Appendix A. Equation Summary
A-14
where f
c
(x) is a function whose inverse is a double rectangular hyperbola, and
whose coefficients (a1…a4) are given on the calibration sheet.
A-15
Solving equation A-15 for C yields the calibration function
A-16
Where
A-17
ψ (W) accounts for band broadening by water vapor.
A-18
The band broadening coefficient h(
α
'
c
) has been determined to be 1.45 for the
instrument for CO
2
concentrations near ambient. At higher concentrations, the
value decreases. We capture this behavior with an empirical relationship (equation
A-19).
A-19
Where z is from equation A-12, and b
w
is the low concentration band broadening
coefficient: 1.45. This is the value shown on the calibration sheet as BB = 1.45.The
typical relationship between h(
α
'
c
) and CO
2
concentration is shown in Figure A-1
on the facing page. (‘Typical’ because the exact relationship depends on the rela-
tionship between absorptance and CO
2
, which is the calibration curve.)
A-4 Using the LI-830 and LI-850 Gas Analyzers
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