How to Correct an Erroneous Calibration for the LI-7700 Open Path Methane Analyzer

How to Correct an Erroneous Calibration for the LI-7700 Open Path Methane Analyzer

The LI-77000 analyzer provides the facility for users to calibrate using standard calibration gases. This option can be used to assure users that the instrument is performing according to specification. However, a mistake or an error in the calibration of the LI-7700 will result in incorrect zero (kz) and span (ks) multipliers. As a result, the computed methane density according to equation 6-12 of the LI-7700 Instruction Manual will be incorrect.

equation1a

Where ρ is measured methane number density before correction for pressure and temperature, i is waveband 1 through M, ks is the span value, kz is the zero value, â[i] is the measured lineshape, and αref[i] is the reference lineshape.

Fortunately, given the nature of the equation, the error can be corrected with knowledge of both the incorrect and correct zero and span multipliers. Simplifying the equation above by renaming the summation as alpha (α) and using subscript ‘c’ for correct values and ‘w’ for wrong values, we can write the following two equations:

ρw=Ksw(α-Kzw)
ρc=Ksc(α-Kzc)

Since the measured lineshape does not change as a result of the erroneous calibration, we can solve for alpha (α) and substitute from the first equation, and substitute in the latter. This will give

equation3

Rearranging the equation, we can present it as a linear scaling with a slope/gain and offset.

equation2

Where Ksc/Ksw is the slope/gain and Ksc(Kzw – Kzc) is the offset. These values can be used in EddyPro-Metadata File Editor – Raw File Description to recompute the measured (incorrect) density to the correct value as part of the flux computation.

For example, the factory values for a unit were -6.75537 for zero (Kzc) and 9.77002*10-5 for span (Ksc). A calibration mistake generated the values -21.341 for zero (Kzw) and 0.000102754 for span (Ksw). Given this set of numbers the slope/gain is 0.951 and the offset is -0.0014.

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