deletions | additions       diff --git a/section_Methods_In_the_past__.tex b/section_Methods_In_the_past__.tex  index d6b81ad..a60c65a 100644  --- a/section_Methods_In_the_past__.tex  +++ b/section_Methods_In_the_past__.tex 
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The determination of $\alpha$ for reversible closed adiabatic systems requires that ice formation should be accounted for. Once ice begins to form the condensation is expected to become a irreversible process, thus following an open rayleigh system \cite{Ciais_1994}. \citet{Ciais_1994} discussed the need for a transition range of temperatures where ice particles and liquid droplets occur, in this case the vapour is supersaturated relative to the liquid, and under saturated relative to the ice. Here we take the approach of \citet{Noone_2012} and set a threshold temperature (T_{threshold}) where above T_{threshold} condensation follows the reversible closed system, and below T_threshold, condensation is an irreversible open system where the $\alpha$ is determined relative to ice. We use \citet{Merlivat_1967} for $\delta$^2H and \citet{MAJOUBE_1970} for $\delta$^{18}O. I set T_{threshold} to -20_oC, which is approximately in the middle of the Bergeron-Findesein process range set by \citet{Ciais_1994}. Although we don't account for mixed clouds and we ignore the diffusion effects at the ice-vapour interface.  \\  \textbf{\citet{Merlivat_1967}}:   \[ln(\alpha_{ice/vap}-O^{18}) \[ln(\alpha_{ice/vap}-^{18}O)  = 11.839/T - 28.224 x \times  10^{-3}\] \\  \textbf{\citet{MAJOUBE_1970}}:   \[ln(\alpha_{ice/vap}-^{2}H) = 16288/T^2 - 9.34 \times 10^{-2}\]  \\  \textbf{Super Rayleigh???}  The idea of super rayleigh produces isotopic ratios that fall below open rayleigh models in $\delta$.H_2O space. \citet{Noone_2012} and \citet{Worden_2007} argued that this is caused by mixing between vapour evaporated from falling rain drops and ambient vapour. \citet{Noone_2012} showed that an increase in $\alpha$ as the rain re-evaporates would lead to this super rayleigh curve -> the slope of $\delta$.H_2O space is steeper than an open rayleigh system where $\alpha$ is smaller. Simply they suggested: