--- MITgcm_contrib/articles/ceaice/ceaice_model.tex	2008/02/27 21:50:42	1.2
+++ MITgcm_contrib/articles/ceaice/ceaice_model.tex	2008/02/28 16:34:56	1.3
@@ -223,21 +223,56 @@
 \subsection{Thermodynamics}
 \label{sec:thermodynamics}
 
-Talk about snow derived from Zhang et al. [1998] but modified and advected,
-about prognostic variable for salinity and about relaxation of mixed layer
-temperature to freezing, rather than resetting to freezing at every time step.
-
 In the original formulation the sea ice model \citep{menemenlis05}
 uses simple thermodynamics following the appendix of
 \citet{semtner76}. This formulation does not allow storage of heat
 (heat capacity of ice is zero, and this type of model is often refered
-to as a ``zero-layer'' model). Upward heat flux is parameterized
+to as a ``zero-layer'' model). Upward conductive heat flux is parameterized
 assuming a linear temperature profile and together with a constant ice
 conductivity. It is expressed as $(K/h)(T_{w}-T_{0})$, where $K$ is
 the ice conductivity, $h$ the ice thickness, and $T_{w}-T_{0}$ the
 difference between water and ice surface temperatures. The surface
-heat budget is computed in a similar way to that of
-\citet{parkinson79} and \citet{manabe79}.
+heat flux is computed in a similar way to that of \citet{parkinson79}
+and \citet{manabe79}.
+
+The conductive heat flux depends strongly on the ice thickness $h$.
+However, the ice thickness in the model represents a mean over a
+potentially very heterogeneous thickness distribution.  In order to
+parameterize this sub-grid scale distribution for heat flux
+computations, the mean ice thickness $h$ is split into seven thickness
+categories $H_{n}$ that are equally distributed between $2h$ and
+minimum imposed ice thickness of $5\text{\,cm}$ by $H_n=
+\frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat flux for all thickness
+categories is averaged to give the total heat flux.
+
+The atmospheric heat flux is balanced by an oceanic heat flux from
+below.  The oceanic flux is proportional to
+$\rho\,c_{p}\left(T_{w}-T_{fr}\right)$ where $\rho$ and $c_{p}$ are
+the density and heat capacity of sea water and $T_{fr}$ is the local
+freezing point temperature that is a function of salinity. Contrary to
+\citet{menemenlis05}, this flux is not assumed to instantaneously melt
+or create ice, but a time scale of three days is used to relax $T_{w}$
+to the freezing point.
+
+The parameterization of lateral and vertical growth of sea ice follows
+that of \citet{hibler79, hibler80}.
+
+On top of the ice there is a layer of snow that modifies the heat flux
+and the albedo \citep{zhang98}. If enough snow accumulates so that its
+weight submerges the ice and the snow is flooded, a simple mass
+conserving parameterization of snowice formation (a flood-freeze
+algorithm following Archimedes' principle) turns snow into ice until
+the ice surface is back at $z=0$ \citep{leppaeranta83}.
+
+Effective ich thickness (ice volume per unit area,
+$c\cdot{h}$), concentration $c$ and effective snow thickness
+($c\cdot{h}_{snow}$) are advected by ice velocities as described in
+\refsec{dynamics}. From the various advection scheme that are
+available in the MITgcm \citep{mitgcm02}, we choose flux-limited
+schemes to preserve sharp gradients and edges and to rule out
+unphysical over- and undershoots (negative thickness or
+concentration). These scheme conserve volume and horizontal area.
+\ml{[do we need to proove that? can we proove that? citation?]}
 
 There is considerable doubt about the reliability of such a simple
 thermodynamic model---\citet{semtner84} found significant errors in
@@ -288,3 +323,8 @@
 \end{enumerate}
 
 \end{itemize}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "ceaice"
+%%% End: