General procedures for CO~2~ and H~2~O calibration of infrared gas
analyzers (IRGA) and secondary gas standards.

T. Ocheltree, H. Loescher

A.  **Rationale**

The purpose of this general procedure is to determine new calibration
coefficients for an IRGA and to develop secondary gas standards from
primary gas standards. Secondary gases are used for both field-site and
in-house IRGA calibrations. Using primary standards for these 'routine'
calibrations is generally unfeasible due to their high cost or loss of
consistency.

B. **Equipment and Setup**

Needed are at least (3) primary standard gases at known concentrations.
We use the WMO-CMDL standards from NOAA with accuracy of ± 0.01 ppm
(http://www.cmdl.noaa.gov/ccgg/refgases/index.html). Other groups
calibrate their primary standards using GC-MS process and dedicate a set
of tanks used only to develop a second set of standards used for routine
IRGA calibrations. In this way, their set of primary standards maintains
assurance and consistency across time in the calibration of the
secondary standards. WMO-CMDL standards need to be maintained as well,
periodic rolling and re-calibration every 2 years are recommended. The
chosen gases need to span the range of CO~2~ concentrations expected in
the field.

A dedicated closed-path IRGA with known history is used to calibrate the
secondary standards. IRGA is mass flow, pressure and temperature
controlled. We place the IRGA inside a temperature-controlled chamber.
Data is collected at 1 sec by a datalogger (model CR23X, Campbell
Scientific, Logan, UT). We use a configuration of valves and solenoids
controlled by the datalogger to switch the flow of different standard
gases. Scrubbed N~2~ is used for reference gas.

The mv output signals used to convert to molar fraction of CO~2~ are
different for each model of IRGA. From the li-6262, the raw \[CO~2~\]
and \[H~2~O\] signals are normalized by pressure, and standard CO~2~
concentration is normalized by temperature, such that 1) the CO~2~ mV
output signal is multiplied by P/P~0~, where P is the pressure of the
cell (KPa) and P~0~ is the average cell pressure over the entire
calibration procedure (KPa), and 2). The CO~2~ concentration is
multiplied by T~0~/T, where T is the cell temperature (˚C) and T~0~ is
the average cell temperature (˚C) during the entire calibration
procedure. To determine new calibration coefficients for the IRGA, fit a
3^rd^-order polynomial such that,
$\lbrack\text{CO}_{2}\rbrack\frac{T_{0}}{T} = a_{1}V\left( \frac{P}{P_{0}} \right) + a_{2}V\left( \frac{P}{P_{0}} \right)^{2} + a_{3}V\left( \frac{P}{P_{0}} \right)^{3}$
Eq. 1

where $a_{1}$, $a_{2}$, and $a_{3}$ are constants (i.e., the calibration
coefficients). Make sure to use the mV signal as the independent
variable when fitting this curve. *Note: Do not use Sigma-Plot to fit
this polynomial.*

The CO~2~ and H~2~O absorbance signals are used by the li-7000 to
determine the calibration coefficients. The normalization for these
signals is slightly different, such that each absorbance signal is
divided by mean cell pressure (KPa) and the scalar concentrations
(predetermined) divided by mean cell temperature (˚K) for each
concentration sampled. Hence, to determine new calibration coefficients
for the IRGA, fit a 3^rd^-order polynomial such that,

$\frac{\left\lbrack \text{CO}_{2} \right\rbrack}{T_{K}} = a_{1}\frac{V}{P} + a_{2}\frac{V}{P}^{2} + a_{3}\frac{V}{P}^{3}$
Eq. 2

where $a_{1}$, $a_{2}$, and $a_{3}$ are constants. Make sure to use the
mV signal as the independent variable when fitting this curve. *Note: Do
not use Sigma-Plot to fit this polynomial.*

C. **Calibration Procedure**

We first determine new calibration coefficients for our dedicated IRGA
by the procedure outlined above by switching between primary standard
gases across three different temperatures, 25, 30, and 35 °C (of course
zero-ing the IRGA first). After the temperature has stabilized, we then
sample the gases from lowest to highest concentration, and then vise
versa (i.e., ramp schedule). In this way, any bias due to the previous
gas can be removed. After cycling through the gases at one temperature,
we increase the temperature of the IRGA and sample the gases again.

We then repeat this process (with the new calibration coefficients) with
both the primary standards and the secondary standards to be calibrated.
Concentrations of secondary standards are then determined using the same
(new) calibration coefficients. We also check the noise to signal ratio,
$\frac{\sigma_{s}}{\mu}$as an indication of repeatability.

The procedure to calibrate the IRGA for water vapor is similar. We use a
dew point generator (model li-610, Li-cor Inc., Lincoln, NE) to automate
the production of water vapor at dew points ranging 6 -20 °C (the
equivalent to a vapor pressure of 0.8 -2.3 kPa) at 2 °C increments with
cell temperatures set at 30 and 35 °C. A chilled-mirror (model D2 with
Optica Monitor, Eastern Instruments Inc.) is used as our primary dew
point standard when calculating new coefficients. We have found that
water vapor made by the dew point generator can drift (particularly when
water levels in the cooler or reservoir are low) or can produce 'slugs'
of higher water vapor concentration as indicated by the chilled-mirror.
Hence, the chilled-mirror allows us to independently monitor the
behavior of the generator, assuring data quality. The dewpoint generator
is held at each dew point temperature for 5 min before switching to the
next dew point. We filter out the first 2 min in each 5 min sampling
period to allow the dewpoint generator and IRGA to stabilize at each new
dew point temperature. We then develop new calibration coefficients
outlined above.

D. **Field Calibration**

Once new coefficients are developed, installed and tested, we re-zero
and span for use in the field. Field calibrations must be performed at
the same sample cell temperature and pressure as you would expect by *in
situ* conditions. Often this is done at the same flow rates as used in
the field. Sometimes this is impractical because this practice results
in 'burning' lots of secondary gas tanks if sampling at \~ 9 lpm. An
alternative methodology is to lower the flow rates but maintain the
pressure and temperature of the cell (for example, 30 ˚C and at 85 KPa
at 1 lpm). Likewise, the 'zero-ing' should also be done with flow and
pressure of the reference cell as that used in the field.

> NOTE: BE SURE TO TURN OFF THE TANKS WHEN YOUR CALIBRATION IS COMPLETE
> OR WHEN YOU LEAVE FOR THE DAY. THIS WILL HOPEFULLY AVOID INADVERTANTLY
> VENTING A TANK
>
> Other notes: care should be used when handling the CMDL-WMO gas
> standards and it is advised to read the recommendations at
> <http://www.cmdl.noaa.gov/ccgg/refgases/airstandard.html>.
> Particularly, any contaminations should be avoided, which includes the
> need for low-volume high precision regulators, periodically rolling
> the tanks, and having the standard tanks re-analyzed every 2 years.