Please not that this page is very much under construction and is developing and changing as I write.
If all the isotopologues have apparent concentrations that rise at the same rate relative to rises in their real concentrations, then there would be no isotopic concentration dependency or other effects that would need fixing! Remember: the isotopic ratios are entirely dependent on the interactions of the concentrations. So we can take it that one or both of these characteristics is not satisfied.
As we have no absolute standard we have to measure each isotopologue curve relative to another. The isotopologues that we are interested in, as noted above, are 626, 627, 628 and 636. We essentially have to treat one concentration curve as flat and normalise the others to it. In the event, we decided to normalise everything to 628. Possibly a minor isotopologue suffers less absolute concentration change and therefore less self-broadening variation? The reasonable assumption is then made that the 18O/16O ratio should remain constant over the concentration range.
We calculate the ratio slightly differently to how Aerodyne does it. We sum all the isotopologues in all the species, after converting the reported concentrations to ppm, using the HITRAN abundances. For example, we multiply [628] by 0.003947. In ppm, total 16O = (2*[626])+(2*[636])+[628]+[627]. Including species such as 638 (with an abundance of 4.43×10-5) has a negligible effect on the outcome. Note that 638 is not measured, so we would have to calculate a concentration based on natural abundance modified by d13C and d18O. We are not ready to deal with non-normal clumping effects! This would be the next frontier! We then calculate a polynomial fit that passes through all these points – one point for each value from our concentration curve. Adding a second concentration curve to the fit should have no effect on the outcome as we are fitting to the form of the isotopologue amplitude increase rather than to an isotopic ratio…
There is a risk, particularly if we are trying to correct more than one effect at a time (for example amplitude dependence due to non-linearity and self-broadening) that a single curve may not be able to describe the changing character. Will there always be an offset that has to be removed?
One possibility is that there is an interaction at the isotopologue scale. If band broadening is greatest when the vibrational characteristics of the second gas are most similar to the first, the isotope shift may be slightly dependent on the isotopic composition! Thus 626 may be measured slightly differently depending on the molar ratio of 628 …