--- MITgcm_contrib/articles/ceaice/ceaice_model.tex	2008/02/28 20:45:29	1.5
+++ MITgcm_contrib/articles/ceaice/ceaice_model.tex	2008/06/04 13:33:45	1.9
@@ -12,11 +12,11 @@
   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{zha97}, EVP
+  momentum equations have been adopted: LSOR \citep{zhang97}, EVP
   \citep{hunke97};
 \item ice-ocean stress can be formulated as in \citet{hibler87};
 \item ice variables are advected by sophisticated advection schemes;
-\item growth and melt parameterizaion have been refined and extended
+\item growth and melt parameterization have been refined and extended
   in order to allow for automatic differentiation of the code.
 \end{itemize}
 The model equations and their numerical realization are summarized
@@ -98,7 +98,7 @@
     \left(\dot{\epsilon}_{11}^2+\dot{\epsilon}_{22}^2\right)
     (1+e^{-2}) +  4e^{-2}\dot{\epsilon}_{12}^2 + 
     2\dot{\epsilon}_{11}\dot{\epsilon}_{22} (1-e^{-2})
-  \right]^{-\frac{1}{2}}
+  \right]^{\frac{1}{2}}
 \end{align*}
 The bulk viscosities are bounded above by imposing both a minimum
 $\Delta_{\min}=10^{-11}\text{\,s}^{-1}$ (for numerical reasons) and a
@@ -147,7 +147,8 @@
 EVP-model is stepped forward in time 120 times within the physical
 ocean model time step (although this parameter is under debate), to
 allow for elastic waves to disappear.  Because the scheme does not
-require a matrix inversion it is fast in spite of the small timestep
+require a matrix inversion it is fast in spite of the small internal
+timestep and simple to implement on parallel computers
 \citep{hunke97}. For completeness, we repeat the equations for the
 components of the stress tensor $\sigma_{1} =
 \sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and
@@ -155,8 +156,8 @@
 \dot{\epsilon}_{11}+\dot{\epsilon}_{22}$, and the horizontal tension
 and shearing strain rates, $D_T =
 \dot{\epsilon}_{11}-\dot{\epsilon}_{22}$ and $D_S =
-2\dot{\epsilon}_{12}$, respectively, and using the above abbreviations,
-the equations can be written as:
+2\dot{\epsilon}_{12}$, respectively, and using the above
+abbreviations, the equations\refeq{evpequation} can be written as:
 \begin{align}
   \label{eq:evpstresstensor1}
   \frac{\partial\sigma_{1}}{\partial{t}} + \frac{\sigma_{1}}{2T} +
@@ -256,7 +257,7 @@
 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=
+a minimum imposed ice thickness of $5\text{\,cm}$ by $H_n=
 \frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each
 thickness category area averaged to give the total heat flux. \ml{[I
   don't have citation for that, anyone?]}
@@ -280,7 +281,7 @@
 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,
+Effective ice thickness (ice volume per unit area,
 $c\cdot{h}$), concentration $c$ and effective snow thickness
 ($c\cdot{h}_{s}$) are advected by ice velocities:
 \begin{equation}
@@ -317,39 +318,39 @@
   flux limiter \citep{roe85}.}
 
 
-\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}
+%\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}
+%\end{itemize}
 
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