To: Participants of the Miami data reduction workshop

Subject: Linearity test of XCO2 output of LiCOR 6252 analyzer

From: Rik, Kevin, and Heike

Attached are the LiCOR 6252 output values for the tests that Kevin ran
to determine the linearity of the output of the XCO2 channel of the
LiCOR 6252. We are looking into various aspects of the results but
thought you\'d like to have the data to play with. A brief description
of our interpretations is listed below.

**Objective:**

1\. Determine the response of the XCO2 output of the LiCO2 6252 infrared
analyzer (IR) and determine appropriate fit to the standards

2\. Treat 2 or 3 standards as unknown and the remainder as knows and see
how well the fits reproduce the unknown, particularly if they are
outside the standard range

3\. Determine the optimal way of standardization of LiCOR IR using the
XCO2 (ppm) output :

a\. Polynomial fit

b\. A linear fit through all standards

c\. A linear fit between two standards bracketing the unknown

4\. Determine how drift in zero and span affect 1, 2 and 3 by
manipulating zero and span setting

**Standards used:**

6 standards were used. Three are CMDL standards and three are standards
prepared in the lab of C.D. Keeling. All are directly traceable to the
WMO-85 scale:

[Port-tank#-origin concentration]{.underline}

P#1-ca01491-CMDL 508.38

P#2-ca06368-CMDL 328.12

P#3-ca06380-CMDL 448.29

P#4-nd01607-keeling 794.94

P#5-nd01606-keeling 350.44

P#6-nd01587-keeling 203.92

**Test setup:**

The 6 standards were connected to a Valco multi-port valve that switched
at 4.5-minute intervals between subsequent ports. The 6-port and IR were
in a PVC box and sheltered from abrupt temperature fluctuations.
However, no direct temperature control was exerted. All standard gases
went through an MgClO4 column, an Acrodisk and into the LiCOR 6252
infrared analyzer. UHP nitrogen was run through the reference channel.
After 4 minutes of flowing standard gas (@ ≈ 50 ml/min) the flow was
stopped. After a 28 second wait period, to stabilize pressure and
temperature in the IR cell, 10 readings were taken and an average is
logged.

For the test on Oct 13, 2005, the zero and span of the IR were set and
multiple cycles were run. Then the zero was increased with the vernier
knob and several more cycles were run. In the second test (17Oct, 2005)
the same procedure was followed. However after the zero was increased
and several cycles were run, the span was increased as well. Several
runs were then performed with both the zero and span adjusted

Details listed below

**Manipulations:**

File: ZeroShift_13Oct05_original

1\. Zero the analyzer with UHP nitrogen and span the detector with the
794.94-ppm standard

2\. Run for 29 cycles

3\. Increase the zero by about 9 ppm (row 177)

4\. Run for 9 cycles

File: ZeroSpanShift_17Oct05_original.xls

1\. Zero the analyzer with UHP nitrogen and span the detector with the
794.94-ppm standard

2\. Run for 32 cycles

3\. Increase the zero by about 12 ppm (row 196)

4\. Run for 5 cycles

5\. Increase the span by about 20 ppm (row 229)

6\. Run 13 cycles

**Column headers for attached files:**

Port: sequential port number on Valco valve

Gas: tank number and origin

Nominal Conc.: concentration of gas as determined by CMDL or SIO

Gas Type: Known= standard; unknown= gas to be calibrated

Date: DD-MMM-YY

Time: HH:MM:SS

YD: yearday

R-T0: resistance of thermistor in the box containing the IR while gas is
flowing through detector

P0: pressure measured with Setra barometer at the exit of the sample
cell outside the IR while gas is flowing through detector

F0: flow of standard gas through the IR (ml/min)

mV0: response of detector (in mV) while gas is flowing

C0: response of detector (XCO2 in ppm) while gas is flowing

IRT0: temperature of the IR while gas is flowing (internal LICOR T
sensor)

T1 degC: temperature of thermistor in box containing the IR while gas
flow is stopped through detector

R-T1: resistance of the thermistor in box containing the IR while
gasflow is stopped through detector

P1: pressure measured with Setra barometer at the exit of the sample
cell outside the IR while gas flow is stopped through detector

F1: flow of standard gas through the IR (ml/min) when gas flow is
stopped (a small non-zero reading is considered a flow meter offset and
no flow)

mV1: response of detector (in mV) while gas flow is stopped

C1: response of detector (XCO2 in ppm) while gas flow is stopped

IRT1: temperature of the IR while gas flow is stopped (internal LICOR T
sensor)

**Results so far:**

Analysis of Rik W. (superficial)

Use file ZeroSpanShift_17Oct05:

Looked at following four series (a series is a run of the six
standards):

Label Series

A. First series (start row 3)

B. Last series before zero was changed (start row 189)

C. First series after the zero was changed (start row 198)

D. Last series after zero and span was changed (start row 303)

Note: Changes in temperature and pressure were not accounted for.

1\. Determine appropriate fit to the standards:

Compare linear and polynomial regressions.

[Series rms deviation linear rms deviation 2nd_order poly]{.underline}

A. 0.71 ppm 0.68 ppm

B. 0. 66 ppm 0.66 ppm

C. 0.64 ppm 0.71 ppm

D. 0.81 ppm 0.68 ppm

Rms = (sum(actual-measured)\^2)\^0.5 for all six standards.

(Actual -measured) ranged from +0.5 ppm (for 508.38 std) to -0.4 ppm
(for 328.12 ppm) std

For the A series, the quadratic term of the second order equation
changes the resultant of the 795 ppm standard by 1.6 ppm (=0.2 %).

2\. Reproduce unknown standards that are outside the calibration range

Using the 4 intermediate standards as knowns and treating 203.92 ppm and
794.94 ppm standards as unknowns

Results known standards:

[Series rms deviation linear rms deviation 2nd_order poly]{.underline}

A. 0.41 ppm 0.38 ppm

B. 0.11 ppm 0.09 ppm

C. 0.14 ppm 0.12 ppm

D. 0.13 ppm 0.12 ppm

Rms = (sum(actual-measured)\^2)\^0.5 for four standards

Results unknown standards:

[Series 204offset linear 795offset linear 204offset poly 795offset
poly]{.underline}

A. 0.83 ppm -1.65 ppm -0.1 ppm -4.87 ppm

B. 1.14 ppm -1.52 ppm 0.78 ppm -2.77 ppm

C. 1 ppm -1.65 ppm 1.5 ppm 0.11 ppm

D 1.24 ppm -2.15 ppm 0.93 ppm -3.22 ppm

Offset = actual value - calculated value using either a linear or
second-order polynomial fit.

3\. Compare optimal fitting routine

Treat 508.38 ppm as unknown and all other standards as known. Compare
linear fit through all remaining 5 standards versus fit through nearest
standards, 448 ppm and 795 ppm.

offset 4 point linear offset 2 point linear

A. -0.62 ppm -0.53 ppm

B. -0.37 ppm -0.38 ppm

C. -0.26 ppm -0.36 ppm

D. -0.37 ppm -0.52 ppm

Offset =(actual conc --calculated) for 508.33 standard.

**Preliminary conclusions for October, 17^th^-experiment (Rik):**

\- It appears that system was not fully stabilized for the first series
(A) as the offsets were consistently higher that for series B.

\- The XCO2 output is linear over a wide range of standards. The 2nd
order term contributes less than 0.2 % for the highest standard and
likely is not statistically significant.

\- The changes in zero and span do not seem to affect the linearity

-When outside the standard range a linear fit does a better job
predicting the standard concentration then a polynomial fit.

\- There does not appear to be an appreciable difference between a
linear interpolation between the two nearest standards or using a fit
through all standards to determine the concentration. I believe that
from a statistical perspective using the entire curve is more
appropriate.