however, finding the initial value for
c
c
'/t requires a little more work.
To do this, f
c
is defined in terms of the CO
2
mole fraction gradient across the soil-
to-chamber interface and a transfer coefficient, to obtain
f
c
=
c
g(c
s
- c
c
) 4-8
where c
s
is the CO
2
mole fraction in the soil surface layer communicating with the
chamber (mol mol
-1
), g is conductance to CO
2
(m s
-1
), and
c
is the density of air
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