deletions | additions       diff --git a/section_Water_Vapor_Calibration_The__.tex b/section_Water_Vapor_Calibration_The__.tex  index e09cd73..fb12ed3 100644  --- a/section_Water_Vapor_Calibration_The__.tex  +++ b/section_Water_Vapor_Calibration_The__.tex 
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\[\delta=\bigg[\frac{\chi_i}{\chi}-1\bigg]\]   The minor water vapour isotopologue calibrations for the FTIR are non-linear (\ref{fig:figure1}) (see figure 1), so the measured isotope ratios including their instrument response functions are shown by:  \[\delta=\bigg[\frac{a_0+a_1\chi_i+a_2\chi_i^2+\cdots+a_n\chi_i^n}{b_0+b_1\chi}-1\bigg]\]   Clearly the instrument response function for $\chi$ are required for the direct calibration and for calculating the true $\chi$_i mixing ratio from the true $\delta$ and $\chi$. The $\chi$ calibration is also subject to drift and is not possible to characterise using the FTIR calibration system. For a general assessment of the instrument response function of the minor isotopologues:  \begin{enumerate}  \item use co-located meteorological measurements to determine the instrument response function for the water vapour mixing ratio. These were collected over several months and are shown in figure 1a. Show some curvature but are ok for a general characterisation of the instrument.  \item Using a single isotope standard vary the mixing ratio of the water vapour supplied to the FTIR.  \item Use the known $\delta$ of the standard and the calibrated mixing ratio to calculate the true $\chi$_i.  \item Fit linear regression to the instrument response function and calculate residuls of the linear fit to determine the curvature of the instrument function.  \begin{itemize}  \item residuals calculated as $\Big[\frac{\chi_i-\rm residuals}{\chi_i}\Big].1000$  \end{itemize}  \item increase order of polynomial fit to instrument response function until residuals are minimised.  \end{enumerate}, we use the co-located meteorological measurements over a period of several months to first est   \\  The real time calibration uses equation 2 to calibrate the FTIR isotope ratio measurements. To account for instrumental drift, regular measurements of a standard are performed:  \begin{enumerate}  \item $\chi$ from met - how?  \item $\chi$_i from met calibrated $\chi$ and known $\delta$  \item only small $\chi$_i and $\chi$ to dynamically span the observe mixing ratios  \item apply linear correction.  \end{enumerate}