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\subsection{Thermodynamics} |
\subsection{Thermodynamics} |
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\label{sec:thermodynamics} |
\label{sec:thermodynamics} |
| 225 |
|
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|
Talk about snow derived from Zhang et al. [1998] but modified and advected, |
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about prognostic variable for salinity and about relaxation of mixed layer |
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temperature to freezing, rather than resetting to freezing at every time step. |
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|
| 226 |
In the original formulation the sea ice model \citep{menemenlis05} |
In the original formulation the sea ice model \citep{menemenlis05} |
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uses simple thermodynamics following the appendix of |
uses simple thermodynamics following the appendix of |
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\citet{semtner76}. This formulation does not allow storage of heat |
\citet{semtner76}. This formulation does not allow storage of heat |
| 229 |
(heat capacity of ice is zero, and this type of model is often refered |
(heat capacity of ice is zero, and this type of model is often refered |
| 230 |
to as a ``zero-layer'' model). Upward heat flux is parameterized |
to as a ``zero-layer'' model). Upward conductive heat flux is parameterized |
| 231 |
assuming a linear temperature profile and together with a constant ice |
assuming a linear temperature profile and together with a constant ice |
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conductivity. It is expressed as $(K/h)(T_{w}-T_{0})$, where $K$ is |
conductivity. It is expressed as $(K/h)(T_{w}-T_{0})$, where $K$ is |
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the ice conductivity, $h$ the ice thickness, and $T_{w}-T_{0}$ the |
the ice conductivity, $h$ the ice thickness, and $T_{w}-T_{0}$ the |
| 234 |
difference between water and ice surface temperatures. The surface |
difference between water and ice surface temperatures. The surface |
| 235 |
heat budget is computed in a similar way to that of |
heat flux is computed in a similar way to that of \citet{parkinson79} |
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\citet{parkinson79} and \citet{manabe79}. |
and \citet{manabe79}. |
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| 238 |
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The conductive heat flux depends strongly on the ice thickness $h$. |
| 239 |
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However, the ice thickness in the model represents a mean over a |
| 240 |
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potentially very heterogeneous thickness distribution. In order to |
| 241 |
|
parameterize this sub-grid scale distribution for heat flux |
| 242 |
|
computations, the mean ice thickness $h$ is split into seven thickness |
| 243 |
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categories $H_{n}$ that are equally distributed between $2h$ and |
| 244 |
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minimum imposed ice thickness of $5\text{\,cm}$ by $H_n= |
| 245 |
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\frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat flux for all thickness |
| 246 |
|
categories is averaged to give the total heat flux. |
| 247 |
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|
| 248 |
|
The atmospheric heat flux is balanced by an oceanic heat flux from |
| 249 |
|
below. The oceanic flux is proportional to |
| 250 |
|
$\rho\,c_{p}\left(T_{w}-T_{fr}\right)$ where $\rho$ and $c_{p}$ are |
| 251 |
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the density and heat capacity of sea water and $T_{fr}$ is the local |
| 252 |
|
freezing point temperature that is a function of salinity. Contrary to |
| 253 |
|
\citet{menemenlis05}, this flux is not assumed to instantaneously melt |
| 254 |
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or create ice, but a time scale of three days is used to relax $T_{w}$ |
| 255 |
|
to the freezing point. |
| 256 |
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|
| 257 |
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The parameterization of lateral and vertical growth of sea ice follows |
| 258 |
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that of \citet{hibler79, hibler80}. |
| 259 |
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|
| 260 |
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On top of the ice there is a layer of snow that modifies the heat flux |
| 261 |
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and the albedo \citep{zhang98}. If enough snow accumulates so that its |
| 262 |
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weight submerges the ice and the snow is flooded, a simple mass |
| 263 |
|
conserving parameterization of snowice formation (a flood-freeze |
| 264 |
|
algorithm following Archimedes' principle) turns snow into ice until |
| 265 |
|
the ice surface is back at $z=0$ \citep{leppaeranta83}. |
| 266 |
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|
| 267 |
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Effective ich thickness (ice volume per unit area, |
| 268 |
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$c\cdot{h}$), concentration $c$ and effective snow thickness |
| 269 |
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($c\cdot{h}_{snow}$) are advected by ice velocities as described in |
| 270 |
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\refsec{dynamics}. From the various advection scheme that are |
| 271 |
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available in the MITgcm \citep{mitgcm02}, we choose flux-limited |
| 272 |
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schemes to preserve sharp gradients and edges and to rule out |
| 273 |
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unphysical over- and undershoots (negative thickness or |
| 274 |
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concentration). These scheme conserve volume and horizontal area. |
| 275 |
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\ml{[do we need to proove that? can we proove that? citation?]} |
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| 277 |
There is considerable doubt about the reliability of such a simple |
There is considerable doubt about the reliability of such a simple |
| 278 |
thermodynamic model---\citet{semtner84} found significant errors in |
thermodynamic model---\citet{semtner84} found significant errors in |
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\end{enumerate} |
\end{enumerate} |
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|
| 325 |
\end{itemize} |
\end{itemize} |
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%%% Local Variables: |
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%%% mode: latex |
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%%% TeX-master: "ceaice" |
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%%% End: |
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