\subsection{Tracer advection}

After multiplying (\ref{C_Layer_IntCurvi}) with $mn$, the advective 
terms in this equation are discretised as follows. 

First advection term in (\ref{C_Layer_IntCurvi}):
\begin{equation}
\left(mn\,\partial_{\cal X}\left(\frac{p_kc_k}{n}\right)\right)_{i,j}\approx 
\frac{
p_{i,j,k}\tilde c_{i,j,k}\Delta y^u_{i,j}-
p_{i-1,j,k}\tilde c_{i-1,j,k}\Delta y^u_{i-1,j}
}{\Delta x^c_{i,j}\Delta y^c_{i,j}}
\end{equation}

Second advection term in (\ref{C_Layer_IntCurvi}):
\begin{equation}
\left(mn\,\partial_{\cal Y}\left(\frac{q_kc_k}{m}\right)\right)_{i,j}\approx 
\frac{
q_{i,j,k}\tilde c_{i,j,k}\Delta y^v_{i,j}-
q_{i,j-1,k}\tilde c_{i,j-1,k}\Delta y^v_{i,j-1}
}{\Delta x^c_{i,j}\Delta y^c_{i,j}}
\end{equation}

Vertical advective fluxes in (\ref{C_Layer_IntCurvi}):
\begin{equation}
\left(\bar w_{k} \tilde c_{k}\right)_{i,j}\approx
w_{i,j,k})\tilde c_{i,j,k}. 
\end{equation}

The interfacial concentrations $\tilde c_{i,j,k}$ are calculated 
according to upwind or higher order directional split
schemes, which are discussed in detail in section 
\ref{SectionHigherOrder}. 

