deletions | additions       diff --git a/section_Water_Vapor_Calibration_The__.tex b/section_Water_Vapor_Calibration_The__.tex  index 017b115..8d67b98 100644  --- a/section_Water_Vapor_Calibration_The__.tex  +++ b/section_Water_Vapor_Calibration_The__.tex 
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\usepackage{textcomp}  \textperthousand  \section{Water Vapor Calibration}  \\  The FTIR has relatively large measurement cell with a large surface area. Sampling lines and buffer volumes also lengthen the response time of the calibration system. The combination of the high frequency calibration requirement and the slow response times makes it impractical to perform the 2 standard calibrations that have been outlined for in-situ analysers by \citet{Bastrikov_2014}. The best approach for the FTIR is to chose a calibration strategy that reduces memory effects and enables the calibration of the humidity-isotope effects and the VSMOW scale \cite{Steen_Larsen_2013}. For the FTIR system calibrations performed every 3 hours presents a suitable trade-off between minimising the effect of instrument drift and loss of measurement time. This presents an inadequate amount of time to measure 2 standards or characterise the humidity-isotope effect over the expected H2O range for a long term-deployment. We therefore explore using the direct isotopologue calibration method introduced by \citet{Griffith_2012} and employed by \citet{Vardag_2015} for CO_2 isotope ratio measurements on a similar FTIR instrument. 
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\\  The direct isotopologue calibration determines the instrument response function for each isotopologue used to calculate isotope ratios. This technique has the advantage that there is no need to charcterise both the VSMOW calibration and humidity-isotope response functions, as these are explicitly accounted for. Breifly, the instrument response function is characterised by supplying the instrument with known mixing ratios of each isotopologue (\textit{X} and \textit{X_i}) that covers the range expected to be observed. By then applying the determined calibration functions the corrected isotope ratios are calculated:  \[\delta=\bigg[\frac{\chi_i}{\chi}-1\bigg]\permil \] \[\delta=\bigg[\frac{\chi_i}{\chi}-1\bigg]\]  $\permil$  \[\delta - \delta_0\ = \bigg[\frac{\alpha\epsilon}{1-\alpha(1-\epsilon)}-1\bigg] \times ln\bigg[\frac{\alpha l_0 + q - \alpha(1-\epsilon)(q - q_0)}{\alpha l_0 + q_0}\bigg]\]