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\end{itemize}  \end{itemize}  \subsubsection{Kinetic Fractionation Factor}  One of the more difficult challenges of modeling isotopic fluxes is the parameterisation of the kinetic fractionation factor. Unlike the equilibrium fractionation that can be determined by careful measurement of surface temperatures, it must be parameterised. From equation \ref{eq:1}, the kinetic fractionation factor has in the past been further broken down to   \label{eq:2}  \[\Delta\epsilon = (1-h)\theta . n . C_D\]  As can be seen by equation \ref{eq:2}, the kinetic fractionation is scaled by vapour pressure deficit (1-h), where greater evaporation in lower humidity conditions enhances the transport of water vapour across the concentration gradient and increasing the role of molecular diffusion\Delta\epsilon. \\  The C_D term is the ratio of molecular diffusivities of water vapour in air. 2 paramterisations have been derived by \citet{Cappa_2003} and \citet{Merlivat_1978}, however, recently \citet{Luz_2009} provided support for \citet{Merlivat_1978}. Although the correct value for C_D remains uncertain, compared to other sources of uncertainty it generally has a small impact on the simulated isotopic composition of the ET flux Dubbert \cite{Dubbert_2013}.  \\  According to the original C-G model, $\theta$ represented the ratio of molecular resistance to total transport resistance $\frac{\rho_m}{\rho_T}$. For a fully developed diffusion layer $\rho_m$ = $\rho_T$ and therefore $\theta$=1. These terms can be difficult to measure, so \citet{Gat_1996} proposed using the $\frac{1-h'}{1-h}$, where h' is at the top of diffusive sublayer and h at the height of $\delta$_a. However, defining these heights can be subjective and change with different conditions.  \\  The \textit{n} term defines the role of turbulent transport using the transient eddy model of \citet{Brutsaert_1965}. Basically this defines how much turbulence erodes the diffusive sub-layer and limits the role of transport by molecular diffusion:  \begin{itemize}  \item rough interface with strong winds \textit{n} = 0.5  \item \textit{n}=0.66 for smoother surfaces and lower winds  \item \textit{n}=1 for stagnant air layers - eg dry soils \cite{Barnes_1988}  \end{itemize}  \\  Often \textit{n} and $\theta$ are included as a single term \cite{Dubbert_2013, Pfahl_2009}  \\  More recently attempts have been made to better parameterise the kinetic fractionation from soil evaporation and plant transpiration. For soil evaporation, \citet{Mathieu_1996} defined $\theta$ in terms of the soil moisture state, which gave modeled soil evaporation isotope ratios that agreed with chamber observations from bare soil plots in a study by \citet{Dubbert_2013}. \citet{Lee_2009} successfully attempt to model the whole canopy water vapour resistance to then define the kinetic fractionation.  Central to the scheme of \citet{Lee_2009}, is the compartmentalisation of transport resistance of water vapour and its isotopes. A summary of the resistances that must be parameterised for the canopy simulation of water isotope fluxes is given by figure \ref{fig:CanopyResistance}.  \begin{enumerate}  \item soil resistance ($r^s_s$) - \citet{Lee_2009} used a value 500 s.m^{-1}. This value comes from \citet{Shuttleworth_1990}, where they define values of 0-2000s.m^{-1} for wet (standing water) to dry soils. The value used by \citet{Lee_2009} is the preferred value for intermediary soil moisture stated \citet{Shuttleworth_1990}.  \end{enumerate}