Section 3
Theory of Operation
3-9
be neglected. Thus, if other atmospheric components are constant, an
equivalent pressure can be defined as
P
e
= a
d
P
d
+ a
w
e
= P(a
d
X
d
+ a
w
X
w
)
3-19
where P
d
is the total pressure of dry air, and a
d
is a dry air weighting factor.
LI-COR calibrates all of its analyzers using CO
2
or water vapor in air, so
a
d
= 1 is taken as the standard condition. Substituting equation 3-18 into
equation 3-19 gives
P
e
= P[1 + (a
w
- 1)X
w
]
3-20
The value of a
w
is not an intrinsic constant comparable to other such values
in the literature because it uses dry air as a reference instead of nitrogen. Its
value has been empirically determined to be about 1.5 against dry air. The
value of a
w
used in 3-20 is entered into the LI-6262 using FCT 78.
Equation 3-20 can be extended to include nitrogen as standard, and both
water vapor and oxygen (or other gases) as variable components. P
e
can be
written in a more general form to anticipate that possibility:
P
e
= P[1 + (a
w
- 1)X
w
+
Σ
(b
i
- 1)X
i
]
3-21
For the present, equation 3-20 is implemented in the LI-6262 software;
equation 3-21 has not yet been tested. Equation 3-20 can be compactly
rewritten as
P
e
= P
χ
(X
a
)
3-22
where
χ
(X
a
) = 1 + (a
w
- 1)X
a
, and then incorporated into the CO
a
calibration
function.
The form of the CO
2
calibration function (equation 3-4) was derived
empirically, but it can also be derived from a "scaling law" called the "non-
overlapping line approximation" which holds when absorber concentrations
are low or pathlengths are short (4). This “scaling law” allows absorption
measured under one set of conditions to be scaled to other conditions (2),
A
P
g u P
=
(
)
/
3-23
