4-8
Theory of Operation
Relationship Between the Model Equation (4-10) and Empirical Equation
(4-13)
The diffusion model provides an equation with a form that allows correction for the
effect of changing gradients on the rate, which in turn, makes it possible to estimate
the initial rate. It is worthwhile to distinguish between the model function given in
equation (4-10) and the empirical function in equation (4-13). As just described,
the units are different in the two expressions; but more important, for the
parameters c
s
and A in equation (4-10) to have their defined meaning, the
assumptions underlying the derivation must be true. By contrast, equations (4-13)
through (4-15) are treated as empirical functions and are used only to estimate the
CO
2
rate of change, C'/t. The parameters C
x
', a and t
0
do not depend upon a
specific theoretical interpretation, and may or may not provide reliable estimates of
soil parameters.
Correcting for Initial CO
2
Concentrations That Differ Between Measurements
Different measurements may begin at different CO
2
concentrations, which
introduces variation into the data, because the flux rate changes with chamber CO
2
concentration. Correcting the measurements to a common target CO
2
concentration may reduce such variation. For a given curve fit, the CO
2
rate of
change can be computed at any CO
2
concentration according to
∂
∂
C
t
aC C
x
'
(' ')= −
target
4-16
This calculation is supported in the Data Analysis software (FV8100) included with
the LI-8100A.
Evaluation of Other Methods for Computing Soil CO
2
Efflux
Other approaches have been used for computing CO
2
flux in transient
measurements. One commonly used method is to fit a linear function to what is
sometimes referred to as "the linear portion" of the curve. Unfortunately, there is
no linear portion, as can be seen from careful inspection of Figure 4-2. The slope
is meaningless in the initial phase before steady mixing is established, and after
steady mixing is established, the extent of the non-linearity depends upon the soil
surface-to-chamber volume ratio and the flux rate. During this time, CO
2
vs time
curves are always concave in a downward direction, meaning that linear regression
over this portion of the data set will give an underestimate of the rate of change. In
every case we have tested so far, the average rate measured by linear regression is
less than the initial rate measured by non-linear regression. Nevertheless, linear
regression is a robust numerical approach and the mean values for the CO
2
efflux
rate reported by the LI-8100A in Type 3 records are computed by this method. We
recommend you use these only for comparison to the initial values, which are
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