Diff of /MITgcm_contrib/articles/ceaice/ceaice_appendix.tex

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--- MITgcm_contrib/articles/ceaice/ceaice_appendix.tex	2008/07/03 18:09:23	1.1
+++ MITgcm_contrib/articles/ceaice/ceaice_appendix.tex	2008/07/25 14:57:43	1.2
@@ -227,9 +227,9 @@
 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. TThis type of model is often refered to as a
+surface temperatures. This type of model is often refered to as a
 ``zero-layer'' model. The surface heat flux is computed in a similar
-way to that of \citet{parkinson79} and \citet{manabe79}.
+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
@@ -252,16 +252,20 @@
 \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}.
+and the albedo \citep{zhang98}. Snow modifies the effective
+conductivity according to 
+\[\frac{K}{h} \rightarrow \frac{1}{\frac{h_{s}}{K_{s}}+\frac{h}{K}},\]
+where $K_s$ is the conductivity of snow and $h_s$ the snow thickness.
+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 ice thickness (ice volume per unit area,
 $c\cdot{h}$), concentration $c$ and effective snow thickness