| 16 |
\citep{hunke97}; |
\citep{hunke97}; |
| 17 |
\item ice-ocean stress can be formulated as in \citet{hibler87}; |
\item ice-ocean stress can be formulated as in \citet{hibler87}; |
| 18 |
\item ice variables are advected by sophisticated advection schemes; |
\item ice variables are advected by sophisticated advection schemes; |
| 19 |
\item growth and melt parameterizaion have been refined and extended |
\item growth and melt parameterization have been refined and extended |
| 20 |
in order to allow for automatic differentiation of the code. |
in order to allow for automatic differentiation of the code. |
| 21 |
\end{itemize} |
\end{itemize} |
| 22 |
The model equations and their numerical realization are summarized |
The model equations and their numerical realization are summarized |
| 147 |
EVP-model is stepped forward in time 120 times within the physical |
EVP-model is stepped forward in time 120 times within the physical |
| 148 |
ocean model time step (although this parameter is under debate), to |
ocean model time step (although this parameter is under debate), to |
| 149 |
allow for elastic waves to disappear. Because the scheme does not |
allow for elastic waves to disappear. Because the scheme does not |
| 150 |
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 |
| 151 |
|
timestep and simple to implement on parallel computers |
| 152 |
\citep{hunke97}. For completeness, we repeat the equations for the |
\citep{hunke97}. For completeness, we repeat the equations for the |
| 153 |
components of the stress tensor $\sigma_{1} = |
components of the stress tensor $\sigma_{1} = |
| 154 |
\sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and |
\sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and |
| 156 |
\dot{\epsilon}_{11}+\dot{\epsilon}_{22}$, and the horizontal tension |
\dot{\epsilon}_{11}+\dot{\epsilon}_{22}$, and the horizontal tension |
| 157 |
and shearing strain rates, $D_T = |
and shearing strain rates, $D_T = |
| 158 |
\dot{\epsilon}_{11}-\dot{\epsilon}_{22}$ and $D_S = |
\dot{\epsilon}_{11}-\dot{\epsilon}_{22}$ and $D_S = |
| 159 |
2\dot{\epsilon}_{12}$, respectively, and using the above abbreviations, |
2\dot{\epsilon}_{12}$, respectively, and using the above |
| 160 |
the equations can be written as: |
abbreviations, the equations\refeq{evpequation} can be written as: |
| 161 |
\begin{align} |
\begin{align} |
| 162 |
\label{eq:evpstresstensor1} |
\label{eq:evpstresstensor1} |
| 163 |
\frac{\partial\sigma_{1}}{\partial{t}} + \frac{\sigma_{1}}{2T} + |
\frac{\partial\sigma_{1}}{\partial{t}} + \frac{\sigma_{1}}{2T} + |
| 257 |
parameterize this sub-grid scale distribution for heat flux |
parameterize this sub-grid scale distribution for heat flux |
| 258 |
computations, the mean ice thickness $h$ is split into seven thickness |
computations, the mean ice thickness $h$ is split into seven thickness |
| 259 |
categories $H_{n}$ that are equally distributed between $2h$ and |
categories $H_{n}$ that are equally distributed between $2h$ and |
| 260 |
minimum imposed ice thickness of $5\text{\,cm}$ by $H_n= |
a minimum imposed ice thickness of $5\text{\,cm}$ by $H_n= |
| 261 |
\frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each |
\frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each |
| 262 |
thickness category area averaged to give the total heat flux. \ml{[I |
thickness category area averaged to give the total heat flux. \ml{[I |
| 263 |
don't have citation for that, anyone?]} |
don't have citation for that, anyone?]} |
| 281 |
algorithm following Archimedes' principle) turns snow into ice until |
algorithm following Archimedes' principle) turns snow into ice until |
| 282 |
the ice surface is back at $z=0$ \citep{leppaeranta83}. |
the ice surface is back at $z=0$ \citep{leppaeranta83}. |
| 283 |
|
|
| 284 |
Effective ich thickness (ice volume per unit area, |
Effective ice thickness (ice volume per unit area, |
| 285 |
$c\cdot{h}$), concentration $c$ and effective snow thickness |
$c\cdot{h}$), concentration $c$ and effective snow thickness |
| 286 |
($c\cdot{h}_{s}$) are advected by ice velocities: |
($c\cdot{h}_{s}$) are advected by ice velocities: |
| 287 |
\begin{equation} |
\begin{equation} |
| 318 |
flux limiter \citep{roe85}.} |
flux limiter \citep{roe85}.} |
| 319 |
|
|
| 320 |
|
|
| 321 |
\subsection{C-grid} |
%\subsection{C-grid} |
| 322 |
\begin{itemize} |
%\begin{itemize} |
| 323 |
\item no-slip vs. free-slip for both lsr and evp; |
%\item no-slip vs. free-slip for both lsr and evp; |
| 324 |
"diagnostics" to look at and use for comparison |
% "diagnostics" to look at and use for comparison |
| 325 |
\begin{itemize} |
% \begin{itemize} |
| 326 |
\item ice transport through Fram Strait/Denmark Strait/Davis |
% \item ice transport through Fram Strait/Denmark Strait/Davis |
| 327 |
Strait/Bering strait (these are general) |
% Strait/Bering strait (these are general) |
| 328 |
\item ice transport through narrow passages, e.g.\ Nares-Strait |
% \item ice transport through narrow passages, e.g.\ Nares-Strait |
| 329 |
\end{itemize} |
% \end{itemize} |
| 330 |
\item compare different advection schemes (if lsr turns out to be more |
%\item compare different advection schemes (if lsr turns out to be more |
| 331 |
effective, then with lsr otherwise I prefer evp), eg. |
% effective, then with lsr otherwise I prefer evp), eg. |
| 332 |
\begin{itemize} |
% \begin{itemize} |
| 333 |
\item default 2nd-order with diff1=0.002 |
% \item default 2nd-order with diff1=0.002 |
| 334 |
\item 1st-order upwind with diff1=0. |
% \item 1st-order upwind with diff1=0. |
| 335 |
\item DST3FL (SEAICEadvScheme=33 with diff1=0., should work, works for me) |
% \item DST3FL (SEAICEadvScheme=33 with diff1=0., should work, works for me) |
| 336 |
\item 2nd-order wit flux limiter (SEAICEadvScheme=77 with diff1=0.) |
% \item 2nd-order wit flux limiter (SEAICEadvScheme=77 with diff1=0.) |
| 337 |
\end{itemize} |
% \end{itemize} |
| 338 |
That should be enough. Here, total ice mass and location of ice edge |
% That should be enough. Here, total ice mass and location of ice edge |
| 339 |
is interesting. However, this comparison can be done in an idealized |
% is interesting. However, this comparison can be done in an idealized |
| 340 |
domain, may not require full Arctic Domain? |
% domain, may not require full Arctic Domain? |
| 341 |
\item |
%\item |
| 342 |
Do a little study on the parameters of LSR and EVP |
%Do a little study on the parameters of LSR and EVP |
| 343 |
\begin{enumerate} |
%\begin{enumerate} |
| 344 |
\item convergence of LSR, how many iterations do you need to get a |
%\item convergence of LSR, how many iterations do you need to get a |
| 345 |
true elliptic yield curve |
% true elliptic yield curve |
| 346 |
\item vary deltaTevp and the relaxation parameter for EVP and see when |
%\item vary deltaTevp and the relaxation parameter for EVP and see when |
| 347 |
the EVP solution breaks down (relative to the forcing time scale). |
% the EVP solution breaks down (relative to the forcing time scale). |
| 348 |
For this, it is essential that the evp solver gives use "stripeless" |
% For this, it is essential that the evp solver gives use "stripeless" |
| 349 |
solutions, that is your dtevp = 1sec solutions/or 10sec solutions |
% solutions, that is your dtevp = 1sec solutions/or 10sec solutions |
| 350 |
with SEAICE\_evpDampC = 615. |
% with SEAICE\_evpDampC = 615. |
| 351 |
\end{enumerate} |
%\end{enumerate} |
| 352 |
|
|
| 353 |
\end{itemize} |
%\end{itemize} |
| 354 |
|
|
| 355 |
%%% Local Variables: |
%%% Local Variables: |
| 356 |
%%% mode: latex |
%%% mode: latex |
Parent Directory
| 
Revision Log
| 
Revision Graph
| 
Patch