articles/ceaice/ceaice_model.tex

\section{Model Formulation}
\label{sec:model}

The MITgcm sea ice model (MITsim) is based on a variant of the
viscous-plastic (VP) dynamic-thermodynamic sea ice model
\citep{zhang97} first introduced by \citet{hibler79, hibler80}. In
order to adapt this model to the requirements of coupled
ice-ocean state estimation, many important aspects of the original code have
been modified and improved:
\begin{itemize}
\item the code has been rewritten for an Arakawa C-grid, both B- and
  C-grid variants are available; the C-grid code allows for no-slip
  and free-slip lateral boundary conditions;
\item two different solution methods for solving the nonlinear
  momentum equations have been adopted: LSOR \citep{zhang97}, and EVP
  \citep{hunke97};
\item ice-ocean stress can be formulated as in \citet{hibler87} or as in \citet{cam08}; 
\item ice variables \ml{can be} advected by sophisticated, \ml{conservative}
  advection schemes \ml{with flux limiting};
\item growth and melt parameterizations have been refined and extended
  in order to allow for more stable automatic differentiation of the code.
\end{itemize}

The sea ice model is tightly coupled to the ocean compontent of the MITgcm
\citep{mar97a}.  Heat, fresh water fluxes and surface stresses are computed
from the atmospheric state and modified by the ice model at every time step.
The model equations and details of their numerical realization are summarized
in the appendix. Further documentation and model code can be found at
\url{http://mitgcm.org}.

%\subsection{C-grid}
%\begin{itemize}
%\item no-slip vs. free-slip for both lsr and evp; 
%  "diagnostics" to look at and use for comparison
%  \begin{itemize}
%  \item ice transport through Fram Strait/Denmark Strait/Davis
%    Strait/Bering strait (these are general) 
%  \item ice transport through narrow passages, e.g.\ Nares-Strait
%  \end{itemize}
%\item compare different advection schemes (if lsr turns out to be more
%  effective, then with lsr otherwise I prefer evp), eg. 
%  \begin{itemize}
%  \item default 2nd-order with diff1=0.002
%  \item 1st-order upwind with diff1=0.
%  \item DST3FL (SEAICEadvScheme=33 with diff1=0., should work, works for me)
%  \item 2nd-order wit flux limiter (SEAICEadvScheme=77 with diff1=0.)
%  \end{itemize}
%  That should be enough. Here, total ice mass and location of ice edge
%  is interesting. However, this comparison can be done in an idealized
%  domain, may not require full Arctic Domain?
%\item
%Do a little study on the parameters of LSR and EVP
%\begin{enumerate}
%\item convergence of LSR, how many iterations do you need to get a
%  true elliptic yield curve 
%\item vary deltaTevp and the relaxation parameter for EVP and see when
%  the EVP solution breaks down (relative to the forcing time scale).
%  For this, it is essential that the evp solver gives use "stripeless"
%  solutions, that is your dtevp = 1sec solutions/or 10sec solutions
%  with SEAICE\_evpDampC = 615.
%\end{enumerate}

%\end{itemize}

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1	mlosch	1.4	\section{Model Formulation}
2	dimitri	1.1	\label{sec:model}
3
4	mlosch	1.4	The MITgcm sea ice model (MITsim) is based on a variant of the
5			viscous-plastic (VP) dynamic-thermodynamic sea ice model
6			\citep{zhang97} first introduced by \citet{hibler79, hibler80}. In
7			order to adapt this model to the requirements of coupled
8	dimitri	1.11	ice-ocean state estimation, many important aspects of the original code have
9	mlosch	1.4	been modified and improved:
10			\begin{itemize}
11			\item the code has been rewritten for an Arakawa C-grid, both B- and
12			C-grid variants are available; the C-grid code allows for no-slip
13			and free-slip lateral boundary conditions;
14			\item two different solution methods for solving the nonlinear
15	dimitri	1.11	momentum equations have been adopted: LSOR \citep{zhang97}, and EVP
16	mlosch	1.4	\citep{hunke97};
17	dimitri	1.11	\item ice-ocean stress can be formulated as in \citet{hibler87} or as in \citet{cam08};
18	mlosch	1.10	\item ice variables \ml{can be} advected by sophisticated, \ml{conservative}
19			advection schemes \ml{with flux limiting};
20			\item growth and melt parameterizations have been refined and extended
21	dimitri	1.11	in order to allow for more stable automatic differentiation of the code.
22	mlosch	1.4	\end{itemize}
23	dimitri	1.1
24	dimitri	1.11	The sea ice model is tightly coupled to the ocean compontent of the MITgcm
25			\citep{mar97a}. Heat, fresh water fluxes and surface stresses are computed
26			from the atmospheric state and modified by the ice model at every time step.
27	mlosch	1.10	The model equations and details of their numerical realization are summarized
28			in the appendix. Further documentation and model code can be found at
29	dimitri	1.11	\url{http://mitgcm.org}.
30	dimitri	1.1
31	mlosch	1.9	%\subsection{C-grid}
32			%\begin{itemize}
33			%\item no-slip vs. free-slip for both lsr and evp;
34			% "diagnostics" to look at and use for comparison
35			% \begin{itemize}
36			% \item ice transport through Fram Strait/Denmark Strait/Davis
37			% Strait/Bering strait (these are general)
38			% \item ice transport through narrow passages, e.g.\ Nares-Strait
39			% \end{itemize}
40			%\item compare different advection schemes (if lsr turns out to be more
41			% effective, then with lsr otherwise I prefer evp), eg.
42			% \begin{itemize}
43			% \item default 2nd-order with diff1=0.002
44			% \item 1st-order upwind with diff1=0.
45			% \item DST3FL (SEAICEadvScheme=33 with diff1=0., should work, works for me)
46			% \item 2nd-order wit flux limiter (SEAICEadvScheme=77 with diff1=0.)
47			% \end{itemize}
48			% That should be enough. Here, total ice mass and location of ice edge
49			% is interesting. However, this comparison can be done in an idealized
50			% domain, may not require full Arctic Domain?
51			%\item
52			%Do a little study on the parameters of LSR and EVP
53			%\begin{enumerate}
54			%\item convergence of LSR, how many iterations do you need to get a
55			% true elliptic yield curve
56			%\item vary deltaTevp and the relaxation parameter for EVP and see when
57			% the EVP solution breaks down (relative to the forcing time scale).
58			% For this, it is essential that the evp solver gives use "stripeless"
59			% solutions, that is your dtevp = 1sec solutions/or 10sec solutions
60			% with SEAICE\_evpDampC = 615.
61			%\end{enumerate}
62	dimitri	1.2
63	mlosch	1.9	%\end{itemize}
64	mlosch	1.3
65			%%% Local Variables:
66			%%% mode: latex
67			%%% TeX-master: "ceaice"
68			%%% End: