Theory of Operation
4-9
obtained by fitting equation (4-13) to the data using a non-linear regression
method.
Another approach that has been used to estimate the initial rate is to fit a
polynomial to the CO
2
concentration vs time data. This approach is theoretically
sound inasmuch as a power series can be generated from a Taylor series
approximation to equation (4-13). Usually, the data are fit with a quadratic
equation. We tested this approach and found that while it can be justified on
theoretical grounds, it does not work very well in practice. The shape of even a
second order polynomial is sensitive to small perturbations in the data. This makes
initial rate calculations subject to much larger variations than when the same data
are analyzed by nonlinear regression using equation (4-13).
Effects of High Chamber CO
2
Concentrations
Finally, we consider the importance of choosing appropriate observation times
and Pre-purge times. We do not have experience on enough soil types to give
absolute recommendations for the best observation length in all situations.
Nevertheless, our experience so far suggests that 60s to 120s will often work well.
This prevents large build-ups in chamber CO
2
concentration at typical change rates
such as 0.5 ppm s
-1
. We have found that optimal dead band length can vary from
about 10s to 60s, with 30s being a good value to use as a first estimate.
Dead bands and observation times can be adjusted after the fact, using the
LI-8100A Data Analysis software (FV8100). This program allows you to recalculate
data easily, using subsets of data selected to give optimal dead bands and
observation lengths. Therefore, it is not critical to choose the right dead band and
observation length in the field; as long as the observation lengths are long enough,
they can be optimized later, if necessary.
Long observations can have the effect of capping the soil and causing the CO
2
concentration to build up in the soil under the chamber. This phenomenon can be
observed by performing a sequence of observations in which the chamber
concentration is allowed to increase several hundred ppm during each observation.
When the Pre-purge is set to be just long enough to allow the chamber atmosphere
to come back to the ambient CO
2
concentration, the initial rates in sequential
observations can often be observed to increase as the soil CO
2
concentration
increases. This is expected according to equation (4-15), C
c
'/t = a(C
x
' -
C
ambient
'), if it is assumed that C
x
' = C
soil
'. Thus, one effect of long observation
lengths may be to perturb the very process we wish to measure.
Another effect of high chamber CO
2
concentrations is to promote leaks between
the chamber and atmosphere. Leaks can be ignored when the gradient between
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